linear_algebra.dfinsupp | Mathlib porting status

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

a148d797

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

f4758115

bump to nightly-2024-04-06-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

e34029c9

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2018 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Kenny Lau
 -/
-import Data.Finsupp.ToDfinsupp
+import Data.Finsupp.ToDFinsupp
 import LinearAlgebra.Basis
 
 #align_import linear_algebra.dfinsupp from "leanprover-community/mathlib"@"f47581155c818e6361af4e4fda60d27d020c226b"

f4758115

bump to nightly-2024-03-17-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

22f01ce4

Diff

@@ -426,14 +426,14 @@ theorem mem_iSup_finset_iff_exists_sum {s : Finset ι} (p : ι → Submodule R N
       rw [mem_support_iff, not_ne_iff]
       ext; rw [coe_zero, ← mem_bot R]; convert coe_mem (μ x)
       symm; exact iSup_neg hx
-    · intro x _ hx; rw [mem_support_iff, not_ne_iff] at hx ; rw [hx]; rfl
+    · intro x _ hx; rw [mem_support_iff, not_ne_iff] at hx; rw [hx]; rfl
   · refine' ⟨DFinsupp.mk s _, _⟩
     · rintro ⟨i, hi⟩; refine' ⟨μ i, _⟩
       rw [iSup_pos]; · exact coe_mem _; · exact hi
     simp only [DFinsupp.sum]
     rw [Finset.sum_subset support_mk_subset, ← hμ]
     exact Finset.sum_congr rfl fun x hx => congr_arg coe <| mk_of_mem hx
-    · intro x _ hx; rw [mem_support_iff, not_ne_iff] at hx ; rw [hx]; rfl
+    · intro x _ hx; rw [mem_support_iff, not_ne_iff] at hx; rw [hx]; rfl
 #align submodule.mem_supr_finset_iff_exists_sum Submodule.mem_iSup_finset_iff_exists_sum
 -/
 
@@ -536,12 +536,12 @@ theorem Independent.dfinsupp_lsum_injective {p : ι → Submodule R N} (h : Inde
     Function.Injective (lsum ℕ fun i => (p i).Subtype) :=
   by
   -- simplify everything down to binders over equalities in `N`
-  rw [independent_iff_forall_dfinsupp] at h 
+  rw [independent_iff_forall_dfinsupp] at h
   suffices (lsum ℕ fun i => (p i).Subtype).ker = ⊥
     by
     -- Lean can't find this without our help
     letI : AddCommGroup (Π₀ i, p i) := @DFinsupp.addCommGroup _ (fun i => p i) _
-    rw [LinearMap.ker_eq_bot] at this ; exact this
+    rw [LinearMap.ker_eq_bot] at this; exact this
   rw [LinearMap.ker_eq_bot']
   intro m hm
   ext i : 1
@@ -549,7 +549,7 @@ theorem Independent.dfinsupp_lsum_injective {p : ι → Submodule R N} (h : Inde
   rw [DFinsupp.zero_apply, ← neg_eq_zero]
   refine' h i (-m i) m _
   rwa [← erase_add_single i m, LinearMap.map_add, lsum_single, Submodule.subtype_apply,
-    add_eq_zero_iff_eq_neg, ← Submodule.coe_neg] at hm 
+    add_eq_zero_iff_eq_neg, ← Submodule.coe_neg] at hm
 #align complete_lattice.independent.dfinsupp_lsum_injective CompleteLattice.Independent.dfinsupp_lsum_injective
 -/
 
@@ -559,7 +559,7 @@ additive subgroups are `complete_lattice.independent`. -/
 theorem Independent.dfinsupp_sumAddHom_injective {p : ι → AddSubgroup N} (h : Independent p) :
     Function.Injective (sumAddHom fun i => (p i).Subtype) :=
   by
-  rw [← independent_map_order_iso_iff (AddSubgroup.toIntSubmodule : AddSubgroup N ≃o _)] at h 
+  rw [← independent_map_order_iso_iff (AddSubgroup.toIntSubmodule : AddSubgroup N ≃o _)] at h
   exact h.dfinsupp_lsum_injective
 #align complete_lattice.independent.dfinsupp_sum_add_hom_injective CompleteLattice.Independent.dfinsupp_sumAddHom_injective
 -/
@@ -601,7 +601,7 @@ theorem Independent.linearIndependent [NoZeroSMulDivisors R N] (p : ι → Submo
       l.to_dfinsupp
   have ha : a = 0 := by
     apply hp.dfinsupp_lsum_injective
-    rwa [← lsum_comp_map_range_to_span_singleton _ hv] at hl 
+    rwa [← lsum_comp_map_range_to_span_singleton _ hv] at hl
   ext i
   apply smul_left_injective R (hv' i)
   have : l i • v i = a i := rfl

f4758115

bump to nightly-2024-02-01-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

5433bded

Diff

@@ -416,7 +416,24 @@ open scoped BigOperators
 
 #print Submodule.mem_iSup_finset_iff_exists_sum /-
 theorem mem_iSup_finset_iff_exists_sum {s : Finset ι} (p : ι → Submodule R N) (a : N) :
-    (a ∈ ⨆ i ∈ s, p i) ↔ ∃ μ : ∀ i, p i, ∑ i in s, (μ i : N) = a := by classical
+    (a ∈ ⨆ i ∈ s, p i) ↔ ∃ μ : ∀ i, p i, ∑ i in s, (μ i : N) = a := by
+  classical
+  rw [Submodule.mem_iSup_iff_exists_dfinsupp']
+  constructor <;> rintro ⟨μ, hμ⟩
+  · use fun i => ⟨μ i, (iSup_const_le : _ ≤ p i) (coe_mem <| μ i)⟩
+    rw [← hμ]; symm; apply Finset.sum_subset
+    · intro x; contrapose; intro hx
+      rw [mem_support_iff, not_ne_iff]
+      ext; rw [coe_zero, ← mem_bot R]; convert coe_mem (μ x)
+      symm; exact iSup_neg hx
+    · intro x _ hx; rw [mem_support_iff, not_ne_iff] at hx ; rw [hx]; rfl
+  · refine' ⟨DFinsupp.mk s _, _⟩
+    · rintro ⟨i, hi⟩; refine' ⟨μ i, _⟩
+      rw [iSup_pos]; · exact coe_mem _; · exact hi
+    simp only [DFinsupp.sum]
+    rw [Finset.sum_subset support_mk_subset, ← hμ]
+    exact Finset.sum_congr rfl fun x hx => congr_arg coe <| mk_of_mem hx
+    · intro x _ hx; rw [mem_support_iff, not_ne_iff] at hx ; rw [hx]; rfl
 #align submodule.mem_supr_finset_iff_exists_sum Submodule.mem_iSup_finset_iff_exists_sum
 -/
 
@@ -575,7 +592,20 @@ forms a linearly independent family.
 See also `complete_lattice.independent.linear_independent'`. -/
 theorem Independent.linearIndependent [NoZeroSMulDivisors R N] (p : ι → Submodule R N)
     (hp : Independent p) {v : ι → N} (hv : ∀ i, v i ∈ p i) (hv' : ∀ i, v i ≠ 0) :
-    LinearIndependent R v := by classical
+    LinearIndependent R v := by
+  classical
+  rw [linearIndependent_iff]
+  intro l hl
+  let a :=
+    DFinsupp.mapRange.linearMap (fun i => LinearMap.toSpanSingleton R (p i) ⟨v i, hv i⟩)
+      l.to_dfinsupp
+  have ha : a = 0 := by
+    apply hp.dfinsupp_lsum_injective
+    rwa [← lsum_comp_map_range_to_span_singleton _ hv] at hl 
+  ext i
+  apply smul_left_injective R (hv' i)
+  have : l i • v i = a i := rfl
+  simp [this, ha]
 #align complete_lattice.independent.linear_independent CompleteLattice.Independent.linearIndependent
 -/

f4758115

bump to nightly-2024-01-31-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

61100fe9

Diff

@@ -416,24 +416,7 @@ open scoped BigOperators
 
 #print Submodule.mem_iSup_finset_iff_exists_sum /-
 theorem mem_iSup_finset_iff_exists_sum {s : Finset ι} (p : ι → Submodule R N) (a : N) :
-    (a ∈ ⨆ i ∈ s, p i) ↔ ∃ μ : ∀ i, p i, ∑ i in s, (μ i : N) = a := by
-  classical
-  rw [Submodule.mem_iSup_iff_exists_dfinsupp']
-  constructor <;> rintro ⟨μ, hμ⟩
-  · use fun i => ⟨μ i, (iSup_const_le : _ ≤ p i) (coe_mem <| μ i)⟩
-    rw [← hμ]; symm; apply Finset.sum_subset
-    · intro x; contrapose; intro hx
-      rw [mem_support_iff, not_ne_iff]
-      ext; rw [coe_zero, ← mem_bot R]; convert coe_mem (μ x)
-      symm; exact iSup_neg hx
-    · intro x _ hx; rw [mem_support_iff, not_ne_iff] at hx ; rw [hx]; rfl
-  · refine' ⟨DFinsupp.mk s _, _⟩
-    · rintro ⟨i, hi⟩; refine' ⟨μ i, _⟩
-      rw [iSup_pos]; · exact coe_mem _; · exact hi
-    simp only [DFinsupp.sum]
-    rw [Finset.sum_subset support_mk_subset, ← hμ]
-    exact Finset.sum_congr rfl fun x hx => congr_arg coe <| mk_of_mem hx
-    · intro x _ hx; rw [mem_support_iff, not_ne_iff] at hx ; rw [hx]; rfl
+    (a ∈ ⨆ i ∈ s, p i) ↔ ∃ μ : ∀ i, p i, ∑ i in s, (μ i : N) = a := by classical
 #align submodule.mem_supr_finset_iff_exists_sum Submodule.mem_iSup_finset_iff_exists_sum
 -/
 
@@ -592,20 +575,7 @@ forms a linearly independent family.
 See also `complete_lattice.independent.linear_independent'`. -/
 theorem Independent.linearIndependent [NoZeroSMulDivisors R N] (p : ι → Submodule R N)
     (hp : Independent p) {v : ι → N} (hv : ∀ i, v i ∈ p i) (hv' : ∀ i, v i ≠ 0) :
-    LinearIndependent R v := by
-  classical
-  rw [linearIndependent_iff]
-  intro l hl
-  let a :=
-    DFinsupp.mapRange.linearMap (fun i => LinearMap.toSpanSingleton R (p i) ⟨v i, hv i⟩)
-      l.to_dfinsupp
-  have ha : a = 0 := by
-    apply hp.dfinsupp_lsum_injective
-    rwa [← lsum_comp_map_range_to_span_singleton _ hv] at hl 
-  ext i
-  apply smul_left_injective R (hv' i)
-  have : l i • v i = a i := rfl
-  simp [this, ha]
+    LinearIndependent R v := by classical
 #align complete_lattice.independent.linear_independent CompleteLattice.Independent.linearIndependent
 -/

f4758115

bump to nightly-2023-09-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2018 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Kenny Lau
 -/
-import Mathbin.Data.Finsupp.ToDfinsupp
-import Mathbin.LinearAlgebra.Basis
+import Data.Finsupp.ToDfinsupp
+import LinearAlgebra.Basis
 
 #align_import linear_algebra.dfinsupp from "leanprover-community/mathlib"@"f47581155c818e6361af4e4fda60d27d020c226b"

f4758115

bump to nightly-2023-07-20-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2018 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Kenny Lau
-
-! This file was ported from Lean 3 source module linear_algebra.dfinsupp
-! leanprover-community/mathlib commit f47581155c818e6361af4e4fda60d27d020c226b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Finsupp.ToDfinsupp
 import Mathbin.LinearAlgebra.Basis
 
+#align_import linear_algebra.dfinsupp from "leanprover-community/mathlib"@"f47581155c818e6361af4e4fda60d27d020c226b"
+
 /-!
 # Properties of the module `Π₀ i, M i`

f4758115

bump to nightly-2023-07-12-07

mathlib commit https://github.com/leanprover-community/mathlib/commit/4e24c4bfcff371c71f7ba22050308aa17815626c

9849f9d1

Diff

@@ -45,39 +45,39 @@ variable {ι : Type _} {R : Type _} {S : Type _} {M : ι → Type _} {N : Type _
 
 variable [dec_ι : DecidableEq ι]
 
-namespace Dfinsupp
+namespace DFinsupp
 
 variable [Semiring R] [∀ i, AddCommMonoid (M i)] [∀ i, Module R (M i)]
 
 variable [AddCommMonoid N] [Module R N]
 
-#print Dfinsupp.lmk /-
+#print DFinsupp.lmk /-
 /-- `dfinsupp.mk` as a `linear_map`. -/
 def lmk (s : Finset ι) : (∀ i : (↑s : Set ι), M i) →ₗ[R] Π₀ i, M i
     where
   toFun := mk s
   map_add' _ _ := mk_add
   map_smul' c x := mk_smul c x
-#align dfinsupp.lmk Dfinsupp.lmk
+#align dfinsupp.lmk DFinsupp.lmk
 -/
 
-#print Dfinsupp.lsingle /-
+#print DFinsupp.lsingle /-
 /-- `dfinsupp.single` as a `linear_map` -/
 def lsingle (i) : M i →ₗ[R] Π₀ i, M i :=
-  { Dfinsupp.singleAddHom _ _ with
+  { DFinsupp.singleAddHom _ _ with
     toFun := single i
     map_smul' := single_smul }
-#align dfinsupp.lsingle Dfinsupp.lsingle
+#align dfinsupp.lsingle DFinsupp.lsingle
 -/
 
-#print Dfinsupp.lhom_ext /-
+#print DFinsupp.lhom_ext /-
 /-- Two `R`-linear maps from `Π₀ i, M i` which agree on each `single i x` agree everywhere. -/
 theorem lhom_ext ⦃φ ψ : (Π₀ i, M i) →ₗ[R] N⦄ (h : ∀ i x, φ (single i x) = ψ (single i x)) : φ = ψ :=
   LinearMap.toAddMonoidHom_injective <| addHom_ext h
-#align dfinsupp.lhom_ext Dfinsupp.lhom_ext
+#align dfinsupp.lhom_ext DFinsupp.lhom_ext
 -/
 
-#print Dfinsupp.lhom_ext' /-
+#print DFinsupp.lhom_ext' /-
 /-- Two `R`-linear maps from `Π₀ i, M i` which agree on each `single i x` agree everywhere.
 
 See note [partially-applied ext lemmas].
@@ -86,52 +86,52 @@ After apply this lemma, if `M = R` then it suffices to verify `φ (single a 1) =
 theorem lhom_ext' ⦃φ ψ : (Π₀ i, M i) →ₗ[R] N⦄ (h : ∀ i, φ.comp (lsingle i) = ψ.comp (lsingle i)) :
     φ = ψ :=
   lhom_ext fun i => LinearMap.congr_fun (h i)
-#align dfinsupp.lhom_ext' Dfinsupp.lhom_ext'
+#align dfinsupp.lhom_ext' DFinsupp.lhom_ext'
 -/
 
-#print Dfinsupp.lapply /-
+#print DFinsupp.lapply /-
 /-- Interpret `λ (f : Π₀ i, M i), f i` as a linear map. -/
 def lapply (i : ι) : (Π₀ i, M i) →ₗ[R] M i
     where
   toFun f := f i
   map_add' f g := add_apply f g i
   map_smul' c f := smul_apply c f i
-#align dfinsupp.lapply Dfinsupp.lapply
+#align dfinsupp.lapply DFinsupp.lapply
 -/
 
-#print Dfinsupp.lmk_apply /-
+#print DFinsupp.lmk_apply /-
 @[simp]
 theorem lmk_apply (s : Finset ι) (x) : (lmk s : _ →ₗ[R] Π₀ i, M i) x = mk s x :=
   rfl
-#align dfinsupp.lmk_apply Dfinsupp.lmk_apply
+#align dfinsupp.lmk_apply DFinsupp.lmk_apply
 -/
 
-#print Dfinsupp.lsingle_apply /-
+#print DFinsupp.lsingle_apply /-
 @[simp]
 theorem lsingle_apply (i : ι) (x : M i) : (lsingle i : _ →ₗ[R] _) x = single i x :=
   rfl
-#align dfinsupp.lsingle_apply Dfinsupp.lsingle_apply
+#align dfinsupp.lsingle_apply DFinsupp.lsingle_apply
 -/
 
-#print Dfinsupp.lapply_apply /-
+#print DFinsupp.lapply_apply /-
 @[simp]
 theorem lapply_apply (i : ι) (f : Π₀ i, M i) : (lapply i : _ →ₗ[R] _) f = f i :=
   rfl
-#align dfinsupp.lapply_apply Dfinsupp.lapply_apply
+#align dfinsupp.lapply_apply DFinsupp.lapply_apply
 -/
 
 section Lsum
 
-#print Dfinsupp.addCommMonoidOfLinearMap /-
+#print DFinsupp.addCommMonoidOfLinearMap /-
 /-- Typeclass inference can't find `dfinsupp.add_comm_monoid` without help for this case.
 This instance allows it to be found where it is needed on the LHS of the colon in
 `dfinsupp.module_of_linear_map`. -/
 instance addCommMonoidOfLinearMap : AddCommMonoid (Π₀ i : ι, M i →ₗ[R] N) :=
-  @Dfinsupp.addCommMonoid _ (fun i => M i →ₗ[R] N) _
-#align dfinsupp.add_comm_monoid_of_linear_map Dfinsupp.addCommMonoidOfLinearMap
+  @DFinsupp.addCommMonoid _ (fun i => M i →ₗ[R] N) _
+#align dfinsupp.add_comm_monoid_of_linear_map DFinsupp.addCommMonoidOfLinearMap
 -/
 
-#print Dfinsupp.moduleOfLinearMap /-
+#print DFinsupp.moduleOfLinearMap /-
 /-- Typeclass inference can't find `dfinsupp.module` without help for this case.
 This is needed to define `dfinsupp.lsum` below.
 
@@ -140,13 +140,13 @@ we have with the `Π i, has_zero (M i →ₗ[R] N)` instance which appears as a
 `dfinsupp` type. -/
 instance moduleOfLinearMap [Semiring S] [Module S N] [SMulCommClass R S N] :
     Module S (Π₀ i : ι, M i →ₗ[R] N) :=
-  @Dfinsupp.module _ _ (fun i => M i →ₗ[R] N) _ _ _
-#align dfinsupp.module_of_linear_map Dfinsupp.moduleOfLinearMap
+  @DFinsupp.module _ _ (fun i => M i →ₗ[R] N) _ _ _
+#align dfinsupp.module_of_linear_map DFinsupp.moduleOfLinearMap
 -/
 
 variable (S)
 
-#print Dfinsupp.lsum /-
+#print DFinsupp.lsum /-
 /-- The `dfinsupp` version of `finsupp.lsum`.
 
 See note [bundled maps over different rings] for why separate `R` and `S` semirings are used. -/
@@ -159,7 +159,7 @@ def lsum [Semiring S] [Module S N] [SMulCommClass R S N] :
       map_add' := (liftAddHom fun i => (F i).toAddMonoidHom).map_add
       map_smul' := fun c f => by
         dsimp
-        apply Dfinsupp.induction f
+        apply DFinsupp.induction f
         · rw [smul_zero, AddMonoidHom.map_zero, smul_zero]
         · intro a b f ha hb hf
           rw [smul_add, AddMonoidHom.map_add, AddMonoidHom.map_add, smul_add, hf, ← single_smul,
@@ -170,16 +170,16 @@ def lsum [Semiring S] [Module S N] [SMulCommClass R S N] :
   right_inv F := by ext x y; simp
   map_add' F G := by ext x y; simp
   map_smul' c F := by ext; simp
-#align dfinsupp.lsum Dfinsupp.lsum
+#align dfinsupp.lsum DFinsupp.lsum
 -/
 
-#print Dfinsupp.lsum_single /-
+#print DFinsupp.lsum_single /-
 /-- While `simp` can prove this, it is often convenient to avoid unfolding `lsum` into `sum_add_hom`
 with `dfinsupp.lsum_apply_apply`. -/
 theorem lsum_single [Semiring S] [Module S N] [SMulCommClass R S N] (F : ∀ i, M i →ₗ[R] N) (i)
     (x : M i) : lsum S F (single i x) = F i x :=
   sumAddHom_single _ _ _
-#align dfinsupp.lsum_single Dfinsupp.lsum_single
+#align dfinsupp.lsum_single DFinsupp.lsum_single
 -/
 
 end Lsum
@@ -198,17 +198,17 @@ variable [∀ i, AddCommMonoid (β i)] [∀ i, AddCommMonoid (β₁ i)] [∀ i,
 
 variable [∀ i, Module R (β i)] [∀ i, Module R (β₁ i)] [∀ i, Module R (β₂ i)]
 
-#print Dfinsupp.mapRange_smul /-
+#print DFinsupp.mapRange_smul /-
 theorem mapRange_smul (f : ∀ i, β₁ i → β₂ i) (hf : ∀ i, f i 0 = 0) (r : R)
     (hf' : ∀ i x, f i (r • x) = r • f i x) (g : Π₀ i, β₁ i) :
     mapRange f hf (r • g) = r • mapRange f hf g :=
   by
   ext
   simp only [map_range_apply f, coe_smul, Pi.smul_apply, hf']
-#align dfinsupp.map_range_smul Dfinsupp.mapRange_smul
+#align dfinsupp.map_range_smul DFinsupp.mapRange_smul
 -/
 
-#print Dfinsupp.mapRange.linearMap /-
+#print DFinsupp.mapRange.linearMap /-
 /-- `dfinsupp.map_range` as an `linear_map`. -/
 @[simps apply]
 def mapRange.linearMap (f : ∀ i, β₁ i →ₗ[R] β₂ i) : (Π₀ i, β₁ i) →ₗ[R] Π₀ i, β₂ i :=
@@ -217,37 +217,37 @@ def mapRange.linearMap (f : ∀ i, β₁ i →ₗ[R] β₂ i) : (Π₀ i, β₁
       (f i).toAddMonoidHom with
     toFun := mapRange (fun i x => f i x) fun i => (f i).map_zero
     map_smul' := fun r => mapRange_smul _ _ _ fun i => (f i).map_smul r }
-#align dfinsupp.map_range.linear_map Dfinsupp.mapRange.linearMap
+#align dfinsupp.map_range.linear_map DFinsupp.mapRange.linearMap
 -/
 
-#print Dfinsupp.mapRange.linearMap_id /-
+#print DFinsupp.mapRange.linearMap_id /-
 @[simp]
 theorem mapRange.linearMap_id :
     (mapRange.linearMap fun i => (LinearMap.id : β₂ i →ₗ[R] _)) = LinearMap.id :=
   LinearMap.ext mapRange_id
-#align dfinsupp.map_range.linear_map_id Dfinsupp.mapRange.linearMap_id
+#align dfinsupp.map_range.linear_map_id DFinsupp.mapRange.linearMap_id
 -/
 
-#print Dfinsupp.mapRange.linearMap_comp /-
+#print DFinsupp.mapRange.linearMap_comp /-
 theorem mapRange.linearMap_comp (f : ∀ i, β₁ i →ₗ[R] β₂ i) (f₂ : ∀ i, β i →ₗ[R] β₁ i) :
     (mapRange.linearMap fun i => (f i).comp (f₂ i)) =
       (mapRange.linearMap f).comp (mapRange.linearMap f₂) :=
   LinearMap.ext <| mapRange_comp (fun i x => f i x) (fun i x => f₂ i x) _ _ _
-#align dfinsupp.map_range.linear_map_comp Dfinsupp.mapRange.linearMap_comp
+#align dfinsupp.map_range.linear_map_comp DFinsupp.mapRange.linearMap_comp
 -/
 
-#print Dfinsupp.sum_mapRange_index.linearMap /-
+#print DFinsupp.sum_mapRange_index.linearMap /-
 theorem sum_mapRange_index.linearMap [∀ (i : ι) (x : β₁ i), Decidable (x ≠ 0)]
     [∀ (i : ι) (x : β₂ i), Decidable (x ≠ 0)] {f : ∀ i, β₁ i →ₗ[R] β₂ i} {h : ∀ i, β₂ i →ₗ[R] N}
     {l : Π₀ i, β₁ i} :
-    Dfinsupp.lsum ℕ h (mapRange.linearMap f l) = Dfinsupp.lsum ℕ (fun i => (h i).comp (f i)) l := by
-  simpa [Dfinsupp.sumAddHom_apply] using
+    DFinsupp.lsum ℕ h (mapRange.linearMap f l) = DFinsupp.lsum ℕ (fun i => (h i).comp (f i)) l := by
+  simpa [DFinsupp.sumAddHom_apply] using
     @sum_map_range_index ι N _ _ _ _ _ _ _ _ (fun i => f i) (fun i => by simp) l (fun i => h i)
       fun i => by simp
-#align dfinsupp.sum_map_range_index.linear_map Dfinsupp.sum_mapRange_index.linearMap
+#align dfinsupp.sum_map_range_index.linear_map DFinsupp.sum_mapRange_index.linearMap
 -/
 
-#print Dfinsupp.mapRange.linearEquiv /-
+#print DFinsupp.mapRange.linearEquiv /-
 /-- `dfinsupp.map_range.linear_map` as an `linear_equiv`. -/
 @[simps apply]
 def mapRange.linearEquiv (e : ∀ i, β₁ i ≃ₗ[R] β₂ i) : (Π₀ i, β₁ i) ≃ₗ[R] Π₀ i, β₂ i :=
@@ -256,31 +256,31 @@ def mapRange.linearEquiv (e : ∀ i, β₁ i ≃ₗ[R] β₂ i) : (Π₀ i, β
       (e i).toLinearMap with
     toFun := mapRange (fun i x => e i x) fun i => (e i).map_zero
     invFun := mapRange (fun i x => (e i).symm x) fun i => (e i).symm.map_zero }
-#align dfinsupp.map_range.linear_equiv Dfinsupp.mapRange.linearEquiv
+#align dfinsupp.map_range.linear_equiv DFinsupp.mapRange.linearEquiv
 -/
 
-#print Dfinsupp.mapRange.linearEquiv_refl /-
+#print DFinsupp.mapRange.linearEquiv_refl /-
 @[simp]
 theorem mapRange.linearEquiv_refl :
     (mapRange.linearEquiv fun i => LinearEquiv.refl R (β₁ i)) = LinearEquiv.refl _ _ :=
   LinearEquiv.ext mapRange_id
-#align dfinsupp.map_range.linear_equiv_refl Dfinsupp.mapRange.linearEquiv_refl
+#align dfinsupp.map_range.linear_equiv_refl DFinsupp.mapRange.linearEquiv_refl
 -/
 
-#print Dfinsupp.mapRange.linearEquiv_trans /-
+#print DFinsupp.mapRange.linearEquiv_trans /-
 theorem mapRange.linearEquiv_trans (f : ∀ i, β i ≃ₗ[R] β₁ i) (f₂ : ∀ i, β₁ i ≃ₗ[R] β₂ i) :
     (mapRange.linearEquiv fun i => (f i).trans (f₂ i)) =
       (mapRange.linearEquiv f).trans (mapRange.linearEquiv f₂) :=
   LinearEquiv.ext <| mapRange_comp (fun i x => f₂ i x) (fun i x => f i x) _ _ _
-#align dfinsupp.map_range.linear_equiv_trans Dfinsupp.mapRange.linearEquiv_trans
+#align dfinsupp.map_range.linear_equiv_trans DFinsupp.mapRange.linearEquiv_trans
 -/
 
-#print Dfinsupp.mapRange.linearEquiv_symm /-
+#print DFinsupp.mapRange.linearEquiv_symm /-
 @[simp]
 theorem mapRange.linearEquiv_symm (e : ∀ i, β₁ i ≃ₗ[R] β₂ i) :
     (mapRange.linearEquiv e).symm = mapRange.linearEquiv fun i => (e i).symm :=
   rfl
-#align dfinsupp.map_range.linear_equiv_symm Dfinsupp.mapRange.linearEquiv_symm
+#align dfinsupp.map_range.linear_equiv_symm DFinsupp.mapRange.linearEquiv_symm
 -/
 
 end MapRange
@@ -289,50 +289,50 @@ section CoprodMap
 
 variable [DecidableEq ι] [∀ x : N, Decidable (x ≠ 0)]
 
-#print Dfinsupp.coprodMap /-
+#print DFinsupp.coprodMap /-
 /-- Given a family of linear maps `f i : M i  →ₗ[R] N`, we can form a linear map
 `(Π₀ i, M i) →ₗ[R] N` which sends `x : Π₀ i, M i` to the sum over `i` of `f i` applied to `x i`.
 This is the map coming from the universal property of `Π₀ i, M i` as the coproduct of the `M i`.
 See also `linear_map.coprod` for the binary product version. -/
 noncomputable def coprodMap (f : ∀ i : ι, M i →ₗ[R] N) : (Π₀ i, M i) →ₗ[R] N :=
   (Finsupp.lsum ℕ fun i : ι => LinearMap.id) ∘ₗ
-    (@finsuppLequivDfinsupp ι R N _ _ _ _ _).symm.toLinearMap ∘ₗ Dfinsupp.mapRange.linearMap f
-#align dfinsupp.coprod_map Dfinsupp.coprodMap
+    (@finsuppLequivDFinsupp ι R N _ _ _ _ _).symm.toLinearMap ∘ₗ DFinsupp.mapRange.linearMap f
+#align dfinsupp.coprod_map DFinsupp.coprodMap
 -/
 
-#print Dfinsupp.coprodMap_apply /-
+#print DFinsupp.coprodMap_apply /-
 theorem coprodMap_apply (f : ∀ i : ι, M i →ₗ[R] N) (x : Π₀ i, M i) :
     coprodMap f x =
       Finsupp.sum (mapRange (fun i => f i) (fun i => LinearMap.map_zero _) x).toFinsupp fun i =>
         id :=
   rfl
-#align dfinsupp.coprod_map_apply Dfinsupp.coprodMap_apply
+#align dfinsupp.coprod_map_apply DFinsupp.coprodMap_apply
 -/
 
 end CoprodMap
 
 section Basis
 
-#print Dfinsupp.basis /-
+#print DFinsupp.basis /-
 /-- The direct sum of free modules is free.
 
 Note that while this is stated for `dfinsupp` not `direct_sum`, the types are defeq. -/
 noncomputable def basis {η : ι → Type _} (b : ∀ i, Basis (η i) R (M i)) :
     Basis (Σ i, η i) R (Π₀ i, M i) :=
   Basis.ofRepr
-    ((mapRange.linearEquiv fun i => (b i).repr).trans (sigmaFinsuppLequivDfinsupp R).symm)
-#align dfinsupp.basis Dfinsupp.basis
+    ((mapRange.linearEquiv fun i => (b i).repr).trans (sigmaFinsuppLequivDFinsupp R).symm)
+#align dfinsupp.basis DFinsupp.basis
 -/
 
 end Basis
 
-end Dfinsupp
+end DFinsupp
 
 namespace Submodule
 
 variable [Semiring R] [AddCommMonoid N] [Module R N]
 
-open Dfinsupp
+open DFinsupp
 
 #print Submodule.dfinsupp_sum_mem /-
 theorem dfinsupp_sum_mem {β : ι → Type _} [∀ i, Zero (β i)] [∀ (i) (x : β i), Decidable (x ≠ 0)]
@@ -345,7 +345,7 @@ theorem dfinsupp_sum_mem {β : ι → Type _} [∀ i, Zero (β i)] [∀ (i) (x :
 #print Submodule.dfinsupp_sumAddHom_mem /-
 theorem dfinsupp_sumAddHom_mem {β : ι → Type _} [∀ i, AddZeroClass (β i)] (S : Submodule R N)
     (f : Π₀ i, β i) (g : ∀ i, β i →+ N) (h : ∀ c, f c ≠ 0 → g c (f c) ∈ S) :
-    Dfinsupp.sumAddHom g f ∈ S :=
+    DFinsupp.sumAddHom g f ∈ S :=
   dfinsupp_sumAddHom_mem S f g h
 #align submodule.dfinsupp_sum_add_hom_mem Submodule.dfinsupp_sumAddHom_mem
 -/
@@ -355,12 +355,12 @@ theorem dfinsupp_sumAddHom_mem {β : ι → Type _} [∀ i, AddZeroClass (β i)]
 every element in the `supr` can be produced from taking a finite number of non-zero elements
 of `p i`, coercing them to `N`, and summing them. -/
 theorem iSup_eq_range_dfinsupp_lsum (p : ι → Submodule R N) :
-    iSup p = (Dfinsupp.lsum ℕ fun i => (p i).Subtype).range :=
+    iSup p = (DFinsupp.lsum ℕ fun i => (p i).Subtype).range :=
   by
   apply le_antisymm
   · apply iSup_le _
     intro i y hy
-    exact ⟨Dfinsupp.single i ⟨y, hy⟩, Dfinsupp.sumAddHom_single _ _ _⟩
+    exact ⟨DFinsupp.single i ⟨y, hy⟩, DFinsupp.sumAddHom_single _ _ _⟩
   · rintro x ⟨v, rfl⟩
     exact dfinsupp_sumAddHom_mem _ v _ fun i _ => (le_iSup p i : p i ≤ _) (v i).Prop
 #align submodule.supr_eq_range_dfinsupp_lsum Submodule.iSup_eq_range_dfinsupp_lsum
@@ -373,12 +373,12 @@ bounded `supr` can be produced from taking a finite number of non-zero elements
 satisfy `p i`, coercing them to `γ`, and summing them. -/
 theorem biSup_eq_range_dfinsupp_lsum (p : ι → Prop) [DecidablePred p] (S : ι → Submodule R N) :
     (⨆ (i) (h : p i), S i) =
-      ((Dfinsupp.lsum ℕ fun i => (S i).Subtype).comp (Dfinsupp.filterLinearMap R _ p)).range :=
+      ((DFinsupp.lsum ℕ fun i => (S i).Subtype).comp (DFinsupp.filterLinearMap R _ p)).range :=
   by
   apply le_antisymm
-  · refine' iSup₂_le fun i hi y hy => ⟨Dfinsupp.single i ⟨y, hy⟩, _⟩
+  · refine' iSup₂_le fun i hi y hy => ⟨DFinsupp.single i ⟨y, hy⟩, _⟩
     rw [LinearMap.comp_apply, filter_linear_map_apply, filter_single_pos _ _ hi]
-    exact Dfinsupp.sumAddHom_single _ _ _
+    exact DFinsupp.sumAddHom_single _ _ _
   · rintro x ⟨v, rfl⟩
     refine' dfinsupp_sumAddHom_mem _ _ _ fun i hi => _
     refine' mem_supr_of_mem i _
@@ -390,7 +390,7 @@ theorem biSup_eq_range_dfinsupp_lsum (p : ι → Prop) [DecidablePred p] (S : ι
 
 #print Submodule.mem_iSup_iff_exists_dfinsupp /-
 theorem mem_iSup_iff_exists_dfinsupp (p : ι → Submodule R N) (x : N) :
-    x ∈ iSup p ↔ ∃ f : Π₀ i, p i, Dfinsupp.lsum ℕ (fun i => (p i).Subtype) f = x :=
+    x ∈ iSup p ↔ ∃ f : Π₀ i, p i, DFinsupp.lsum ℕ (fun i => (p i).Subtype) f = x :=
   SetLike.ext_iff.mp (iSup_eq_range_dfinsupp_lsum p) x
 #align submodule.mem_supr_iff_exists_dfinsupp Submodule.mem_iSup_iff_exists_dfinsupp
 -/
@@ -401,7 +401,7 @@ theorem mem_iSup_iff_exists_dfinsupp' (p : ι → Submodule R N) [∀ (i) (x : p
     (x : N) : x ∈ iSup p ↔ ∃ f : Π₀ i, p i, (f.Sum fun i xi => ↑xi) = x :=
   by
   rw [mem_supr_iff_exists_dfinsupp]
-  simp_rw [Dfinsupp.lsum_apply_apply, Dfinsupp.sumAddHom_apply]
+  simp_rw [DFinsupp.lsum_apply_apply, DFinsupp.sumAddHom_apply]
   congr
 #align submodule.mem_supr_iff_exists_dfinsupp' Submodule.mem_iSup_iff_exists_dfinsupp'
 -/
@@ -410,7 +410,7 @@ theorem mem_iSup_iff_exists_dfinsupp' (p : ι → Submodule R N) [∀ (i) (x : p
 theorem mem_biSup_iff_exists_dfinsupp (p : ι → Prop) [DecidablePred p] (S : ι → Submodule R N)
     (x : N) :
     (x ∈ ⨆ (i) (h : p i), S i) ↔
-      ∃ f : Π₀ i, S i, Dfinsupp.lsum ℕ (fun i => (S i).Subtype) (f.filterₓ p) = x :=
+      ∃ f : Π₀ i, S i, DFinsupp.lsum ℕ (fun i => (S i).Subtype) (f.filterₓ p) = x :=
   SetLike.ext_iff.mp (biSup_eq_range_dfinsupp_lsum p S) x
 #align submodule.mem_bsupr_iff_exists_dfinsupp Submodule.mem_biSup_iff_exists_dfinsupp
 -/
@@ -430,10 +430,10 @@ theorem mem_iSup_finset_iff_exists_sum {s : Finset ι} (p : ι → Submodule R N
       ext; rw [coe_zero, ← mem_bot R]; convert coe_mem (μ x)
       symm; exact iSup_neg hx
     · intro x _ hx; rw [mem_support_iff, not_ne_iff] at hx ; rw [hx]; rfl
-  · refine' ⟨Dfinsupp.mk s _, _⟩
+  · refine' ⟨DFinsupp.mk s _, _⟩
     · rintro ⟨i, hi⟩; refine' ⟨μ i, _⟩
       rw [iSup_pos]; · exact coe_mem _; · exact hi
-    simp only [Dfinsupp.sum]
+    simp only [DFinsupp.sum]
     rw [Finset.sum_subset support_mk_subset, ← hμ]
     exact Finset.sum_congr rfl fun x hx => congr_arg coe <| mk_of_mem hx
     · intro x _ hx; rw [mem_support_iff, not_ne_iff] at hx ; rw [hx]; rfl
@@ -444,7 +444,7 @@ end Submodule
 
 namespace CompleteLattice
 
-open Dfinsupp
+open DFinsupp
 
 section Semiring
 
@@ -504,7 +504,7 @@ theorem lsum_comp_mapRange_toSpanSingleton [∀ m : R, Decidable (m ≠ 0)] (p :
     ((lsum ℕ) fun i => (p i).Subtype : _ →ₗ[R] _).comp
         ((mapRange.linearMap fun i => LinearMap.toSpanSingleton R (↥(p i)) ⟨v i, hv i⟩ :
               _ →ₗ[R] _).comp
-          (finsuppLequivDfinsupp R : (ι →₀ R) ≃ₗ[R] _).toLinearMap) =
+          (finsuppLequivDFinsupp R : (ι →₀ R) ≃ₗ[R] _).toLinearMap) =
       Finsupp.total ι N R v :=
   by ext; simp
 #align complete_lattice.lsum_comp_map_range_to_span_singleton CompleteLattice.lsum_comp_mapRange_toSpanSingleton
@@ -543,13 +543,13 @@ theorem Independent.dfinsupp_lsum_injective {p : ι → Submodule R N} (h : Inde
   suffices (lsum ℕ fun i => (p i).Subtype).ker = ⊥
     by
     -- Lean can't find this without our help
-    letI : AddCommGroup (Π₀ i, p i) := @Dfinsupp.addCommGroup _ (fun i => p i) _
+    letI : AddCommGroup (Π₀ i, p i) := @DFinsupp.addCommGroup _ (fun i => p i) _
     rw [LinearMap.ker_eq_bot] at this ; exact this
   rw [LinearMap.ker_eq_bot']
   intro m hm
   ext i : 1
   -- split `m` into the piece at `i` and the pieces elsewhere, to match `h`
-  rw [Dfinsupp.zero_apply, ← neg_eq_zero]
+  rw [DFinsupp.zero_apply, ← neg_eq_zero]
   refine' h i (-m i) m _
   rwa [← erase_add_single i m, LinearMap.map_add, lsum_single, Submodule.subtype_apply,
     add_eq_zero_iff_eq_neg, ← Submodule.coe_neg] at hm 
@@ -600,7 +600,7 @@ theorem Independent.linearIndependent [NoZeroSMulDivisors R N] (p : ι → Submo
   rw [linearIndependent_iff]
   intro l hl
   let a :=
-    Dfinsupp.mapRange.linearMap (fun i => LinearMap.toSpanSingleton R (p i) ⟨v i, hv i⟩)
+    DFinsupp.mapRange.linearMap (fun i => LinearMap.toSpanSingleton R (p i) ⟨v i, hv i⟩)
       l.to_dfinsupp
   have ha : a = 0 := by
     apply hp.dfinsupp_lsum_injective

f4758115

bump to nightly-2023-06-20-01

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

9b351f8c

Diff

@@ -166,9 +166,9 @@ def lsum [Semiring S] [Module S N] [SMulCommClass R S N] :
             sum_add_hom_single, sum_add_hom_single, LinearMap.toAddMonoidHom_coe,
             LinearMap.map_smul] }
   invFun F i := F.comp (lsingle i)
-  left_inv F := by ext (x y); simp
-  right_inv F := by ext (x y); simp
-  map_add' F G := by ext (x y); simp
+  left_inv F := by ext x y; simp
+  right_inv F := by ext x y; simp
+  map_add' F G := by ext x y; simp
   map_smul' c F := by ext; simp
 #align dfinsupp.lsum Dfinsupp.lsum
 -/

f4758115

bump to nightly-2023-06-13-21

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

829520ac

Diff

@@ -51,8 +51,7 @@ variable [Semiring R] [∀ i, AddCommMonoid (M i)] [∀ i, Module R (M i)]
 
 variable [AddCommMonoid N] [Module R N]
 
-include dec_ι
-
+#print Dfinsupp.lmk /-
 /-- `dfinsupp.mk` as a `linear_map`. -/
 def lmk (s : Finset ι) : (∀ i : (↑s : Set ι), M i) →ₗ[R] Π₀ i, M i
     where
@@ -60,19 +59,25 @@ def lmk (s : Finset ι) : (∀ i : (↑s : Set ι), M i) →ₗ[R] Π₀ i, M i
   map_add' _ _ := mk_add
   map_smul' c x := mk_smul c x
 #align dfinsupp.lmk Dfinsupp.lmk
+-/
 
+#print Dfinsupp.lsingle /-
 /-- `dfinsupp.single` as a `linear_map` -/
 def lsingle (i) : M i →ₗ[R] Π₀ i, M i :=
   { Dfinsupp.singleAddHom _ _ with
     toFun := single i
     map_smul' := single_smul }
 #align dfinsupp.lsingle Dfinsupp.lsingle
+-/
 
+#print Dfinsupp.lhom_ext /-
 /-- Two `R`-linear maps from `Π₀ i, M i` which agree on each `single i x` agree everywhere. -/
 theorem lhom_ext ⦃φ ψ : (Π₀ i, M i) →ₗ[R] N⦄ (h : ∀ i x, φ (single i x) = ψ (single i x)) : φ = ψ :=
   LinearMap.toAddMonoidHom_injective <| addHom_ext h
 #align dfinsupp.lhom_ext Dfinsupp.lhom_ext
+-/
 
+#print Dfinsupp.lhom_ext' /-
 /-- Two `R`-linear maps from `Π₀ i, M i` which agree on each `single i x` agree everywhere.
 
 See note [partially-applied ext lemmas].
@@ -82,9 +87,9 @@ theorem lhom_ext' ⦃φ ψ : (Π₀ i, M i) →ₗ[R] N⦄ (h : ∀ i, φ.comp (
     φ = ψ :=
   lhom_ext fun i => LinearMap.congr_fun (h i)
 #align dfinsupp.lhom_ext' Dfinsupp.lhom_ext'
+-/
 
-omit dec_ι
-
+#print Dfinsupp.lapply /-
 /-- Interpret `λ (f : Π₀ i, M i), f i` as a linear map. -/
 def lapply (i : ι) : (Π₀ i, M i) →ₗ[R] M i
     where
@@ -92,35 +97,41 @@ def lapply (i : ι) : (Π₀ i, M i) →ₗ[R] M i
   map_add' f g := add_apply f g i
   map_smul' c f := smul_apply c f i
 #align dfinsupp.lapply Dfinsupp.lapply
+-/
 
-include dec_ι
-
+#print Dfinsupp.lmk_apply /-
 @[simp]
 theorem lmk_apply (s : Finset ι) (x) : (lmk s : _ →ₗ[R] Π₀ i, M i) x = mk s x :=
   rfl
 #align dfinsupp.lmk_apply Dfinsupp.lmk_apply
+-/
 
+#print Dfinsupp.lsingle_apply /-
 @[simp]
 theorem lsingle_apply (i : ι) (x : M i) : (lsingle i : _ →ₗ[R] _) x = single i x :=
   rfl
 #align dfinsupp.lsingle_apply Dfinsupp.lsingle_apply
+-/
 
-omit dec_ι
-
+#print Dfinsupp.lapply_apply /-
 @[simp]
 theorem lapply_apply (i : ι) (f : Π₀ i, M i) : (lapply i : _ →ₗ[R] _) f = f i :=
   rfl
 #align dfinsupp.lapply_apply Dfinsupp.lapply_apply
+-/
 
 section Lsum
 
+#print Dfinsupp.addCommMonoidOfLinearMap /-
 /-- Typeclass inference can't find `dfinsupp.add_comm_monoid` without help for this case.
 This instance allows it to be found where it is needed on the LHS of the colon in
 `dfinsupp.module_of_linear_map`. -/
 instance addCommMonoidOfLinearMap : AddCommMonoid (Π₀ i : ι, M i →ₗ[R] N) :=
   @Dfinsupp.addCommMonoid _ (fun i => M i →ₗ[R] N) _
 #align dfinsupp.add_comm_monoid_of_linear_map Dfinsupp.addCommMonoidOfLinearMap
+-/
 
+#print Dfinsupp.moduleOfLinearMap /-
 /-- Typeclass inference can't find `dfinsupp.module` without help for this case.
 This is needed to define `dfinsupp.lsum` below.
 
@@ -131,11 +142,11 @@ instance moduleOfLinearMap [Semiring S] [Module S N] [SMulCommClass R S N] :
     Module S (Π₀ i : ι, M i →ₗ[R] N) :=
   @Dfinsupp.module _ _ (fun i => M i →ₗ[R] N) _ _ _
 #align dfinsupp.module_of_linear_map Dfinsupp.moduleOfLinearMap
+-/
 
 variable (S)
 
-include dec_ι
-
+#print Dfinsupp.lsum /-
 /-- The `dfinsupp` version of `finsupp.lsum`.
 
 See note [bundled maps over different rings] for why separate `R` and `S` semirings are used. -/
@@ -160,13 +171,16 @@ def lsum [Semiring S] [Module S N] [SMulCommClass R S N] :
   map_add' F G := by ext (x y); simp
   map_smul' c F := by ext; simp
 #align dfinsupp.lsum Dfinsupp.lsum
+-/
 
+#print Dfinsupp.lsum_single /-
 /-- While `simp` can prove this, it is often convenient to avoid unfolding `lsum` into `sum_add_hom`
 with `dfinsupp.lsum_apply_apply`. -/
 theorem lsum_single [Semiring S] [Module S N] [SMulCommClass R S N] (F : ∀ i, M i →ₗ[R] N) (i)
     (x : M i) : lsum S F (single i x) = F i x :=
   sumAddHom_single _ _ _
 #align dfinsupp.lsum_single Dfinsupp.lsum_single
+-/
 
 end Lsum
 
@@ -184,6 +198,7 @@ variable [∀ i, AddCommMonoid (β i)] [∀ i, AddCommMonoid (β₁ i)] [∀ i,
 
 variable [∀ i, Module R (β i)] [∀ i, Module R (β₁ i)] [∀ i, Module R (β₂ i)]
 
+#print Dfinsupp.mapRange_smul /-
 theorem mapRange_smul (f : ∀ i, β₁ i → β₂ i) (hf : ∀ i, f i 0 = 0) (r : R)
     (hf' : ∀ i x, f i (r • x) = r • f i x) (g : Π₀ i, β₁ i) :
     mapRange f hf (r • g) = r • mapRange f hf g :=
@@ -191,7 +206,9 @@ theorem mapRange_smul (f : ∀ i, β₁ i → β₂ i) (hf : ∀ i, f i 0 = 0) (
   ext
   simp only [map_range_apply f, coe_smul, Pi.smul_apply, hf']
 #align dfinsupp.map_range_smul Dfinsupp.mapRange_smul
+-/
 
+#print Dfinsupp.mapRange.linearMap /-
 /-- `dfinsupp.map_range` as an `linear_map`. -/
 @[simps apply]
 def mapRange.linearMap (f : ∀ i, β₁ i →ₗ[R] β₂ i) : (Π₀ i, β₁ i) →ₗ[R] Π₀ i, β₂ i :=
@@ -201,21 +218,25 @@ def mapRange.linearMap (f : ∀ i, β₁ i →ₗ[R] β₂ i) : (Π₀ i, β₁
     toFun := mapRange (fun i x => f i x) fun i => (f i).map_zero
     map_smul' := fun r => mapRange_smul _ _ _ fun i => (f i).map_smul r }
 #align dfinsupp.map_range.linear_map Dfinsupp.mapRange.linearMap
+-/
 
+#print Dfinsupp.mapRange.linearMap_id /-
 @[simp]
 theorem mapRange.linearMap_id :
     (mapRange.linearMap fun i => (LinearMap.id : β₂ i →ₗ[R] _)) = LinearMap.id :=
   LinearMap.ext mapRange_id
 #align dfinsupp.map_range.linear_map_id Dfinsupp.mapRange.linearMap_id
+-/
 
+#print Dfinsupp.mapRange.linearMap_comp /-
 theorem mapRange.linearMap_comp (f : ∀ i, β₁ i →ₗ[R] β₂ i) (f₂ : ∀ i, β i →ₗ[R] β₁ i) :
     (mapRange.linearMap fun i => (f i).comp (f₂ i)) =
       (mapRange.linearMap f).comp (mapRange.linearMap f₂) :=
   LinearMap.ext <| mapRange_comp (fun i x => f i x) (fun i x => f₂ i x) _ _ _
 #align dfinsupp.map_range.linear_map_comp Dfinsupp.mapRange.linearMap_comp
+-/
 
-include dec_ι
-
+#print Dfinsupp.sum_mapRange_index.linearMap /-
 theorem sum_mapRange_index.linearMap [∀ (i : ι) (x : β₁ i), Decidable (x ≠ 0)]
     [∀ (i : ι) (x : β₂ i), Decidable (x ≠ 0)] {f : ∀ i, β₁ i →ₗ[R] β₂ i} {h : ∀ i, β₂ i →ₗ[R] N}
     {l : Π₀ i, β₁ i} :
@@ -224,9 +245,9 @@ theorem sum_mapRange_index.linearMap [∀ (i : ι) (x : β₁ i), Decidable (x 
     @sum_map_range_index ι N _ _ _ _ _ _ _ _ (fun i => f i) (fun i => by simp) l (fun i => h i)
       fun i => by simp
 #align dfinsupp.sum_map_range_index.linear_map Dfinsupp.sum_mapRange_index.linearMap
+-/
 
-omit dec_ι
-
+#print Dfinsupp.mapRange.linearEquiv /-
 /-- `dfinsupp.map_range.linear_map` as an `linear_equiv`. -/
 @[simps apply]
 def mapRange.linearEquiv (e : ∀ i, β₁ i ≃ₗ[R] β₂ i) : (Π₀ i, β₁ i) ≃ₗ[R] Π₀ i, β₂ i :=
@@ -236,24 +257,31 @@ def mapRange.linearEquiv (e : ∀ i, β₁ i ≃ₗ[R] β₂ i) : (Π₀ i, β
     toFun := mapRange (fun i x => e i x) fun i => (e i).map_zero
     invFun := mapRange (fun i x => (e i).symm x) fun i => (e i).symm.map_zero }
 #align dfinsupp.map_range.linear_equiv Dfinsupp.mapRange.linearEquiv
+-/
 
+#print Dfinsupp.mapRange.linearEquiv_refl /-
 @[simp]
 theorem mapRange.linearEquiv_refl :
     (mapRange.linearEquiv fun i => LinearEquiv.refl R (β₁ i)) = LinearEquiv.refl _ _ :=
   LinearEquiv.ext mapRange_id
 #align dfinsupp.map_range.linear_equiv_refl Dfinsupp.mapRange.linearEquiv_refl
+-/
 
+#print Dfinsupp.mapRange.linearEquiv_trans /-
 theorem mapRange.linearEquiv_trans (f : ∀ i, β i ≃ₗ[R] β₁ i) (f₂ : ∀ i, β₁ i ≃ₗ[R] β₂ i) :
     (mapRange.linearEquiv fun i => (f i).trans (f₂ i)) =
       (mapRange.linearEquiv f).trans (mapRange.linearEquiv f₂) :=
   LinearEquiv.ext <| mapRange_comp (fun i x => f₂ i x) (fun i x => f i x) _ _ _
 #align dfinsupp.map_range.linear_equiv_trans Dfinsupp.mapRange.linearEquiv_trans
+-/
 
+#print Dfinsupp.mapRange.linearEquiv_symm /-
 @[simp]
 theorem mapRange.linearEquiv_symm (e : ∀ i, β₁ i ≃ₗ[R] β₂ i) :
     (mapRange.linearEquiv e).symm = mapRange.linearEquiv fun i => (e i).symm :=
   rfl
 #align dfinsupp.map_range.linear_equiv_symm Dfinsupp.mapRange.linearEquiv_symm
+-/
 
 end MapRange
 
@@ -261,6 +289,7 @@ section CoprodMap
 
 variable [DecidableEq ι] [∀ x : N, Decidable (x ≠ 0)]
 
+#print Dfinsupp.coprodMap /-
 /-- Given a family of linear maps `f i : M i  →ₗ[R] N`, we can form a linear map
 `(Π₀ i, M i) →ₗ[R] N` which sends `x : Π₀ i, M i` to the sum over `i` of `f i` applied to `x i`.
 This is the map coming from the universal property of `Π₀ i, M i` as the coproduct of the `M i`.
@@ -269,18 +298,22 @@ noncomputable def coprodMap (f : ∀ i : ι, M i →ₗ[R] N) : (Π₀ i, M i) 
   (Finsupp.lsum ℕ fun i : ι => LinearMap.id) ∘ₗ
     (@finsuppLequivDfinsupp ι R N _ _ _ _ _).symm.toLinearMap ∘ₗ Dfinsupp.mapRange.linearMap f
 #align dfinsupp.coprod_map Dfinsupp.coprodMap
+-/
 
+#print Dfinsupp.coprodMap_apply /-
 theorem coprodMap_apply (f : ∀ i : ι, M i →ₗ[R] N) (x : Π₀ i, M i) :
     coprodMap f x =
       Finsupp.sum (mapRange (fun i => f i) (fun i => LinearMap.map_zero _) x).toFinsupp fun i =>
         id :=
   rfl
 #align dfinsupp.coprod_map_apply Dfinsupp.coprodMap_apply
+-/
 
 end CoprodMap
 
 section Basis
 
+#print Dfinsupp.basis /-
 /-- The direct sum of free modules is free.
 
 Note that while this is stated for `dfinsupp` not `direct_sum`, the types are defeq. -/
@@ -289,31 +322,35 @@ noncomputable def basis {η : ι → Type _} (b : ∀ i, Basis (η i) R (M i)) :
   Basis.ofRepr
     ((mapRange.linearEquiv fun i => (b i).repr).trans (sigmaFinsuppLequivDfinsupp R).symm)
 #align dfinsupp.basis Dfinsupp.basis
+-/
 
 end Basis
 
 end Dfinsupp
 
-include dec_ι
-
 namespace Submodule
 
 variable [Semiring R] [AddCommMonoid N] [Module R N]
 
 open Dfinsupp
 
+#print Submodule.dfinsupp_sum_mem /-
 theorem dfinsupp_sum_mem {β : ι → Type _} [∀ i, Zero (β i)] [∀ (i) (x : β i), Decidable (x ≠ 0)]
     (S : Submodule R N) (f : Π₀ i, β i) (g : ∀ i, β i → N) (h : ∀ c, f c ≠ 0 → g c (f c) ∈ S) :
     f.Sum g ∈ S :=
   dfinsupp_sum_mem S f g h
 #align submodule.dfinsupp_sum_mem Submodule.dfinsupp_sum_mem
+-/
 
+#print Submodule.dfinsupp_sumAddHom_mem /-
 theorem dfinsupp_sumAddHom_mem {β : ι → Type _} [∀ i, AddZeroClass (β i)] (S : Submodule R N)
     (f : Π₀ i, β i) (g : ∀ i, β i →+ N) (h : ∀ c, f c ≠ 0 → g c (f c) ∈ S) :
     Dfinsupp.sumAddHom g f ∈ S :=
   dfinsupp_sumAddHom_mem S f g h
 #align submodule.dfinsupp_sum_add_hom_mem Submodule.dfinsupp_sumAddHom_mem
+-/
 
+#print Submodule.iSup_eq_range_dfinsupp_lsum /-
 /-- The supremum of a family of submodules is equal to the range of `dfinsupp.lsum`; that is
 every element in the `supr` can be produced from taking a finite number of non-zero elements
 of `p i`, coercing them to `N`, and summing them. -/
@@ -327,7 +364,9 @@ theorem iSup_eq_range_dfinsupp_lsum (p : ι → Submodule R N) :
   · rintro x ⟨v, rfl⟩
     exact dfinsupp_sumAddHom_mem _ v _ fun i _ => (le_iSup p i : p i ≤ _) (v i).Prop
 #align submodule.supr_eq_range_dfinsupp_lsum Submodule.iSup_eq_range_dfinsupp_lsum
+-/
 
+#print Submodule.biSup_eq_range_dfinsupp_lsum /-
 /-- The bounded supremum of a family of commutative additive submonoids is equal to the range of
 `dfinsupp.sum_add_hom` composed with `dfinsupp.filter_add_monoid_hom`; that is, every element in the
 bounded `supr` can be produced from taking a finite number of non-zero elements from the `S i` that
@@ -347,12 +386,16 @@ theorem biSup_eq_range_dfinsupp_lsum (p : ι → Prop) [DecidablePred p] (S : ι
     · simp [hp]
     · simp [hp]
 #align submodule.bsupr_eq_range_dfinsupp_lsum Submodule.biSup_eq_range_dfinsupp_lsum
+-/
 
+#print Submodule.mem_iSup_iff_exists_dfinsupp /-
 theorem mem_iSup_iff_exists_dfinsupp (p : ι → Submodule R N) (x : N) :
     x ∈ iSup p ↔ ∃ f : Π₀ i, p i, Dfinsupp.lsum ℕ (fun i => (p i).Subtype) f = x :=
   SetLike.ext_iff.mp (iSup_eq_range_dfinsupp_lsum p) x
 #align submodule.mem_supr_iff_exists_dfinsupp Submodule.mem_iSup_iff_exists_dfinsupp
+-/
 
+#print Submodule.mem_iSup_iff_exists_dfinsupp' /-
 /-- A variant of `submodule.mem_supr_iff_exists_dfinsupp` with the RHS fully unfolded. -/
 theorem mem_iSup_iff_exists_dfinsupp' (p : ι → Submodule R N) [∀ (i) (x : p i), Decidable (x ≠ 0)]
     (x : N) : x ∈ iSup p ↔ ∃ f : Π₀ i, p i, (f.Sum fun i xi => ↑xi) = x :=
@@ -361,18 +404,20 @@ theorem mem_iSup_iff_exists_dfinsupp' (p : ι → Submodule R N) [∀ (i) (x : p
   simp_rw [Dfinsupp.lsum_apply_apply, Dfinsupp.sumAddHom_apply]
   congr
 #align submodule.mem_supr_iff_exists_dfinsupp' Submodule.mem_iSup_iff_exists_dfinsupp'
+-/
 
+#print Submodule.mem_biSup_iff_exists_dfinsupp /-
 theorem mem_biSup_iff_exists_dfinsupp (p : ι → Prop) [DecidablePred p] (S : ι → Submodule R N)
     (x : N) :
     (x ∈ ⨆ (i) (h : p i), S i) ↔
       ∃ f : Π₀ i, S i, Dfinsupp.lsum ℕ (fun i => (S i).Subtype) (f.filterₓ p) = x :=
   SetLike.ext_iff.mp (biSup_eq_range_dfinsupp_lsum p S) x
 #align submodule.mem_bsupr_iff_exists_dfinsupp Submodule.mem_biSup_iff_exists_dfinsupp
+-/
 
 open scoped BigOperators
 
-omit dec_ι
-
+#print Submodule.mem_iSup_finset_iff_exists_sum /-
 theorem mem_iSup_finset_iff_exists_sum {s : Finset ι} (p : ι → Submodule R N) (a : N) :
     (a ∈ ⨆ i ∈ s, p i) ↔ ∃ μ : ∀ i, p i, ∑ i in s, (μ i : N) = a := by
   classical
@@ -393,6 +438,7 @@ theorem mem_iSup_finset_iff_exists_sum {s : Finset ι} (p : ι → Submodule R N
     exact Finset.sum_congr rfl fun x hx => congr_arg coe <| mk_of_mem hx
     · intro x _ hx; rw [mem_support_iff, not_ne_iff] at hx ; rw [hx]; rfl
 #align submodule.mem_supr_finset_iff_exists_sum Submodule.mem_iSup_finset_iff_exists_sum
+-/
 
 end Submodule
 
@@ -404,6 +450,7 @@ section Semiring
 
 variable [Semiring R] [AddCommMonoid N] [Module R N]
 
+#print CompleteLattice.independent_iff_forall_dfinsupp /-
 /-- Independence of a family of submodules can be expressed as a quantifier over `dfinsupp`s.
 
 This is an intermediate result used to prove
@@ -421,7 +468,9 @@ theorem independent_iff_forall_dfinsupp (p : ι → Submodule R N) :
   simp_rw [Submodule.coe_eq_zero]
   rfl
 #align complete_lattice.independent_iff_forall_dfinsupp CompleteLattice.independent_iff_forall_dfinsupp
+-/
 
+#print CompleteLattice.independent_of_dfinsupp_lsum_injective /-
 /- If `dfinsupp.lsum` applied with `submodule.subtype` is injective then the submodules are
 independent. -/
 theorem independent_of_dfinsupp_lsum_injective (p : ι → Submodule R N)
@@ -435,7 +484,9 @@ theorem independent_of_dfinsupp_lsum_injective (p : ι → Submodule R N)
   have := dfinsupp.ext_iff.mp (h hv) i
   simpa [eq_comm] using this
 #align complete_lattice.independent_of_dfinsupp_lsum_injective CompleteLattice.independent_of_dfinsupp_lsum_injective
+-/
 
+#print CompleteLattice.independent_of_dfinsupp_sumAddHom_injective /-
 /- If `dfinsupp.sum_add_hom` applied with `add_submonoid.subtype` is injective then the additive
 submonoids are independent. -/
 theorem independent_of_dfinsupp_sumAddHom_injective (p : ι → AddSubmonoid N)
@@ -444,7 +495,9 @@ theorem independent_of_dfinsupp_sumAddHom_injective (p : ι → AddSubmonoid N)
   rw [← independent_map_order_iso_iff (AddSubmonoid.toNatSubmodule : AddSubmonoid N ≃o _)]
   exact independent_of_dfinsupp_lsum_injective _ h
 #align complete_lattice.independent_of_dfinsupp_sum_add_hom_injective CompleteLattice.independent_of_dfinsupp_sumAddHom_injective
+-/
 
+#print CompleteLattice.lsum_comp_mapRange_toSpanSingleton /-
 /-- Combining `dfinsupp.lsum` with `linear_map.to_span_singleton` is the same as `finsupp.total` -/
 theorem lsum_comp_mapRange_toSpanSingleton [∀ m : R, Decidable (m ≠ 0)] (p : ι → Submodule R N)
     {v : ι → N} (hv : ∀ i : ι, v i ∈ p i) :
@@ -455,6 +508,7 @@ theorem lsum_comp_mapRange_toSpanSingleton [∀ m : R, Decidable (m ≠ 0)] (p :
       Finsupp.total ι N R v :=
   by ext; simp
 #align complete_lattice.lsum_comp_map_range_to_span_singleton CompleteLattice.lsum_comp_mapRange_toSpanSingleton
+-/
 
 end Semiring
 
@@ -462,6 +516,7 @@ section Ring
 
 variable [Ring R] [AddCommGroup N] [Module R N]
 
+#print CompleteLattice.independent_of_dfinsupp_sumAddHom_injective' /-
 /- If `dfinsupp.sum_add_hom` applied with `add_submonoid.subtype` is injective then the additive
 subgroups are independent. -/
 theorem independent_of_dfinsupp_sumAddHom_injective' (p : ι → AddSubgroup N)
@@ -470,7 +525,9 @@ theorem independent_of_dfinsupp_sumAddHom_injective' (p : ι → AddSubgroup N)
   rw [← independent_map_order_iso_iff (AddSubgroup.toIntSubmodule : AddSubgroup N ≃o _)]
   exact independent_of_dfinsupp_lsum_injective _ h
 #align complete_lattice.independent_of_dfinsupp_sum_add_hom_injective' CompleteLattice.independent_of_dfinsupp_sumAddHom_injective'
+-/
 
+#print CompleteLattice.Independent.dfinsupp_lsum_injective /-
 /-- The canonical map out of a direct sum of a family of submodules is injective when the submodules
 are `complete_lattice.independent`.
 
@@ -497,7 +554,9 @@ theorem Independent.dfinsupp_lsum_injective {p : ι → Submodule R N} (h : Inde
   rwa [← erase_add_single i m, LinearMap.map_add, lsum_single, Submodule.subtype_apply,
     add_eq_zero_iff_eq_neg, ← Submodule.coe_neg] at hm 
 #align complete_lattice.independent.dfinsupp_lsum_injective CompleteLattice.Independent.dfinsupp_lsum_injective
+-/
 
+#print CompleteLattice.Independent.dfinsupp_sumAddHom_injective /-
 /-- The canonical map out of a direct sum of a family of additive subgroups is injective when the
 additive subgroups are `complete_lattice.independent`. -/
 theorem Independent.dfinsupp_sumAddHom_injective {p : ι → AddSubgroup N} (h : Independent p) :
@@ -506,7 +565,9 @@ theorem Independent.dfinsupp_sumAddHom_injective {p : ι → AddSubgroup N} (h :
   rw [← independent_map_order_iso_iff (AddSubgroup.toIntSubmodule : AddSubgroup N ≃o _)] at h 
   exact h.dfinsupp_lsum_injective
 #align complete_lattice.independent.dfinsupp_sum_add_hom_injective CompleteLattice.Independent.dfinsupp_sumAddHom_injective
+-/
 
+#print CompleteLattice.independent_iff_dfinsupp_lsum_injective /-
 /-- A family of submodules over an additive group are independent if and only iff `dfinsupp.lsum`
 applied with `submodule.subtype` is injective.
 
@@ -516,16 +577,18 @@ theorem independent_iff_dfinsupp_lsum_injective (p : ι → Submodule R N) :
     Independent p ↔ Function.Injective (lsum ℕ fun i => (p i).Subtype) :=
   ⟨Independent.dfinsupp_lsum_injective, independent_of_dfinsupp_lsum_injective p⟩
 #align complete_lattice.independent_iff_dfinsupp_lsum_injective CompleteLattice.independent_iff_dfinsupp_lsum_injective
+-/
 
+#print CompleteLattice.independent_iff_dfinsupp_sumAddHom_injective /-
 /-- A family of additive subgroups over an additive group are independent if and only if
 `dfinsupp.sum_add_hom` applied with `add_subgroup.subtype` is injective. -/
 theorem independent_iff_dfinsupp_sumAddHom_injective (p : ι → AddSubgroup N) :
     Independent p ↔ Function.Injective (sumAddHom fun i => (p i).Subtype) :=
   ⟨Independent.dfinsupp_sumAddHom_injective, independent_of_dfinsupp_sumAddHom_injective' p⟩
 #align complete_lattice.independent_iff_dfinsupp_sum_add_hom_injective CompleteLattice.independent_iff_dfinsupp_sumAddHom_injective
+-/
 
-omit dec_ι
-
+#print CompleteLattice.Independent.linearIndependent /-
 /-- If a family of submodules is `independent`, then a choice of nonzero vector from each submodule
 forms a linearly independent family.
 
@@ -547,12 +610,15 @@ theorem Independent.linearIndependent [NoZeroSMulDivisors R N] (p : ι → Submo
   have : l i • v i = a i := rfl
   simp [this, ha]
 #align complete_lattice.independent.linear_independent CompleteLattice.Independent.linearIndependent
+-/
 
+#print CompleteLattice.independent_iff_linearIndependent_of_ne_zero /-
 theorem independent_iff_linearIndependent_of_ne_zero [NoZeroSMulDivisors R N] {v : ι → N}
     (h_ne_zero : ∀ i, v i ≠ 0) : (Independent fun i => R ∙ v i) ↔ LinearIndependent R v :=
   ⟨fun hv => hv.LinearIndependent _ (fun i => Submodule.mem_span_singleton_self <| v i) h_ne_zero,
     fun hv => hv.independent_span_singleton⟩
 #align complete_lattice.independent_iff_linear_independent_of_ne_zero CompleteLattice.independent_iff_linearIndependent_of_ne_zero
+-/
 
 end Ring

f4758115

bump to nightly-2023-06-10-07

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3

3fdc57bc

Diff

@@ -374,7 +374,7 @@ open scoped BigOperators
 omit dec_ι
 
 theorem mem_iSup_finset_iff_exists_sum {s : Finset ι} (p : ι → Submodule R N) (a : N) :
-    (a ∈ ⨆ i ∈ s, p i) ↔ ∃ μ : ∀ i, p i, (∑ i in s, (μ i : N)) = a := by
+    (a ∈ ⨆ i ∈ s, p i) ↔ ∃ μ : ∀ i, p i, ∑ i in s, (μ i : N) = a := by
   classical
   rw [Submodule.mem_iSup_iff_exists_dfinsupp']
   constructor <;> rintro ⟨μ, hμ⟩

f4758115

bump to nightly-2023-06-04-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

3fb4268b

Diff

@@ -376,22 +376,22 @@ omit dec_ι
 theorem mem_iSup_finset_iff_exists_sum {s : Finset ι} (p : ι → Submodule R N) (a : N) :
     (a ∈ ⨆ i ∈ s, p i) ↔ ∃ μ : ∀ i, p i, (∑ i in s, (μ i : N)) = a := by
   classical
-    rw [Submodule.mem_iSup_iff_exists_dfinsupp']
-    constructor <;> rintro ⟨μ, hμ⟩
-    · use fun i => ⟨μ i, (iSup_const_le : _ ≤ p i) (coe_mem <| μ i)⟩
-      rw [← hμ]; symm; apply Finset.sum_subset
-      · intro x; contrapose; intro hx
-        rw [mem_support_iff, not_ne_iff]
-        ext; rw [coe_zero, ← mem_bot R]; convert coe_mem (μ x)
-        symm; exact iSup_neg hx
-      · intro x _ hx; rw [mem_support_iff, not_ne_iff] at hx ; rw [hx]; rfl
-    · refine' ⟨Dfinsupp.mk s _, _⟩
-      · rintro ⟨i, hi⟩; refine' ⟨μ i, _⟩
-        rw [iSup_pos]; · exact coe_mem _; · exact hi
-      simp only [Dfinsupp.sum]
-      rw [Finset.sum_subset support_mk_subset, ← hμ]
-      exact Finset.sum_congr rfl fun x hx => congr_arg coe <| mk_of_mem hx
-      · intro x _ hx; rw [mem_support_iff, not_ne_iff] at hx ; rw [hx]; rfl
+  rw [Submodule.mem_iSup_iff_exists_dfinsupp']
+  constructor <;> rintro ⟨μ, hμ⟩
+  · use fun i => ⟨μ i, (iSup_const_le : _ ≤ p i) (coe_mem <| μ i)⟩
+    rw [← hμ]; symm; apply Finset.sum_subset
+    · intro x; contrapose; intro hx
+      rw [mem_support_iff, not_ne_iff]
+      ext; rw [coe_zero, ← mem_bot R]; convert coe_mem (μ x)
+      symm; exact iSup_neg hx
+    · intro x _ hx; rw [mem_support_iff, not_ne_iff] at hx ; rw [hx]; rfl
+  · refine' ⟨Dfinsupp.mk s _, _⟩
+    · rintro ⟨i, hi⟩; refine' ⟨μ i, _⟩
+      rw [iSup_pos]; · exact coe_mem _; · exact hi
+    simp only [Dfinsupp.sum]
+    rw [Finset.sum_subset support_mk_subset, ← hμ]
+    exact Finset.sum_congr rfl fun x hx => congr_arg coe <| mk_of_mem hx
+    · intro x _ hx; rw [mem_support_iff, not_ne_iff] at hx ; rw [hx]; rfl
 #align submodule.mem_supr_finset_iff_exists_sum Submodule.mem_iSup_finset_iff_exists_sum
 
 end Submodule
@@ -534,18 +534,18 @@ theorem Independent.linearIndependent [NoZeroSMulDivisors R N] (p : ι → Submo
     (hp : Independent p) {v : ι → N} (hv : ∀ i, v i ∈ p i) (hv' : ∀ i, v i ≠ 0) :
     LinearIndependent R v := by
   classical
-    rw [linearIndependent_iff]
-    intro l hl
-    let a :=
-      Dfinsupp.mapRange.linearMap (fun i => LinearMap.toSpanSingleton R (p i) ⟨v i, hv i⟩)
-        l.to_dfinsupp
-    have ha : a = 0 := by
-      apply hp.dfinsupp_lsum_injective
-      rwa [← lsum_comp_map_range_to_span_singleton _ hv] at hl 
-    ext i
-    apply smul_left_injective R (hv' i)
-    have : l i • v i = a i := rfl
-    simp [this, ha]
+  rw [linearIndependent_iff]
+  intro l hl
+  let a :=
+    Dfinsupp.mapRange.linearMap (fun i => LinearMap.toSpanSingleton R (p i) ⟨v i, hv i⟩)
+      l.to_dfinsupp
+  have ha : a = 0 := by
+    apply hp.dfinsupp_lsum_injective
+    rwa [← lsum_comp_map_range_to_span_singleton _ hv] at hl 
+  ext i
+  apply smul_left_injective R (hv' i)
+  have : l i • v i = a i := rfl
+  simp [this, ha]
 #align complete_lattice.independent.linear_independent CompleteLattice.Independent.linearIndependent
 
 theorem independent_iff_linearIndependent_of_ne_zero [NoZeroSMulDivisors R N] {v : ι → N}

f4758115

bump to nightly-2023-06-01-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

b9c87c70

Diff

@@ -285,7 +285,7 @@ section Basis
 
 Note that while this is stated for `dfinsupp` not `direct_sum`, the types are defeq. -/
 noncomputable def basis {η : ι → Type _} (b : ∀ i, Basis (η i) R (M i)) :
-    Basis (Σi, η i) R (Π₀ i, M i) :=
+    Basis (Σ i, η i) R (Π₀ i, M i) :=
   Basis.ofRepr
     ((mapRange.linearEquiv fun i => (b i).repr).trans (sigmaFinsuppLequivDfinsupp R).symm)
 #align dfinsupp.basis Dfinsupp.basis
@@ -384,14 +384,14 @@ theorem mem_iSup_finset_iff_exists_sum {s : Finset ι} (p : ι → Submodule R N
         rw [mem_support_iff, not_ne_iff]
         ext; rw [coe_zero, ← mem_bot R]; convert coe_mem (μ x)
         symm; exact iSup_neg hx
-      · intro x _ hx; rw [mem_support_iff, not_ne_iff] at hx; rw [hx]; rfl
+      · intro x _ hx; rw [mem_support_iff, not_ne_iff] at hx ; rw [hx]; rfl
     · refine' ⟨Dfinsupp.mk s _, _⟩
       · rintro ⟨i, hi⟩; refine' ⟨μ i, _⟩
         rw [iSup_pos]; · exact coe_mem _; · exact hi
       simp only [Dfinsupp.sum]
       rw [Finset.sum_subset support_mk_subset, ← hμ]
       exact Finset.sum_congr rfl fun x hx => congr_arg coe <| mk_of_mem hx
-      · intro x _ hx; rw [mem_support_iff, not_ne_iff] at hx; rw [hx]; rfl
+      · intro x _ hx; rw [mem_support_iff, not_ne_iff] at hx ; rw [hx]; rfl
 #align submodule.mem_supr_finset_iff_exists_sum Submodule.mem_iSup_finset_iff_exists_sum
 
 end Submodule
@@ -482,12 +482,12 @@ theorem Independent.dfinsupp_lsum_injective {p : ι → Submodule R N} (h : Inde
     Function.Injective (lsum ℕ fun i => (p i).Subtype) :=
   by
   -- simplify everything down to binders over equalities in `N`
-  rw [independent_iff_forall_dfinsupp] at h
+  rw [independent_iff_forall_dfinsupp] at h 
   suffices (lsum ℕ fun i => (p i).Subtype).ker = ⊥
     by
     -- Lean can't find this without our help
     letI : AddCommGroup (Π₀ i, p i) := @Dfinsupp.addCommGroup _ (fun i => p i) _
-    rw [LinearMap.ker_eq_bot] at this; exact this
+    rw [LinearMap.ker_eq_bot] at this ; exact this
   rw [LinearMap.ker_eq_bot']
   intro m hm
   ext i : 1
@@ -495,7 +495,7 @@ theorem Independent.dfinsupp_lsum_injective {p : ι → Submodule R N} (h : Inde
   rw [Dfinsupp.zero_apply, ← neg_eq_zero]
   refine' h i (-m i) m _
   rwa [← erase_add_single i m, LinearMap.map_add, lsum_single, Submodule.subtype_apply,
-    add_eq_zero_iff_eq_neg, ← Submodule.coe_neg] at hm
+    add_eq_zero_iff_eq_neg, ← Submodule.coe_neg] at hm 
 #align complete_lattice.independent.dfinsupp_lsum_injective CompleteLattice.Independent.dfinsupp_lsum_injective
 
 /-- The canonical map out of a direct sum of a family of additive subgroups is injective when the
@@ -503,7 +503,7 @@ additive subgroups are `complete_lattice.independent`. -/
 theorem Independent.dfinsupp_sumAddHom_injective {p : ι → AddSubgroup N} (h : Independent p) :
     Function.Injective (sumAddHom fun i => (p i).Subtype) :=
   by
-  rw [← independent_map_order_iso_iff (AddSubgroup.toIntSubmodule : AddSubgroup N ≃o _)] at h
+  rw [← independent_map_order_iso_iff (AddSubgroup.toIntSubmodule : AddSubgroup N ≃o _)] at h 
   exact h.dfinsupp_lsum_injective
 #align complete_lattice.independent.dfinsupp_sum_add_hom_injective CompleteLattice.Independent.dfinsupp_sumAddHom_injective
 
@@ -541,7 +541,7 @@ theorem Independent.linearIndependent [NoZeroSMulDivisors R N] (p : ι → Submo
         l.to_dfinsupp
     have ha : a = 0 := by
       apply hp.dfinsupp_lsum_injective
-      rwa [← lsum_comp_map_range_to_span_singleton _ hv] at hl
+      rwa [← lsum_comp_map_range_to_span_singleton _ hv] at hl 
     ext i
     apply smul_left_injective R (hv' i)
     have : l i • v i = a i := rfl

f4758115

bump to nightly-2023-05-28-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

8d353152

Diff

@@ -369,7 +369,7 @@ theorem mem_biSup_iff_exists_dfinsupp (p : ι → Prop) [DecidablePred p] (S : 
   SetLike.ext_iff.mp (biSup_eq_range_dfinsupp_lsum p S) x
 #align submodule.mem_bsupr_iff_exists_dfinsupp Submodule.mem_biSup_iff_exists_dfinsupp
 
-open BigOperators
+open scoped BigOperators
 
 omit dec_ι

f4758115

bump to nightly-2023-05-28-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

ba5d8b97

Diff

@@ -53,9 +53,6 @@ variable [AddCommMonoid N] [Module R N]
 
 include dec_ι
 
-/- warning: dfinsupp.lmk -> Dfinsupp.lmk is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align dfinsupp.lmk Dfinsupp.lmkₓ'. -/
 /-- `dfinsupp.mk` as a `linear_map`. -/
 def lmk (s : Finset ι) : (∀ i : (↑s : Set ι), M i) →ₗ[R] Π₀ i, M i
     where
@@ -64,12 +61,6 @@ def lmk (s : Finset ι) : (∀ i : (↑s : Set ι), M i) →ₗ[R] Π₀ i, M i
   map_smul' c x := mk_smul c x
 #align dfinsupp.lmk Dfinsupp.lmk
 
-/- warning: dfinsupp.lsingle -> Dfinsupp.lsingle is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align dfinsupp.lsingle Dfinsupp.lsingleₓ'. -/
 /-- `dfinsupp.single` as a `linear_map` -/
 def lsingle (i) : M i →ₗ[R] Π₀ i, M i :=
   { Dfinsupp.singleAddHom _ _ with
@@ -77,17 +68,11 @@ def lsingle (i) : M i →ₗ[R] Π₀ i, M i :=
     map_smul' := single_smul }
 #align dfinsupp.lsingle Dfinsupp.lsingle
 
-/- warning: dfinsupp.lhom_ext -> Dfinsupp.lhom_ext is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align dfinsupp.lhom_ext Dfinsupp.lhom_extₓ'. -/
 /-- Two `R`-linear maps from `Π₀ i, M i` which agree on each `single i x` agree everywhere. -/
 theorem lhom_ext ⦃φ ψ : (Π₀ i, M i) →ₗ[R] N⦄ (h : ∀ i x, φ (single i x) = ψ (single i x)) : φ = ψ :=
   LinearMap.toAddMonoidHom_injective <| addHom_ext h
 #align dfinsupp.lhom_ext Dfinsupp.lhom_ext
 
-/- warning: dfinsupp.lhom_ext' -> Dfinsupp.lhom_ext' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align dfinsupp.lhom_ext' Dfinsupp.lhom_ext'ₓ'. -/
 /-- Two `R`-linear maps from `Π₀ i, M i` which agree on each `single i x` agree everywhere.
 
 See note [partially-applied ext lemmas].
@@ -100,12 +85,6 @@ theorem lhom_ext' ⦃φ ψ : (Π₀ i, M i) →ₗ[R] N⦄ (h : ∀ i, φ.comp (
 
 omit dec_ι
 
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-Case conversion may be inaccurate. Consider using '#align dfinsupp.lapply Dfinsupp.lapplyₓ'. -/
 /-- Interpret `λ (f : Π₀ i, M i), f i` as a linear map. -/
 def lapply (i : ι) : (Π₀ i, M i) →ₗ[R] M i
     where
@@ -116,20 +95,11 @@ def lapply (i : ι) : (Π₀ i, M i) →ₗ[R] M i
 
 include dec_ι
 
-/- warning: dfinsupp.lmk_apply -> Dfinsupp.lmk_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align dfinsupp.lmk_apply Dfinsupp.lmk_applyₓ'. -/
 @[simp]
 theorem lmk_apply (s : Finset ι) (x) : (lmk s : _ →ₗ[R] Π₀ i, M i) x = mk s x :=
   rfl
 #align dfinsupp.lmk_apply Dfinsupp.lmk_apply
 
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-Case conversion may be inaccurate. Consider using '#align dfinsupp.lsingle_apply Dfinsupp.lsingle_applyₓ'. -/
 @[simp]
 theorem lsingle_apply (i : ι) (x : M i) : (lsingle i : _ →ₗ[R] _) x = single i x :=
   rfl
@@ -137,12 +107,6 @@ theorem lsingle_apply (i : ι) (x : M i) : (lsingle i : _ →ₗ[R] _) x = singl
 
 omit dec_ι
 
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 @[simp]
 theorem lapply_apply (i : ι) (f : Π₀ i, M i) : (lapply i : _ →ₗ[R] _) f = f i :=
   rfl
@@ -150,12 +114,6 @@ theorem lapply_apply (i : ι) (f : Π₀ i, M i) : (lapply i : _ →ₗ[R] _) f
 
 section Lsum
 
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 /-- Typeclass inference can't find `dfinsupp.add_comm_monoid` without help for this case.
 This instance allows it to be found where it is needed on the LHS of the colon in
 `dfinsupp.module_of_linear_map`. -/
@@ -163,12 +121,6 @@ instance addCommMonoidOfLinearMap : AddCommMonoid (Π₀ i : ι, M i →ₗ[R] N
   @Dfinsupp.addCommMonoid _ (fun i => M i →ₗ[R] N) _
 #align dfinsupp.add_comm_monoid_of_linear_map Dfinsupp.addCommMonoidOfLinearMap
 
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 /-- Typeclass inference can't find `dfinsupp.module` without help for this case.
 This is needed to define `dfinsupp.lsum` below.
 
@@ -184,9 +136,6 @@ variable (S)
 
 include dec_ι
 
-/- warning: dfinsupp.lsum -> Dfinsupp.lsum is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align dfinsupp.lsum Dfinsupp.lsumₓ'. -/
 /-- The `dfinsupp` version of `finsupp.lsum`.
 
 See note [bundled maps over different rings] for why separate `R` and `S` semirings are used. -/
@@ -212,9 +161,6 @@ def lsum [Semiring S] [Module S N] [SMulCommClass R S N] :
   map_smul' c F := by ext; simp
 #align dfinsupp.lsum Dfinsupp.lsum
 
-/- warning: dfinsupp.lsum_single -> Dfinsupp.lsum_single is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align dfinsupp.lsum_single Dfinsupp.lsum_singleₓ'. -/
 /-- While `simp` can prove this, it is often convenient to avoid unfolding `lsum` into `sum_add_hom`
 with `dfinsupp.lsum_apply_apply`. -/
 theorem lsum_single [Semiring S] [Module S N] [SMulCommClass R S N] (F : ∀ i, M i →ₗ[R] N) (i)
@@ -238,9 +184,6 @@ variable [∀ i, AddCommMonoid (β i)] [∀ i, AddCommMonoid (β₁ i)] [∀ i,
 
 variable [∀ i, Module R (β i)] [∀ i, Module R (β₁ i)] [∀ i, Module R (β₂ i)]
 
-/- warning: dfinsupp.map_range_smul -> Dfinsupp.mapRange_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align dfinsupp.map_range_smul Dfinsupp.mapRange_smulₓ'. -/
 theorem mapRange_smul (f : ∀ i, β₁ i → β₂ i) (hf : ∀ i, f i 0 = 0) (r : R)
     (hf' : ∀ i x, f i (r • x) = r • f i x) (g : Π₀ i, β₁ i) :
     mapRange f hf (r • g) = r • mapRange f hf g :=
@@ -249,12 +192,6 @@ theorem mapRange_smul (f : ∀ i, β₁ i → β₂ i) (hf : ∀ i, f i 0 = 0) (
   simp only [map_range_apply f, coe_smul, Pi.smul_apply, hf']
 #align dfinsupp.map_range_smul Dfinsupp.mapRange_smul
 
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-Case conversion may be inaccurate. Consider using '#align dfinsupp.map_range.linear_map Dfinsupp.mapRange.linearMapₓ'. -/
 /-- `dfinsupp.map_range` as an `linear_map`. -/
 @[simps apply]
 def mapRange.linearMap (f : ∀ i, β₁ i →ₗ[R] β₂ i) : (Π₀ i, β₁ i) →ₗ[R] Π₀ i, β₂ i :=
@@ -265,21 +202,12 @@ def mapRange.linearMap (f : ∀ i, β₁ i →ₗ[R] β₂ i) : (Π₀ i, β₁
     map_smul' := fun r => mapRange_smul _ _ _ fun i => (f i).map_smul r }
 #align dfinsupp.map_range.linear_map Dfinsupp.mapRange.linearMap
 
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-Case conversion may be inaccurate. Consider using '#align dfinsupp.map_range.linear_map_id Dfinsupp.mapRange.linearMap_idₓ'. -/
 @[simp]
 theorem mapRange.linearMap_id :
     (mapRange.linearMap fun i => (LinearMap.id : β₂ i →ₗ[R] _)) = LinearMap.id :=
   LinearMap.ext mapRange_id
 #align dfinsupp.map_range.linear_map_id Dfinsupp.mapRange.linearMap_id
 
-/- warning: dfinsupp.map_range.linear_map_comp -> Dfinsupp.mapRange.linearMap_comp is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align dfinsupp.map_range.linear_map_comp Dfinsupp.mapRange.linearMap_compₓ'. -/
 theorem mapRange.linearMap_comp (f : ∀ i, β₁ i →ₗ[R] β₂ i) (f₂ : ∀ i, β i →ₗ[R] β₁ i) :
     (mapRange.linearMap fun i => (f i).comp (f₂ i)) =
       (mapRange.linearMap f).comp (mapRange.linearMap f₂) :=
@@ -288,9 +216,6 @@ theorem mapRange.linearMap_comp (f : ∀ i, β₁ i →ₗ[R] β₂ i) (f₂ : 
 
 include dec_ι
 
-/- warning: dfinsupp.sum_map_range_index.linear_map -> Dfinsupp.sum_mapRange_index.linearMap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align dfinsupp.sum_map_range_index.linear_map Dfinsupp.sum_mapRange_index.linearMapₓ'. -/
 theorem sum_mapRange_index.linearMap [∀ (i : ι) (x : β₁ i), Decidable (x ≠ 0)]
     [∀ (i : ι) (x : β₂ i), Decidable (x ≠ 0)] {f : ∀ i, β₁ i →ₗ[R] β₂ i} {h : ∀ i, β₂ i →ₗ[R] N}
     {l : Π₀ i, β₁ i} :
@@ -302,12 +227,6 @@ theorem sum_mapRange_index.linearMap [∀ (i : ι) (x : β₁ i), Decidable (x 
 
 omit dec_ι
 
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-Case conversion may be inaccurate. Consider using '#align dfinsupp.map_range.linear_equiv Dfinsupp.mapRange.linearEquivₓ'. -/
 /-- `dfinsupp.map_range.linear_map` as an `linear_equiv`. -/
 @[simps apply]
 def mapRange.linearEquiv (e : ∀ i, β₁ i ≃ₗ[R] β₂ i) : (Π₀ i, β₁ i) ≃ₗ[R] Π₀ i, β₂ i :=
@@ -318,30 +237,18 @@ def mapRange.linearEquiv (e : ∀ i, β₁ i ≃ₗ[R] β₂ i) : (Π₀ i, β
     invFun := mapRange (fun i x => (e i).symm x) fun i => (e i).symm.map_zero }
 #align dfinsupp.map_range.linear_equiv Dfinsupp.mapRange.linearEquiv
 
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 @[simp]
 theorem mapRange.linearEquiv_refl :
     (mapRange.linearEquiv fun i => LinearEquiv.refl R (β₁ i)) = LinearEquiv.refl _ _ :=
   LinearEquiv.ext mapRange_id
 #align dfinsupp.map_range.linear_equiv_refl Dfinsupp.mapRange.linearEquiv_refl
 
-/- warning: dfinsupp.map_range.linear_equiv_trans -> Dfinsupp.mapRange.linearEquiv_trans is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align dfinsupp.map_range.linear_equiv_trans Dfinsupp.mapRange.linearEquiv_transₓ'. -/
 theorem mapRange.linearEquiv_trans (f : ∀ i, β i ≃ₗ[R] β₁ i) (f₂ : ∀ i, β₁ i ≃ₗ[R] β₂ i) :
     (mapRange.linearEquiv fun i => (f i).trans (f₂ i)) =
       (mapRange.linearEquiv f).trans (mapRange.linearEquiv f₂) :=
   LinearEquiv.ext <| mapRange_comp (fun i x => f₂ i x) (fun i x => f i x) _ _ _
 #align dfinsupp.map_range.linear_equiv_trans Dfinsupp.mapRange.linearEquiv_trans
 
-/- warning: dfinsupp.map_range.linear_equiv_symm -> Dfinsupp.mapRange.linearEquiv_symm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align dfinsupp.map_range.linear_equiv_symm Dfinsupp.mapRange.linearEquiv_symmₓ'. -/
 @[simp]
 theorem mapRange.linearEquiv_symm (e : ∀ i, β₁ i ≃ₗ[R] β₂ i) :
     (mapRange.linearEquiv e).symm = mapRange.linearEquiv fun i => (e i).symm :=
@@ -354,12 +261,6 @@ section CoprodMap
 
 variable [DecidableEq ι] [∀ x : N, Decidable (x ≠ 0)]
 
-/- warning: dfinsupp.coprod_map -> Dfinsupp.coprodMap is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align dfinsupp.coprod_map Dfinsupp.coprodMapₓ'. -/
 /-- Given a family of linear maps `f i : M i  →ₗ[R] N`, we can form a linear map
 `(Π₀ i, M i) →ₗ[R] N` which sends `x : Π₀ i, M i` to the sum over `i` of `f i` applied to `x i`.
 This is the map coming from the universal property of `Π₀ i, M i` as the coproduct of the `M i`.
@@ -369,9 +270,6 @@ noncomputable def coprodMap (f : ∀ i : ι, M i →ₗ[R] N) : (Π₀ i, M i) 
     (@finsuppLequivDfinsupp ι R N _ _ _ _ _).symm.toLinearMap ∘ₗ Dfinsupp.mapRange.linearMap f
 #align dfinsupp.coprod_map Dfinsupp.coprodMap
 
-/- warning: dfinsupp.coprod_map_apply -> Dfinsupp.coprodMap_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align dfinsupp.coprod_map_apply Dfinsupp.coprodMap_applyₓ'. -/
 theorem coprodMap_apply (f : ∀ i : ι, M i →ₗ[R] N) (x : Π₀ i, M i) :
     coprodMap f x =
       Finsupp.sum (mapRange (fun i => f i) (fun i => LinearMap.map_zero _) x).toFinsupp fun i =>
@@ -383,12 +281,6 @@ end CoprodMap
 
 section Basis
 
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-Case conversion may be inaccurate. Consider using '#align dfinsupp.basis Dfinsupp.basisₓ'. -/
 /-- The direct sum of free modules is free.
 
 Note that while this is stated for `dfinsupp` not `direct_sum`, the types are defeq. -/
@@ -410,27 +302,18 @@ variable [Semiring R] [AddCommMonoid N] [Module R N]
 
 open Dfinsupp
 
-/- warning: submodule.dfinsupp_sum_mem -> Submodule.dfinsupp_sum_mem is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.dfinsupp_sum_mem Submodule.dfinsupp_sum_memₓ'. -/
 theorem dfinsupp_sum_mem {β : ι → Type _} [∀ i, Zero (β i)] [∀ (i) (x : β i), Decidable (x ≠ 0)]
     (S : Submodule R N) (f : Π₀ i, β i) (g : ∀ i, β i → N) (h : ∀ c, f c ≠ 0 → g c (f c) ∈ S) :
     f.Sum g ∈ S :=
   dfinsupp_sum_mem S f g h
 #align submodule.dfinsupp_sum_mem Submodule.dfinsupp_sum_mem
 
-/- warning: submodule.dfinsupp_sum_add_hom_mem -> Submodule.dfinsupp_sumAddHom_mem is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.dfinsupp_sum_add_hom_mem Submodule.dfinsupp_sumAddHom_memₓ'. -/
 theorem dfinsupp_sumAddHom_mem {β : ι → Type _} [∀ i, AddZeroClass (β i)] (S : Submodule R N)
     (f : Π₀ i, β i) (g : ∀ i, β i →+ N) (h : ∀ c, f c ≠ 0 → g c (f c) ∈ S) :
     Dfinsupp.sumAddHom g f ∈ S :=
   dfinsupp_sumAddHom_mem S f g h
 #align submodule.dfinsupp_sum_add_hom_mem Submodule.dfinsupp_sumAddHom_mem
 
-/- warning: submodule.supr_eq_range_dfinsupp_lsum -> Submodule.iSup_eq_range_dfinsupp_lsum is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.supr_eq_range_dfinsupp_lsum Submodule.iSup_eq_range_dfinsupp_lsumₓ'. -/
 /-- The supremum of a family of submodules is equal to the range of `dfinsupp.lsum`; that is
 every element in the `supr` can be produced from taking a finite number of non-zero elements
 of `p i`, coercing them to `N`, and summing them. -/
@@ -445,9 +328,6 @@ theorem iSup_eq_range_dfinsupp_lsum (p : ι → Submodule R N) :
     exact dfinsupp_sumAddHom_mem _ v _ fun i _ => (le_iSup p i : p i ≤ _) (v i).Prop
 #align submodule.supr_eq_range_dfinsupp_lsum Submodule.iSup_eq_range_dfinsupp_lsum
 
-/- warning: submodule.bsupr_eq_range_dfinsupp_lsum -> Submodule.biSup_eq_range_dfinsupp_lsum is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.bsupr_eq_range_dfinsupp_lsum Submodule.biSup_eq_range_dfinsupp_lsumₓ'. -/
 /-- The bounded supremum of a family of commutative additive submonoids is equal to the range of
 `dfinsupp.sum_add_hom` composed with `dfinsupp.filter_add_monoid_hom`; that is, every element in the
 bounded `supr` can be produced from taking a finite number of non-zero elements from the `S i` that
@@ -468,17 +348,11 @@ theorem biSup_eq_range_dfinsupp_lsum (p : ι → Prop) [DecidablePred p] (S : ι
     · simp [hp]
 #align submodule.bsupr_eq_range_dfinsupp_lsum Submodule.biSup_eq_range_dfinsupp_lsum
 
-/- warning: submodule.mem_supr_iff_exists_dfinsupp -> Submodule.mem_iSup_iff_exists_dfinsupp is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_iff_exists_dfinsupp Submodule.mem_iSup_iff_exists_dfinsuppₓ'. -/
 theorem mem_iSup_iff_exists_dfinsupp (p : ι → Submodule R N) (x : N) :
     x ∈ iSup p ↔ ∃ f : Π₀ i, p i, Dfinsupp.lsum ℕ (fun i => (p i).Subtype) f = x :=
   SetLike.ext_iff.mp (iSup_eq_range_dfinsupp_lsum p) x
 #align submodule.mem_supr_iff_exists_dfinsupp Submodule.mem_iSup_iff_exists_dfinsupp
 
-/- warning: submodule.mem_supr_iff_exists_dfinsupp' -> Submodule.mem_iSup_iff_exists_dfinsupp' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_iff_exists_dfinsupp' Submodule.mem_iSup_iff_exists_dfinsupp'ₓ'. -/
 /-- A variant of `submodule.mem_supr_iff_exists_dfinsupp` with the RHS fully unfolded. -/
 theorem mem_iSup_iff_exists_dfinsupp' (p : ι → Submodule R N) [∀ (i) (x : p i), Decidable (x ≠ 0)]
     (x : N) : x ∈ iSup p ↔ ∃ f : Π₀ i, p i, (f.Sum fun i xi => ↑xi) = x :=
@@ -488,9 +362,6 @@ theorem mem_iSup_iff_exists_dfinsupp' (p : ι → Submodule R N) [∀ (i) (x : p
   congr
 #align submodule.mem_supr_iff_exists_dfinsupp' Submodule.mem_iSup_iff_exists_dfinsupp'
 
-/- warning: submodule.mem_bsupr_iff_exists_dfinsupp -> Submodule.mem_biSup_iff_exists_dfinsupp is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.mem_bsupr_iff_exists_dfinsupp Submodule.mem_biSup_iff_exists_dfinsuppₓ'. -/
 theorem mem_biSup_iff_exists_dfinsupp (p : ι → Prop) [DecidablePred p] (S : ι → Submodule R N)
     (x : N) :
     (x ∈ ⨆ (i) (h : p i), S i) ↔
@@ -502,9 +373,6 @@ open BigOperators
 
 omit dec_ι
 
-/- warning: submodule.mem_supr_finset_iff_exists_sum -> Submodule.mem_iSup_finset_iff_exists_sum is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_finset_iff_exists_sum Submodule.mem_iSup_finset_iff_exists_sumₓ'. -/
 theorem mem_iSup_finset_iff_exists_sum {s : Finset ι} (p : ι → Submodule R N) (a : N) :
     (a ∈ ⨆ i ∈ s, p i) ↔ ∃ μ : ∀ i, p i, (∑ i in s, (μ i : N)) = a := by
   classical
@@ -536,9 +404,6 @@ section Semiring
 
 variable [Semiring R] [AddCommMonoid N] [Module R N]
 
-/- warning: complete_lattice.independent_iff_forall_dfinsupp -> CompleteLattice.independent_iff_forall_dfinsupp is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align complete_lattice.independent_iff_forall_dfinsupp CompleteLattice.independent_iff_forall_dfinsuppₓ'. -/
 /-- Independence of a family of submodules can be expressed as a quantifier over `dfinsupp`s.
 
 This is an intermediate result used to prove
@@ -557,9 +422,6 @@ theorem independent_iff_forall_dfinsupp (p : ι → Submodule R N) :
   rfl
 #align complete_lattice.independent_iff_forall_dfinsupp CompleteLattice.independent_iff_forall_dfinsupp
 
-/- warning: complete_lattice.independent_of_dfinsupp_lsum_injective -> CompleteLattice.independent_of_dfinsupp_lsum_injective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align complete_lattice.independent_of_dfinsupp_lsum_injective CompleteLattice.independent_of_dfinsupp_lsum_injectiveₓ'. -/
 /- If `dfinsupp.lsum` applied with `submodule.subtype` is injective then the submodules are
 independent. -/
 theorem independent_of_dfinsupp_lsum_injective (p : ι → Submodule R N)
@@ -574,9 +436,6 @@ theorem independent_of_dfinsupp_lsum_injective (p : ι → Submodule R N)
   simpa [eq_comm] using this
 #align complete_lattice.independent_of_dfinsupp_lsum_injective CompleteLattice.independent_of_dfinsupp_lsum_injective
 
-/- warning: complete_lattice.independent_of_dfinsupp_sum_add_hom_injective -> CompleteLattice.independent_of_dfinsupp_sumAddHom_injective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align complete_lattice.independent_of_dfinsupp_sum_add_hom_injective CompleteLattice.independent_of_dfinsupp_sumAddHom_injectiveₓ'. -/
 /- If `dfinsupp.sum_add_hom` applied with `add_submonoid.subtype` is injective then the additive
 submonoids are independent. -/
 theorem independent_of_dfinsupp_sumAddHom_injective (p : ι → AddSubmonoid N)
@@ -586,9 +445,6 @@ theorem independent_of_dfinsupp_sumAddHom_injective (p : ι → AddSubmonoid N)
   exact independent_of_dfinsupp_lsum_injective _ h
 #align complete_lattice.independent_of_dfinsupp_sum_add_hom_injective CompleteLattice.independent_of_dfinsupp_sumAddHom_injective
 
-/- warning: complete_lattice.lsum_comp_map_range_to_span_singleton -> CompleteLattice.lsum_comp_mapRange_toSpanSingleton is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align complete_lattice.lsum_comp_map_range_to_span_singleton CompleteLattice.lsum_comp_mapRange_toSpanSingletonₓ'. -/
 /-- Combining `dfinsupp.lsum` with `linear_map.to_span_singleton` is the same as `finsupp.total` -/
 theorem lsum_comp_mapRange_toSpanSingleton [∀ m : R, Decidable (m ≠ 0)] (p : ι → Submodule R N)
     {v : ι → N} (hv : ∀ i : ι, v i ∈ p i) :
@@ -606,9 +462,6 @@ section Ring
 
 variable [Ring R] [AddCommGroup N] [Module R N]
 
-/- warning: complete_lattice.independent_of_dfinsupp_sum_add_hom_injective' -> CompleteLattice.independent_of_dfinsupp_sumAddHom_injective' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align complete_lattice.independent_of_dfinsupp_sum_add_hom_injective' CompleteLattice.independent_of_dfinsupp_sumAddHom_injective'ₓ'. -/
 /- If `dfinsupp.sum_add_hom` applied with `add_submonoid.subtype` is injective then the additive
 subgroups are independent. -/
 theorem independent_of_dfinsupp_sumAddHom_injective' (p : ι → AddSubgroup N)
@@ -618,9 +471,6 @@ theorem independent_of_dfinsupp_sumAddHom_injective' (p : ι → AddSubgroup N)
   exact independent_of_dfinsupp_lsum_injective _ h
 #align complete_lattice.independent_of_dfinsupp_sum_add_hom_injective' CompleteLattice.independent_of_dfinsupp_sumAddHom_injective'
 
-/- warning: complete_lattice.independent.dfinsupp_lsum_injective -> CompleteLattice.Independent.dfinsupp_lsum_injective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align complete_lattice.independent.dfinsupp_lsum_injective CompleteLattice.Independent.dfinsupp_lsum_injectiveₓ'. -/
 /-- The canonical map out of a direct sum of a family of submodules is injective when the submodules
 are `complete_lattice.independent`.
 
@@ -648,9 +498,6 @@ theorem Independent.dfinsupp_lsum_injective {p : ι → Submodule R N} (h : Inde
     add_eq_zero_iff_eq_neg, ← Submodule.coe_neg] at hm
 #align complete_lattice.independent.dfinsupp_lsum_injective CompleteLattice.Independent.dfinsupp_lsum_injective
 
-/- warning: complete_lattice.independent.dfinsupp_sum_add_hom_injective -> CompleteLattice.Independent.dfinsupp_sumAddHom_injective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align complete_lattice.independent.dfinsupp_sum_add_hom_injective CompleteLattice.Independent.dfinsupp_sumAddHom_injectiveₓ'. -/
 /-- The canonical map out of a direct sum of a family of additive subgroups is injective when the
 additive subgroups are `complete_lattice.independent`. -/
 theorem Independent.dfinsupp_sumAddHom_injective {p : ι → AddSubgroup N} (h : Independent p) :
@@ -660,9 +507,6 @@ theorem Independent.dfinsupp_sumAddHom_injective {p : ι → AddSubgroup N} (h :
   exact h.dfinsupp_lsum_injective
 #align complete_lattice.independent.dfinsupp_sum_add_hom_injective CompleteLattice.Independent.dfinsupp_sumAddHom_injective
 
-/- warning: complete_lattice.independent_iff_dfinsupp_lsum_injective -> CompleteLattice.independent_iff_dfinsupp_lsum_injective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align complete_lattice.independent_iff_dfinsupp_lsum_injective CompleteLattice.independent_iff_dfinsupp_lsum_injectiveₓ'. -/
 /-- A family of submodules over an additive group are independent if and only iff `dfinsupp.lsum`
 applied with `submodule.subtype` is injective.
 
@@ -673,9 +517,6 @@ theorem independent_iff_dfinsupp_lsum_injective (p : ι → Submodule R N) :
   ⟨Independent.dfinsupp_lsum_injective, independent_of_dfinsupp_lsum_injective p⟩
 #align complete_lattice.independent_iff_dfinsupp_lsum_injective CompleteLattice.independent_iff_dfinsupp_lsum_injective
 
-/- warning: complete_lattice.independent_iff_dfinsupp_sum_add_hom_injective -> CompleteLattice.independent_iff_dfinsupp_sumAddHom_injective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align complete_lattice.independent_iff_dfinsupp_sum_add_hom_injective CompleteLattice.independent_iff_dfinsupp_sumAddHom_injectiveₓ'. -/
 /-- A family of additive subgroups over an additive group are independent if and only if
 `dfinsupp.sum_add_hom` applied with `add_subgroup.subtype` is injective. -/
 theorem independent_iff_dfinsupp_sumAddHom_injective (p : ι → AddSubgroup N) :
@@ -685,12 +526,6 @@ theorem independent_iff_dfinsupp_sumAddHom_injective (p : ι → AddSubgroup N)
 
 omit dec_ι
 
-/- warning: complete_lattice.independent.linear_independent -> CompleteLattice.Independent.linearIndependent is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align complete_lattice.independent.linear_independent CompleteLattice.Independent.linearIndependentₓ'. -/
 /-- If a family of submodules is `independent`, then a choice of nonzero vector from each submodule
 forms a linearly independent family.
 
@@ -713,12 +548,6 @@ theorem Independent.linearIndependent [NoZeroSMulDivisors R N] (p : ι → Submo
     simp [this, ha]
 #align complete_lattice.independent.linear_independent CompleteLattice.Independent.linearIndependent
 
-/- warning: complete_lattice.independent_iff_linear_independent_of_ne_zero -> CompleteLattice.independent_iff_linearIndependent_of_ne_zero is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align complete_lattice.independent_iff_linear_independent_of_ne_zero CompleteLattice.independent_iff_linearIndependent_of_ne_zeroₓ'. -/
 theorem independent_iff_linearIndependent_of_ne_zero [NoZeroSMulDivisors R N] {v : ι → N}
     (h_ne_zero : ∀ i, v i ≠ 0) : (Independent fun i => R ∙ v i) ↔ LinearIndependent R v :=
   ⟨fun hv => hv.LinearIndependent _ (fun i => Submodule.mem_span_singleton_self <| v i) h_ne_zero,

f4758115

bump to nightly-2023-05-28-04

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

6797a637

Diff

@@ -206,18 +206,10 @@ def lsum [Semiring S] [Module S N] [SMulCommClass R S N] :
             sum_add_hom_single, sum_add_hom_single, LinearMap.toAddMonoidHom_coe,
             LinearMap.map_smul] }
   invFun F i := F.comp (lsingle i)
-  left_inv F := by
-    ext (x y)
-    simp
-  right_inv F := by
-    ext (x y)
-    simp
-  map_add' F G := by
-    ext (x y)
-    simp
-  map_smul' c F := by
-    ext
-    simp
+  left_inv F := by ext (x y); simp
+  right_inv F := by ext (x y); simp
+  map_add' F G := by ext (x y); simp
+  map_smul' c F := by ext; simp
 #align dfinsupp.lsum Dfinsupp.lsum
 
 /- warning: dfinsupp.lsum_single -> Dfinsupp.lsum_single is a dubious translation:
@@ -519,35 +511,19 @@ theorem mem_iSup_finset_iff_exists_sum {s : Finset ι} (p : ι → Submodule R N
     rw [Submodule.mem_iSup_iff_exists_dfinsupp']
     constructor <;> rintro ⟨μ, hμ⟩
     · use fun i => ⟨μ i, (iSup_const_le : _ ≤ p i) (coe_mem <| μ i)⟩
-      rw [← hμ]
-      symm
-      apply Finset.sum_subset
-      · intro x
-        contrapose
-        intro hx
+      rw [← hμ]; symm; apply Finset.sum_subset
+      · intro x; contrapose; intro hx
         rw [mem_support_iff, not_ne_iff]
-        ext
-        rw [coe_zero, ← mem_bot R]
-        convert coe_mem (μ x)
-        symm
-        exact iSup_neg hx
-      · intro x _ hx
-        rw [mem_support_iff, not_ne_iff] at hx
-        rw [hx]
-        rfl
+        ext; rw [coe_zero, ← mem_bot R]; convert coe_mem (μ x)
+        symm; exact iSup_neg hx
+      · intro x _ hx; rw [mem_support_iff, not_ne_iff] at hx; rw [hx]; rfl
     · refine' ⟨Dfinsupp.mk s _, _⟩
-      · rintro ⟨i, hi⟩
-        refine' ⟨μ i, _⟩
-        rw [iSup_pos]
-        · exact coe_mem _
-        · exact hi
+      · rintro ⟨i, hi⟩; refine' ⟨μ i, _⟩
+        rw [iSup_pos]; · exact coe_mem _; · exact hi
       simp only [Dfinsupp.sum]
       rw [Finset.sum_subset support_mk_subset, ← hμ]
       exact Finset.sum_congr rfl fun x hx => congr_arg coe <| mk_of_mem hx
-      · intro x _ hx
-        rw [mem_support_iff, not_ne_iff] at hx
-        rw [hx]
-        rfl
+      · intro x _ hx; rw [mem_support_iff, not_ne_iff] at hx; rw [hx]; rfl
 #align submodule.mem_supr_finset_iff_exists_sum Submodule.mem_iSup_finset_iff_exists_sum
 
 end Submodule
@@ -621,9 +597,7 @@ theorem lsum_comp_mapRange_toSpanSingleton [∀ m : R, Decidable (m ≠ 0)] (p :
               _ →ₗ[R] _).comp
           (finsuppLequivDfinsupp R : (ι →₀ R) ≃ₗ[R] _).toLinearMap) =
       Finsupp.total ι N R v :=
-  by
-  ext
-  simp
+  by ext; simp
 #align complete_lattice.lsum_comp_map_range_to_span_singleton CompleteLattice.lsum_comp_mapRange_toSpanSingleton
 
 end Semiring
@@ -663,8 +637,7 @@ theorem Independent.dfinsupp_lsum_injective {p : ι → Submodule R N} (h : Inde
     by
     -- Lean can't find this without our help
     letI : AddCommGroup (Π₀ i, p i) := @Dfinsupp.addCommGroup _ (fun i => p i) _
-    rw [LinearMap.ker_eq_bot] at this
-    exact this
+    rw [LinearMap.ker_eq_bot] at this; exact this
   rw [LinearMap.ker_eq_bot']
   intro m hm
   ext i : 1

f4758115

bump to nightly-2023-05-28-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

6c6011cf

Diff

@@ -54,10 +54,7 @@ variable [AddCommMonoid N] [Module R N]
 include dec_ι
 
 /- warning: dfinsupp.lmk -> Dfinsupp.lmk is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align dfinsupp.lmk Dfinsupp.lmkₓ'. -/
 /-- `dfinsupp.mk` as a `linear_map`. -/
 def lmk (s : Finset ι) : (∀ i : (↑s : Set ι), M i) →ₗ[R] Π₀ i, M i
@@ -81,10 +78,7 @@ def lsingle (i) : M i →ₗ[R] Π₀ i, M i :=
 #align dfinsupp.lsingle Dfinsupp.lsingle
 
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 Case conversion may be inaccurate. Consider using '#align dfinsupp.lhom_ext Dfinsupp.lhom_extₓ'. -/
 /-- Two `R`-linear maps from `Π₀ i, M i` which agree on each `single i x` agree everywhere. -/
 theorem lhom_ext ⦃φ ψ : (Π₀ i, M i) →ₗ[R] N⦄ (h : ∀ i x, φ (single i x) = ψ (single i x)) : φ = ψ :=
@@ -92,10 +86,7 @@ theorem lhom_ext ⦃φ ψ : (Π₀ i, M i) →ₗ[R] N⦄ (h : ∀ i x, φ (sing
 #align dfinsupp.lhom_ext Dfinsupp.lhom_ext
 
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 Case conversion may be inaccurate. Consider using '#align dfinsupp.lhom_ext' Dfinsupp.lhom_ext'ₓ'. -/
 /-- Two `R`-linear maps from `Π₀ i, M i` which agree on each `single i x` agree everywhere.
 
@@ -126,10 +117,7 @@ def lapply (i : ι) : (Π₀ i, M i) →ₗ[R] M i
 include dec_ι
 
 /- warning: dfinsupp.lmk_apply -> Dfinsupp.lmk_apply is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align dfinsupp.lmk_apply Dfinsupp.lmk_applyₓ'. -/
 @[simp]
 theorem lmk_apply (s : Finset ι) (x) : (lmk s : _ →ₗ[R] Π₀ i, M i) x = mk s x :=
@@ -197,10 +185,7 @@ variable (S)
 include dec_ι
 
 /- warning: dfinsupp.lsum -> Dfinsupp.lsum is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align dfinsupp.lsum Dfinsupp.lsumₓ'. -/
 /-- The `dfinsupp` version of `finsupp.lsum`.
 
@@ -236,10 +221,7 @@ def lsum [Semiring S] [Module S N] [SMulCommClass R S N] :
 #align dfinsupp.lsum Dfinsupp.lsum
 
 /- warning: dfinsupp.lsum_single -> Dfinsupp.lsum_single is a dubious translation:
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(forall (i : ι), LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (AddMonoid.toAddZeroClass.{max (max u1 u2) u4} (forall (i : ι), LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u4} (forall (i : ι), LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (Pi.addCommMonoid.{u1, max u2 u4} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u4} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u5, max (max u1 u2) u4} S (forall (i : ι), LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (MonoidWithZero.toMonoid.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u4} (forall (i : ι), LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (Pi.addCommMonoid.{u1, max u2 u4} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u4} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Module.toDistribMulAction.{u5, max (max u1 u2) u4} S (forall (i : ι), LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) _inst_6 (Pi.addCommMonoid.{u1, max u2 u4} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u4} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Pi.module.{u1, max u2 u4, u5} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) S _inst_6 (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u4} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u5, u2, u4} R R S (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) _inst_6 _inst_7 _inst_8)))))) (SMulZeroClass.toSMul.{u5, max (max u1 u2) u4} S (LinearMap.{u3, u3, max u2 u1, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5) (AddMonoid.toZero.{max (max u1 u2) u4} (LinearMap.{u3, u3, max u2 u1, u4} R R _inst_1 _inst_1 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ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u2 u4, u5} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) S _inst_6 (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u4} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u5, u2, u4} R R S (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) _inst_6 _inst_7 _inst_8)) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u5, max u1 u2, u4} R R S (Dfinsupp.{u1, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) _inst_6 _inst_7 _inst_8) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_6)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_6)) (RingHomInvPair.ids.{u5} S _inst_6) (RingHomInvPair.ids.{u5} S _inst_6)))))) (Dfinsupp.lsum.{u1, u3, u5, u2, u4} ι R S M N (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) _inst_4 _inst_5 _inst_6 _inst_7 _inst_8) F) (Dfinsupp.single.{u1, u2} ι (fun (i : ι) => M i) (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i))) i x)) (FunLike.coe.{max (succ u2) (succ u4), succ u2, succ u4} (LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (M i) (fun (_x : M i) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M i) => N) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u4} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (F i) x)
+<too large>
 Case conversion may be inaccurate. Consider using '#align dfinsupp.lsum_single Dfinsupp.lsum_singleₓ'. -/
 /-- While `simp` can prove this, it is often convenient to avoid unfolding `lsum` into `sum_add_hom`
 with `dfinsupp.lsum_apply_apply`. -/
@@ -265,10 +247,7 @@ variable [∀ i, AddCommMonoid (β i)] [∀ i, AddCommMonoid (β₁ i)] [∀ i,
 variable [∀ i, Module R (β i)] [∀ i, Module R (β₁ i)] [∀ i, Module R (β₂ i)]
 
 /- warning: dfinsupp.map_range_smul -> Dfinsupp.mapRange_smul is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align dfinsupp.map_range_smul Dfinsupp.mapRange_smulₓ'. -/
 theorem mapRange_smul (f : ∀ i, β₁ i → β₂ i) (hf : ∀ i, f i 0 = 0) (r : R)
     (hf' : ∀ i x, f i (r • x) = r • f i x) (g : Π₀ i, β₁ i) :
@@ -307,10 +286,7 @@ theorem mapRange.linearMap_id :
 #align dfinsupp.map_range.linear_map_id Dfinsupp.mapRange.linearMap_id
 
 /- warning: dfinsupp.map_range.linear_map_comp -> Dfinsupp.mapRange.linearMap_comp is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align dfinsupp.map_range.linear_map_comp Dfinsupp.mapRange.linearMap_compₓ'. -/
 theorem mapRange.linearMap_comp (f : ∀ i, β₁ i →ₗ[R] β₂ i) (f₂ : ∀ i, β i →ₗ[R] β₁ i) :
     (mapRange.linearMap fun i => (f i).comp (f₂ i)) =
@@ -321,10 +297,7 @@ theorem mapRange.linearMap_comp (f : ∀ i, β₁ i →ₗ[R] β₂ i) (f₂ : 
 include dec_ι
 
 /- warning: dfinsupp.sum_map_range_index.linear_map -> Dfinsupp.sum_mapRange_index.linearMap is a dubious translation:
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_inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat.semiring (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Pi.module.{u1, max u4 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => 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ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u1 u4) u2} Nat (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u3, u3, max u1 u4, u2} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u4, u2} R R Nat (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} 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(Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) Nat (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u1 u4) u2} (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u1 u4) u2} (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) (LinearMap.addCommMonoid.{u3, u3, max u1 u4, u2} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u1 u4) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat.semiring (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Pi.module.{u1, max u4 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u4, u2} R R Nat (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))))) (Module.toDistribMulAction.{0, max (max u1 u4) u2} Nat (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u3, u3, max u1 u4, u2} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u4, u2} R R Nat (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (SemilinearMapClass.distribMulActionHomClass.{0, max (max u1 u4) u2, max (max u1 u4) u2, max (max u1 u4) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) 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(_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u4 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u4, u2} R R Nat (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u4, u2} R R Nat (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R 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_inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{0, 0, max (max u1 u4) u2, max (max u1 u4) u2} Nat Nat (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) 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(LinearMap.addCommMonoid.{u3, u3, max u1 u4, u2} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u4 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) 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(fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (SMulZeroClass.toSMul.{0, max (max u1 u5) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (AddMonoid.toZero.{max (max u1 u5) u2} (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u1 u5) u2} (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{0, max (max u1 u5) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (AddMonoid.toAddZeroClass.{max (max u1 u5) u2} (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u1 u5) u2} (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (DistribMulAction.toDistribSMul.{0, max (max u1 u5) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u1 u5) u2} (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Module.toDistribMulAction.{0, max (max u1 u5) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) Nat.semiring (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Pi.module.{u1, max u5 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u5, u2} R R Nat (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))))))) (SMulZeroClass.toSMul.{0, max (max u1 u5) u2} Nat (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (AddMonoid.toZero.{max (max u1 u5) u2} (LinearMap.{u3, u3, max 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(Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (LinearMap.addCommMonoid.{u3, u3, max u1 u5, u2} R R (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (DistribSMul.toSMulZeroClass.{0, max (max u1 u5) u2} Nat (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (AddMonoid.toAddZeroClass.{max (max u1 u5) u2} (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u1 u5) u2} (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (LinearMap.addCommMonoid.{u3, u3, max u1 u5, u2} R R (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (DistribMulAction.toDistribSMul.{0, max (max u1 u5) u2} Nat (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u1 u5) u2} (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ 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_inst_1 _inst_4 _inst_5))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u5) u2, 0, max (max u1 u5) u2, max (max u1 u5) u2} (LinearEquiv.{0, 0, max (max u1 u5) u2, max u2 u5 u1} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι 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R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u5 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u5, u2} R R Nat (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) 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(AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))))) (Module.toDistribMulAction.{0, max (max u1 u5) u2} Nat (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u3, u3, max u1 u5, u2} R R (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) 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(fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))) (SemilinearEquivClass.instSemilinearMapClass.{0, 0, max (max u1 u5) u2, max (max u1 u5) u2, max (max u1 u5) u2} Nat Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R 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_inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, max u1 u5, u2} R R (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u5 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 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+<too large>
 Case conversion may be inaccurate. Consider using '#align dfinsupp.sum_map_range_index.linear_map Dfinsupp.sum_mapRange_index.linearMapₓ'. -/
 theorem sum_mapRange_index.linearMap [∀ (i : ι) (x : β₁ i), Decidable (x ≠ 0)]
     [∀ (i : ι) (x : β₂ i), Decidable (x ≠ 0)] {f : ∀ i, β₁ i →ₗ[R] β₂ i} {h : ∀ i, β₂ i →ₗ[R] N}
@@ -366,10 +339,7 @@ theorem mapRange.linearEquiv_refl :
 #align dfinsupp.map_range.linear_equiv_refl Dfinsupp.mapRange.linearEquiv_refl
 
 /- warning: dfinsupp.map_range.linear_equiv_trans -> Dfinsupp.mapRange.linearEquiv_trans is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align dfinsupp.map_range.linear_equiv_trans Dfinsupp.mapRange.linearEquiv_transₓ'. -/
 theorem mapRange.linearEquiv_trans (f : ∀ i, β i ≃ₗ[R] β₁ i) (f₂ : ∀ i, β₁ i ≃ₗ[R] β₂ i) :
     (mapRange.linearEquiv fun i => (f i).trans (f₂ i)) =
@@ -378,10 +348,7 @@ theorem mapRange.linearEquiv_trans (f : ∀ i, β i ≃ₗ[R] β₁ i) (f₂ : 
 #align dfinsupp.map_range.linear_equiv_trans Dfinsupp.mapRange.linearEquiv_trans
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align dfinsupp.map_range.linear_equiv_symm Dfinsupp.mapRange.linearEquiv_symmₓ'. -/
 @[simp]
 theorem mapRange.linearEquiv_symm (e : ∀ i, β₁ i ≃ₗ[R] β₂ i) :
@@ -411,10 +378,7 @@ noncomputable def coprodMap (f : ∀ i : ι, M i →ₗ[R] N) : (Π₀ i, M i) 
 #align dfinsupp.coprod_map Dfinsupp.coprodMap
 
 /- warning: dfinsupp.coprod_map_apply -> Dfinsupp.coprodMap_apply is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align dfinsupp.coprod_map_apply Dfinsupp.coprodMap_applyₓ'. -/
 theorem coprodMap_apply (f : ∀ i : ι, M i →ₗ[R] N) (x : Π₀ i, M i) :
     coprodMap f x =
@@ -455,10 +419,7 @@ variable [Semiring R] [AddCommMonoid N] [Module R N]
 open Dfinsupp
 
 /- warning: submodule.dfinsupp_sum_mem -> Submodule.dfinsupp_sum_mem is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.dfinsupp_sum_mem Submodule.dfinsupp_sum_memₓ'. -/
 theorem dfinsupp_sum_mem {β : ι → Type _} [∀ i, Zero (β i)] [∀ (i) (x : β i), Decidable (x ≠ 0)]
     (S : Submodule R N) (f : Π₀ i, β i) (g : ∀ i, β i → N) (h : ∀ c, f c ≠ 0 → g c (f c) ∈ S) :
@@ -467,10 +428,7 @@ theorem dfinsupp_sum_mem {β : ι → Type _} [∀ i, Zero (β i)] [∀ (i) (x :
 #align submodule.dfinsupp_sum_mem Submodule.dfinsupp_sum_mem
 
 /- warning: submodule.dfinsupp_sum_add_hom_mem -> Submodule.dfinsupp_sumAddHom_mem is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.dfinsupp_sum_add_hom_mem Submodule.dfinsupp_sumAddHom_memₓ'. -/
 theorem dfinsupp_sumAddHom_mem {β : ι → Type _} [∀ i, AddZeroClass (β i)] (S : Submodule R N)
     (f : Π₀ i, β i) (g : ∀ i, β i →+ N) (h : ∀ c, f c ≠ 0 → g c (f c) ∈ S) :
@@ -479,10 +437,7 @@ theorem dfinsupp_sumAddHom_mem {β : ι → Type _} [∀ i, AddZeroClass (β i)]
 #align submodule.dfinsupp_sum_add_hom_mem Submodule.dfinsupp_sumAddHom_mem
 
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_inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 _inst_3 Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3))) (fun (i : ι) => Submodule.subtype.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.supr_eq_range_dfinsupp_lsum Submodule.iSup_eq_range_dfinsupp_lsumₓ'. -/
 /-- The supremum of a family of submodules is equal to the range of `dfinsupp.lsum`; that is
 every element in the `supr` can be produced from taking a finite number of non-zero elements
@@ -499,10 +454,7 @@ theorem iSup_eq_range_dfinsupp_lsum (p : ι → Submodule R N) :
 #align submodule.supr_eq_range_dfinsupp_lsum Submodule.iSup_eq_range_dfinsupp_lsum
 
 /- warning: submodule.bsupr_eq_range_dfinsupp_lsum -> Submodule.biSup_eq_range_dfinsupp_lsum is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.bsupr_eq_range_dfinsupp_lsum Submodule.biSup_eq_range_dfinsupp_lsumₓ'. -/
 /-- The bounded supremum of a family of commutative additive submonoids is equal to the range of
 `dfinsupp.sum_add_hom` composed with `dfinsupp.filter_add_monoid_hom`; that is, every element in the
@@ -525,10 +477,7 @@ theorem biSup_eq_range_dfinsupp_lsum (p : ι → Prop) [DecidablePred p] (S : ι
 #align submodule.bsupr_eq_range_dfinsupp_lsum Submodule.biSup_eq_range_dfinsupp_lsum
 
 /- warning: submodule.mem_supr_iff_exists_dfinsupp -> Submodule.mem_iSup_iff_exists_dfinsupp is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_iff_exists_dfinsupp Submodule.mem_iSup_iff_exists_dfinsuppₓ'. -/
 theorem mem_iSup_iff_exists_dfinsupp (p : ι → Submodule R N) (x : N) :
     x ∈ iSup p ↔ ∃ f : Π₀ i, p i, Dfinsupp.lsum ℕ (fun i => (p i).Subtype) f = x :=
@@ -536,10 +485,7 @@ theorem mem_iSup_iff_exists_dfinsupp (p : ι → Submodule R N) (x : N) :
 #align submodule.mem_supr_iff_exists_dfinsupp Submodule.mem_iSup_iff_exists_dfinsupp
 
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 Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_iff_exists_dfinsupp' Submodule.mem_iSup_iff_exists_dfinsupp'ₓ'. -/
 /-- A variant of `submodule.mem_supr_iff_exists_dfinsupp` with the RHS fully unfolded. -/
 theorem mem_iSup_iff_exists_dfinsupp' (p : ι → Submodule R N) [∀ (i) (x : p i), Decidable (x ≠ 0)]
@@ -551,10 +497,7 @@ theorem mem_iSup_iff_exists_dfinsupp' (p : ι → Submodule R N) [∀ (i) (x : p
 #align submodule.mem_supr_iff_exists_dfinsupp' Submodule.mem_iSup_iff_exists_dfinsupp'
 
 /- warning: submodule.mem_bsupr_iff_exists_dfinsupp -> Submodule.mem_biSup_iff_exists_dfinsupp is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align submodule.mem_bsupr_iff_exists_dfinsupp Submodule.mem_biSup_iff_exists_dfinsuppₓ'. -/
 theorem mem_biSup_iff_exists_dfinsupp (p : ι → Prop) [DecidablePred p] (S : ι → Submodule R N)
     (x : N) :
@@ -568,10 +511,7 @@ open BigOperators
 omit dec_ι
 
 /- warning: submodule.mem_supr_finset_iff_exists_sum -> Submodule.mem_iSup_finset_iff_exists_sum is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_finset_iff_exists_sum Submodule.mem_iSup_finset_iff_exists_sumₓ'. -/
 theorem mem_iSup_finset_iff_exists_sum {s : Finset ι} (p : ι → Submodule R N) (a : N) :
     (a ∈ ⨆ i ∈ s, p i) ↔ ∃ μ : ∀ i, p i, (∑ i in s, (μ i : N)) = a := by
@@ -621,10 +561,7 @@ section Semiring
 variable [Semiring R] [AddCommMonoid N] [Module R N]
 
 /- warning: complete_lattice.independent_iff_forall_dfinsupp -> CompleteLattice.independent_iff_forall_dfinsupp is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align complete_lattice.independent_iff_forall_dfinsupp CompleteLattice.independent_iff_forall_dfinsuppₓ'. -/
 /-- Independence of a family of submodules can be expressed as a quantifier over `dfinsupp`s.
 
@@ -645,10 +582,7 @@ theorem independent_iff_forall_dfinsupp (p : ι → Submodule R N) :
 #align complete_lattice.independent_iff_forall_dfinsupp CompleteLattice.independent_iff_forall_dfinsupp
 
 /- warning: complete_lattice.independent_of_dfinsupp_lsum_injective -> CompleteLattice.independent_of_dfinsupp_lsum_injective is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align complete_lattice.independent_of_dfinsupp_lsum_injective CompleteLattice.independent_of_dfinsupp_lsum_injectiveₓ'. -/
 /- If `dfinsupp.lsum` applied with `submodule.subtype` is injective then the submodules are
 independent. -/
@@ -665,10 +599,7 @@ theorem independent_of_dfinsupp_lsum_injective (p : ι → Submodule R N)
 #align complete_lattice.independent_of_dfinsupp_lsum_injective CompleteLattice.independent_of_dfinsupp_lsum_injective
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align complete_lattice.independent_of_dfinsupp_sum_add_hom_injective CompleteLattice.independent_of_dfinsupp_sumAddHom_injectiveₓ'. -/
 /- If `dfinsupp.sum_add_hom` applied with `add_submonoid.subtype` is injective then the additive
 submonoids are independent. -/
@@ -680,10 +611,7 @@ theorem independent_of_dfinsupp_sumAddHom_injective (p : ι → AddSubmonoid N)
 #align complete_lattice.independent_of_dfinsupp_sum_add_hom_injective CompleteLattice.independent_of_dfinsupp_sumAddHom_injective
 
 /- warning: complete_lattice.lsum_comp_map_range_to_span_singleton -> CompleteLattice.lsum_comp_mapRange_toSpanSingleton is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align complete_lattice.lsum_comp_map_range_to_span_singleton CompleteLattice.lsum_comp_mapRange_toSpanSingletonₓ'. -/
 /-- Combining `dfinsupp.lsum` with `linear_map.to_span_singleton` is the same as `finsupp.total` -/
 theorem lsum_comp_mapRange_toSpanSingleton [∀ m : R, Decidable (m ≠ 0)] (p : ι → Submodule R N)
@@ -705,10 +633,7 @@ section Ring
 variable [Ring R] [AddCommGroup N] [Module R N]
 
 /- warning: complete_lattice.independent_of_dfinsupp_sum_add_hom_injective' -> CompleteLattice.independent_of_dfinsupp_sumAddHom_injective' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align complete_lattice.independent_of_dfinsupp_sum_add_hom_injective' CompleteLattice.independent_of_dfinsupp_sumAddHom_injective'ₓ'. -/
 /- If `dfinsupp.sum_add_hom` applied with `add_submonoid.subtype` is injective then the additive
 subgroups are independent. -/
@@ -720,10 +645,7 @@ theorem independent_of_dfinsupp_sumAddHom_injective' (p : ι → AddSubgroup N)
 #align complete_lattice.independent_of_dfinsupp_sum_add_hom_injective' CompleteLattice.independent_of_dfinsupp_sumAddHom_injective'
 
 /- warning: complete_lattice.independent.dfinsupp_lsum_injective -> CompleteLattice.Independent.dfinsupp_lsum_injective is a dubious translation:
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u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)))) Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x 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(SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{0, max u1 u2} Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R 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_inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max u1 u2} (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))))) (Module.toDistribMulAction.{0, 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(Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))))) (Pi.module.{u1, u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) (fun (i : ι) => 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Nat.semiring (AddCommMonoid.natModule.{u2} N (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)))))))) (SMulZeroClass.toSMul.{0, max u1 u2} Nat (LinearMap.{u3, u3, max u2 u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} 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_inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (Ring.toSemiring.{u3} R _inst_1) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) _inst_3) (AddMonoid.toZero.{max u1 u2} (LinearMap.{u3, u3, 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+<too large>
 Case conversion may be inaccurate. Consider using '#align complete_lattice.independent.dfinsupp_lsum_injective CompleteLattice.Independent.dfinsupp_lsum_injectiveₓ'. -/
 /-- The canonical map out of a direct sum of a family of submodules is injective when the submodules
 are `complete_lattice.independent`.
@@ -754,10 +676,7 @@ theorem Independent.dfinsupp_lsum_injective {p : ι → Submodule R N} (h : Inde
 #align complete_lattice.independent.dfinsupp_lsum_injective CompleteLattice.Independent.dfinsupp_lsum_injective
 
 /- warning: complete_lattice.independent.dfinsupp_sum_add_hom_injective -> CompleteLattice.Independent.dfinsupp_sumAddHom_injective is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align complete_lattice.independent.dfinsupp_sum_add_hom_injective CompleteLattice.Independent.dfinsupp_sumAddHom_injectiveₓ'. -/
 /-- The canonical map out of a direct sum of a family of additive subgroups is injective when the
 additive subgroups are `complete_lattice.independent`. -/
@@ -769,10 +688,7 @@ theorem Independent.dfinsupp_sumAddHom_injective {p : ι → AddSubgroup N} (h :
 #align complete_lattice.independent.dfinsupp_sum_add_hom_injective CompleteLattice.Independent.dfinsupp_sumAddHom_injective
 
 /- warning: complete_lattice.independent_iff_dfinsupp_lsum_injective -> CompleteLattice.independent_iff_dfinsupp_lsum_injective is a dubious translation:
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(AddCommGroup.toAddCommMonoid.{u2} N _inst_2)) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u2, u2} R R Nat (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) 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u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)))) Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (LinearMap.{u3, u3, max u2 u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (Ring.toSemiring.{u3} R _inst_1) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) _inst_3) (SMulZeroClass.toSMul.{0, max u1 u2} Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (AddMonoid.toZero.{max u1 u2} (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{0, max u1 u2} Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R 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(Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R 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(Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))))))) (DistribMulAction.toDistribSMul.{0, max u1 u2} Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max u1 u2} (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))))) (Module.toDistribMulAction.{0, max u1 u2} Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) Nat.semiring (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) 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R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) Nat.semiring (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N 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+<too large>
 Case conversion may be inaccurate. Consider using '#align complete_lattice.independent_iff_dfinsupp_lsum_injective CompleteLattice.independent_iff_dfinsupp_lsum_injectiveₓ'. -/
 /-- A family of submodules over an additive group are independent if and only iff `dfinsupp.lsum`
 applied with `submodule.subtype` is injective.
@@ -785,10 +701,7 @@ theorem independent_iff_dfinsupp_lsum_injective (p : ι → Submodule R N) :
 #align complete_lattice.independent_iff_dfinsupp_lsum_injective CompleteLattice.independent_iff_dfinsupp_lsum_injective
 
 /- warning: complete_lattice.independent_iff_dfinsupp_sum_add_hom_injective -> CompleteLattice.independent_iff_dfinsupp_sumAddHom_injective is a dubious translation:
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(AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) (SetLike.instMembership.{u2, u2} (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) N (AddSubgroup.instSetLikeAddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) x (p i))) (fun (i : ι) => AddSubmonoid.toAddZeroClass.{u2} N (AddMonoid.toAddZeroClass.{u2} N (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)))) (AddSubgroup.toAddSubmonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2) (p i)))) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)))))) (Dfinsupp.sumAddHom.{u1, u2, u2} ι N (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) (SetLike.instMembership.{u2, u2} (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) N (AddSubgroup.instSetLikeAddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) x (p i))) (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => AddSubmonoid.toAddZeroClass.{u2} N (AddMonoid.toAddZeroClass.{u2} N (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)))) (AddSubgroup.toAddSubmonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2) (p i))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (fun (i : ι) => AddSubgroup.subtype.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2) (p i)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align complete_lattice.independent_iff_dfinsupp_sum_add_hom_injective CompleteLattice.independent_iff_dfinsupp_sumAddHom_injectiveₓ'. -/
 /-- A family of additive subgroups over an additive group are independent if and only if
 `dfinsupp.sum_add_hom` applied with `add_subgroup.subtype` is injective. -/

f4758115

bump to nightly-2023-05-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

fbc7b476

Diff

@@ -84,7 +84,7 @@ def lsingle (i) : M i →ₗ[R] Π₀ i, M i :=
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : ι -> Type.{u3}} {N : Type.{u4}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (M i)] [_inst_3 : forall (i : ι), Module.{u2, u3} R (M i) _inst_1 (_inst_2 i)] [_inst_4 : AddCommMonoid.{u4} N] [_inst_5 : Module.{u2, u4} R N _inst_1 _inst_4] {{φ : LinearMap.{u2, u2, max u1 u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))))) N (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5}} {{ψ : LinearMap.{u2, u2, max u1 u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R 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 but is expected to have type
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+  forall {ι : Type.{u2}} {R : Type.{u4}} {M : ι -> Type.{u3}} {N : Type.{u1}} [dec_ι : DecidableEq.{succ u2} ι] [_inst_1 : Semiring.{u4} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (M i)] [_inst_3 : forall (i : ι), Module.{u4, u3} R (M i) _inst_1 (_inst_2 i)] [_inst_4 : AddCommMonoid.{u1} N] [_inst_5 : Module.{u4, u1} R N _inst_1 _inst_4] {{φ : LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Dfinsupp.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u2, u3, u4} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5}} {{ψ : LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R 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(AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i))) i x))) -> (Eq.{max (max (succ u2) (succ u3)) (succ u1)} (LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Dfinsupp.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u2, u3, u4} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5) φ ψ)
 Case conversion may be inaccurate. Consider using '#align dfinsupp.lhom_ext Dfinsupp.lhom_extₓ'. -/
 /-- Two `R`-linear maps from `Π₀ i, M i` which agree on each `single i x` agree everywhere. -/
 theorem lhom_ext ⦃φ ψ : (Π₀ i, M i) →ₗ[R] N⦄ (h : ∀ i x, φ (single i x) = ψ (single i x)) : φ = ψ :=
@@ -129,7 +129,7 @@ include dec_ι
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : ι -> Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (M i)] [_inst_3 : forall (i : ι), Module.{u2, u3} R (M i) _inst_1 (_inst_2 i)] (s : Finset.{u1} ι) (x : forall (i : coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} ι) (Set.{u1} ι) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (Finset.Set.hasCoeT.{u1} ι))) s)), (fun (i : ι) => M i) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} ι) (Set.{u1} ι) (HasLiftT.mk.{succ u1, succ u1} 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 but is expected to have type
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(Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x (Finset.toSet.{u3} ι s)) i)) R _inst_1 (fun (i : Set.Elem.{u3} ι (Finset.toSet.{u3} ι s)) => _inst_2 (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x (Finset.toSet.{u3} ι s)) i)) (fun (i : Set.Elem.{u3} ι (Finset.toSet.{u3} ι s)) => _inst_3 (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x (Finset.toSet.{u3} ι s)) i))) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Dfinsupp.lmk.{u3, u1, u2} ι R (fun (i : ι) => M i) (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) s) x) (Dfinsupp.mk.{u3, u2} ι M (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => AddMonoid.toZero.{u2} (M i) (AddCommMonoid.toAddMonoid.{u2} (M i) (_inst_2 i))) s x)
+  forall {ι : Type.{u3}} {R : Type.{u1}} {M : ι -> Type.{u2}} [dec_ι : DecidableEq.{succ u3} ι] [_inst_1 : Semiring.{u1} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (M i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (M i) _inst_1 (_inst_2 i)] (s : Finset.{u3} ι) (x : forall (i : Set.Elem.{u3} ι (Finset.toSet.{u3} ι s)), M (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x (Finset.toSet.{u3} ι s)) i)), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : forall (i : Set.Elem.{u3} ι (Finset.toSet.{u3} ι s)), M (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x (Finset.toSet.{u3} ι s)) i)) => Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) x) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ 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 Case conversion may be inaccurate. Consider using '#align dfinsupp.lmk_apply Dfinsupp.lmk_applyₓ'. -/
 @[simp]
 theorem lmk_apply (s : Finset ι) (x) : (lmk s : _ →ₗ[R] Π₀ i, M i) x = mk s x :=
@@ -140,7 +140,7 @@ theorem lmk_apply (s : Finset ι) (x) : (lmk s : _ →ₗ[R] Π₀ i, M i) x = m
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : ι -> Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (M i)] [_inst_3 : forall (i : ι), Module.{u2, u3} R (M i) _inst_1 (_inst_2 i)] (i : ι) (x : M i), Eq.{succ (max u1 u3)} (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))))) (coeFn.{max (succ u3) (succ (max u1 u3)), max (succ u3) (succ (max u1 u3))} (LinearMap.{u2, u2, u3, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (M i) (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))))) (_inst_2 i) (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (fun (_x : LinearMap.{u2, u2, u3, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (M i) (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))))) (_inst_2 i) (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) => (M i) -> (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i)))))) (LinearMap.hasCoeToFun.{u2, u2, u3, max u1 u3} R R (M i) (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))))) _inst_1 _inst_1 (_inst_2 i) (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Dfinsupp.lsingle.{u1, u2, u3} ι R (fun (i : ι) => M i) (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i) x) (Dfinsupp.single.{u1, u3} ι (fun (i : ι) => M i) (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i)))) i x)
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u1}} {M : ι -> Type.{u2}} [dec_ι : DecidableEq.{succ u3} ι] [_inst_1 : Semiring.{u1} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (M i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (M i) _inst_1 (_inst_2 i)] (i : ι) (x : M i), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M i) => Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) x) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (M i) (Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) (_inst_2 i) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (M i) (fun (_x : M i) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M i) => Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u2} R R (M i) (Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) _inst_1 _inst_1 (_inst_2 i) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Dfinsupp.lsingle.{u3, u1, u2} ι R M (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i) x) (Dfinsupp.single.{u3, u2} ι M (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => AddMonoid.toZero.{u2} (M i) (AddCommMonoid.toAddMonoid.{u2} (M i) (_inst_2 i))) i x)
+  forall {ι : Type.{u3}} {R : Type.{u1}} {M : ι -> Type.{u2}} [dec_ι : DecidableEq.{succ u3} ι] [_inst_1 : Semiring.{u1} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (M i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (M i) _inst_1 (_inst_2 i)] (i : ι) (x : M i), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M i) => Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) x) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (M i) (Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) (_inst_2 i) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (M i) (fun (_x : M i) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M i) => Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u2} R R (M i) (Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) _inst_1 _inst_1 (_inst_2 i) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Dfinsupp.lsingle.{u3, u1, u2} ι R M (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i) x) (Dfinsupp.single.{u3, u2} ι M (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => AddMonoid.toZero.{u2} (M i) (AddCommMonoid.toAddMonoid.{u2} (M i) (_inst_2 i))) i x)
 Case conversion may be inaccurate. Consider using '#align dfinsupp.lsingle_apply Dfinsupp.lsingle_applyₓ'. -/
 @[simp]
 theorem lsingle_apply (i : ι) (x : M i) : (lsingle i : _ →ₗ[R] _) x = single i x :=
@@ -153,7 +153,7 @@ omit dec_ι
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : ι -> Type.{u3}} [_inst_1 : Semiring.{u2} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (M i)] [_inst_3 : forall (i : ι), Module.{u2, u3} R (M i) _inst_1 (_inst_2 i)] (i : ι) (f : Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} ((fun (i : ι) => M i) i) (AddMonoid.toAddZeroClass.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i))))), Eq.{succ u3} (M i) (coeFn.{max (succ (max u1 u3)) (succ u3), max (succ (max u1 u3)) (succ u3)} (LinearMap.{u2, u2, max u1 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))))) (M i) (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i)) (fun (_x : LinearMap.{u2, u2, max u1 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))))) (M i) (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i)) => (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))))) -> (M i)) (LinearMap.hasCoeToFun.{u2, u2, max u1 u3, u3} R R (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))))) (M i) _inst_1 _inst_1 (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Dfinsupp.lapply.{u1, u2, u3} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i) f) (coeFn.{succ (max u1 u3), max (succ u1) (succ u3)} (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} ((fun (i : ι) => M i) i) (AddMonoid.toAddZeroClass.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i))))) (fun (_x : Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} ((fun (i : ι) => M i) i) (AddMonoid.toAddZeroClass.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i))))) => forall (i : ι), M i) (Dfinsupp.hasCoeToFun.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} ((fun (i : ι) => M i) i) (AddMonoid.toAddZeroClass.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i))))) f i)
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u1}} {M : ι -> Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (M i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (M i) _inst_1 (_inst_2 i)] (i : ι) (f : Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) => M i) f) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), succ u2} (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) (M i) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i)) (Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) (fun (_x : Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) => M i) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u2, u2} R R (Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) (M i) _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Dfinsupp.lapply.{u3, u1, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i) f) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Dfinsupp.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => M i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => M i) i) _x) (Dfinsupp.funLike.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => M i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i))) i)) f i)
+  forall {ι : Type.{u3}} {R : Type.{u1}} {M : ι -> Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (M i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (M i) _inst_1 (_inst_2 i)] (i : ι) (f : Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) => M i) f) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), succ u2} (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) (M i) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i)) (Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) (fun (_x : Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) => M i) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u2, u2} R R (Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) (M i) _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Dfinsupp.lapply.{u3, u1, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i) f) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Dfinsupp.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => M i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => M i) i) _x) (Dfinsupp.funLike.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => M i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i))) i)) f i)
 Case conversion may be inaccurate. Consider using '#align dfinsupp.lapply_apply Dfinsupp.lapply_applyₓ'. -/
 @[simp]
 theorem lapply_apply (i : ι) (f : Π₀ i, M i) : (lapply i : _ →ₗ[R] _) f = f i :=
@@ -239,7 +239,7 @@ def lsum [Semiring S] [Module S N] [SMulCommClass R S N] :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} (S : Type.{u3}) {M : ι -> Type.{u4}} {N : Type.{u5}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u4} (M i)] [_inst_3 : forall (i : ι), Module.{u2, u4} R (M i) _inst_1 (_inst_2 i)] [_inst_4 : AddCommMonoid.{u5} N] [_inst_5 : Module.{u2, u5} R N _inst_1 _inst_4] [_inst_6 : Semiring.{u3} S] [_inst_7 : Module.{u3, u5} S N _inst_6 _inst_4] [_inst_8 : SMulCommClass.{u2, u3, u5} R S N (SMulZeroClass.toHasSmul.{u2, u5} R N (AddZeroClass.toHasZero.{u5} N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4))) (SMulWithZero.toSmulZeroClass.{u2, u5} R N (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))) (AddZeroClass.toHasZero.{u5} N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4))) (MulActionWithZero.toSMulWithZero.{u2, u5} R N (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddZeroClass.toHasZero.{u5} N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4))) (Module.toMulActionWithZero.{u2, u5} R N _inst_1 _inst_4 _inst_5)))) (SMulZeroClass.toHasSmul.{u3, u5} S N (AddZeroClass.toHasZero.{u5} N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4))) (SMulWithZero.toSmulZeroClass.{u3, u5} S N (MulZeroClass.toHasZero.{u3} S (MulZeroOneClass.toMulZeroClass.{u3} S (MonoidWithZero.toMulZeroOneClass.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_6)))) (AddZeroClass.toHasZero.{u5} N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4))) (MulActionWithZero.toSMulWithZero.{u3, u5} S N (Semiring.toMonoidWithZero.{u3} S _inst_6) (AddZeroClass.toHasZero.{u5} N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4))) (Module.toMulActionWithZero.{u3, u5} S N _inst_6 _inst_4 _inst_7))))] (F : forall (i : ι), LinearMap.{u2, u2, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (i : ι) (x : M i), Eq.{succ u5} N (coeFn.{max (succ (max u1 u4)) (succ u5), max (succ (max u1 u4)) (succ u5)} (LinearMap.{u2, u2, max u1 u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} (M i) (AddMonoid.toAddZeroClass.{u4} (M i) (AddCommMonoid.toAddMonoid.{u4} (M i) (_inst_2 i))))) N (Dfinsupp.addCommMonoid.{u1, u4} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u4, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5) (fun (_x : LinearMap.{u2, u2, max u1 u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} (M i) (AddMonoid.toAddZeroClass.{u4} (M i) (AddCommMonoid.toAddMonoid.{u4} (M i) (_inst_2 i))))) N (Dfinsupp.addCommMonoid.{u1, u4} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u4, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5) => (Dfinsupp.{u1, u4} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} (M i) (AddMonoid.toAddZeroClass.{u4} (M i) (AddCommMonoid.toAddMonoid.{u4} (M i) (_inst_2 i))))) -> N) (LinearMap.hasCoeToFun.{u2, u2, max u1 u4, u5} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} (M i) (AddMonoid.toAddZeroClass.{u4} (M i) (AddCommMonoid.toAddMonoid.{u4} (M i) (_inst_2 i))))) N _inst_1 _inst_1 (Dfinsupp.addCommMonoid.{u1, u4} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u4, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5 (RingHom.id.{u2} R 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 but is expected to have type
-  forall {ι : Type.{u1}} {R : Type.{u3}} (S : Type.{u5}) {M : ι -> Type.{u2}} {N : Type.{u4}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u3} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (M i)] [_inst_3 : forall (i : ι), Module.{u3, u2} R (M i) _inst_1 (_inst_2 i)] [_inst_4 : AddCommMonoid.{u4} N] [_inst_5 : Module.{u3, u4} R N _inst_1 _inst_4] [_inst_6 : Semiring.{u5} S] [_inst_7 : Module.{u5, u4} S N _inst_6 _inst_4] [_inst_8 : SMulCommClass.{u3, u5, u4} R S N (SMulZeroClass.toSMul.{u3, u4} R N (AddMonoid.toZero.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_4)) (SMulWithZero.toSMulZeroClass.{u3, u4} R N (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddMonoid.toZero.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_4)) (MulActionWithZero.toSMulWithZero.{u3, u4} R N (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddMonoid.toZero.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_4)) (Module.toMulActionWithZero.{u3, u4} R N _inst_1 _inst_4 _inst_5)))) 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(forall (i : ι), LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (AddMonoid.toAddZeroClass.{max (max u1 u2) u4} (forall (i : ι), LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u4} (forall (i : ι), LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (Pi.addCommMonoid.{u1, max u2 u4} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u4} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u5, max (max u1 u2) u4} S (forall (i : ι), LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (MonoidWithZero.toMonoid.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u4} (forall (i : ι), LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (Pi.addCommMonoid.{u1, max u2 u4} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u4} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Module.toDistribMulAction.{u5, max (max u1 u2) u4} S (forall (i : ι), LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) _inst_6 (Pi.addCommMonoid.{u1, max u2 u4} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u4} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Pi.module.{u1, max u2 u4, u5} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) S _inst_6 (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u4} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u5, u2, u4} R R S (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) _inst_6 _inst_7 _inst_8)))))) (SMulZeroClass.toSMul.{u5, max (max u1 u2) u4} S (LinearMap.{u3, u3, max u2 u1, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5) (AddMonoid.toZero.{max (max u1 u2) u4} (LinearMap.{u3, u3, max u2 u1, u4} R R _inst_1 _inst_1 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dec_ι a b) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) _inst_4 _inst_5 _inst_6 _inst_7 _inst_8) F) (Dfinsupp.single.{u1, u2} ι (fun (i : ι) => M i) (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i))) i x)) (FunLike.coe.{max (succ u2) (succ u4), succ u2, succ u4} (LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (M i) (fun (_x : M i) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M i) => N) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u4} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (F i) x)
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(forall (i : ι), LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (AddMonoid.toAddZeroClass.{max (max u1 u2) u4} (forall (i : ι), LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u4} (forall (i : ι), LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (Pi.addCommMonoid.{u1, max u2 u4} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u4} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u5, max (max u1 u2) u4} S (forall (i : ι), LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (MonoidWithZero.toMonoid.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u4} (forall (i : ι), LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (Pi.addCommMonoid.{u1, max u2 u4} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u4} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Module.toDistribMulAction.{u5, max (max u1 u2) u4} S (forall (i : ι), LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) _inst_6 (Pi.addCommMonoid.{u1, max u2 u4} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u4} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Pi.module.{u1, max u2 u4, u5} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) S _inst_6 (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u4} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u5, u2, u4} R R S (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) _inst_6 _inst_7 _inst_8)))))) (SMulZeroClass.toSMul.{u5, max (max u1 u2) u4} S (LinearMap.{u3, u3, max u2 u1, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5) (AddMonoid.toZero.{max (max u1 u2) u4} (LinearMap.{u3, u3, max u2 u1, u4} R R _inst_1 _inst_1 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dec_ι a b) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) _inst_4 _inst_5 _inst_6 _inst_7 _inst_8) F) (Dfinsupp.single.{u1, u2} ι (fun (i : ι) => M i) (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i))) i x)) (FunLike.coe.{max (succ u2) (succ u4), succ u2, succ u4} (LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (M i) (fun (_x : M i) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M i) => N) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u4} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (F i) x)
 Case conversion may be inaccurate. Consider using '#align dfinsupp.lsum_single Dfinsupp.lsum_singleₓ'. -/
 /-- While `simp` can prove this, it is often convenient to avoid unfolding `lsum` into `sum_add_hom`
 with `dfinsupp.lsum_apply_apply`. -/
@@ -324,7 +324,7 @@ include dec_ι
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u2, u3} R N _inst_1 _inst_4] {β₁ : ι -> Type.{u4}} {β₂ : ι -> Type.{u5}} [_inst_7 : forall (i : ι), AddCommMonoid.{u4} (β₁ i)] [_inst_8 : forall (i : ι), AddCommMonoid.{u5} (β₂ i)] [_inst_10 : forall (i : ι), Module.{u2, u4} R (β₁ i) _inst_1 (_inst_7 i)] [_inst_11 : forall (i : ι), Module.{u2, u5} R (β₂ i) _inst_1 (_inst_8 i)] [_inst_12 : forall (i : ι) (x : β₁ i), Decidable (Ne.{succ u4} (β₁ i) x (OfNat.ofNat.{u4} (β₁ i) 0 (OfNat.mk.{u4} (β₁ i) 0 (Zero.zero.{u4} (β₁ i) (AddZeroClass.toHasZero.{u4} (β₁ i) (AddMonoid.toAddZeroClass.{u4} (β₁ i) (AddCommMonoid.toAddMonoid.{u4} (β₁ i) (_inst_7 i))))))))] [_inst_13 : forall (i : ι) (x : β₂ i), Decidable (Ne.{succ u5} (β₂ i) x (OfNat.ofNat.{u5} (β₂ i) 0 (OfNat.mk.{u5} (β₂ i) 0 (Zero.zero.{u5} (β₂ i) (AddZeroClass.toHasZero.{u5} (β₂ i) (AddMonoid.toAddZeroClass.{u5} (β₂ i) (AddCommMonoid.toAddMonoid.{u5} (β₂ i) (_inst_8 i))))))))] {f : forall (i : ι), LinearMap.{u2, u2, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (β₁ i) (β₂ i) (_inst_7 i) (_inst_8 i) (_inst_10 i) (_inst_11 i)} {h : forall (i : ι), LinearMap.{u2, u2, u5, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5} {l : Dfinsupp.{u1, u4} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} ((fun (i : ι) => β₁ i) i) (AddMonoid.toAddZeroClass.{u4} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₁ i) i) (_inst_7 i))))}, Eq.{succ u3} N (coeFn.{max (succ (max u1 u5)) (succ u3), max (succ (max u1 u5)) (succ u3)} (LinearMap.{u2, u2, max u1 u5, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddZeroClass.toHasZero.{u5} (β₂ i) 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i) _inst_4 _inst_5 Nat.semiring (AddCommMonoid.natModule.{u3} N _inst_4) (AddMonoid.nat_smulCommClass'.{u2, u3} R N (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} N _inst_4) (Module.toDistribMulAction.{u2, u3} R N _inst_1 _inst_4 _inst_5))) (fun (i : ι) => LinearMap.comp.{u2, u2, u2, u4, u5, u3} R R R (β₁ i) (β₂ i) N _inst_1 _inst_1 _inst_1 (_inst_7 i) (_inst_8 i) _inst_4 (_inst_10 i) (_inst_11 i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomCompTriple.right_ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (h i) (f i))) l)
 but is expected to have type
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_inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) _x) (SMulHomClass.toFunLike.{max (max u1 u4) u2, 0, max (max u1 u4) u2, max (max u1 u4) u2} (LinearEquiv.{0, 0, max (max u1 u4) u2, max u2 u4 u1} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, max u1 u4, u2} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u4 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u4, u2} R R Nat (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u4, u2} R R Nat (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) Nat (forall 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(forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u1 u4) u2} (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{0, max (max u1 u4) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (AddMonoid.toAddZeroClass.{max (max u1 u4) u2} (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u1 u4) u2} (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (DistribMulAction.toDistribSMul.{0, max (max u1 u4) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u1 u4) u2} (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Module.toDistribMulAction.{0, max (max u1 u4) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat.semiring (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Pi.module.{u1, max u4 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u4, u2} R R Nat (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))))))) (SMulZeroClass.toSMul.{0, max (max u1 u4) u2} Nat (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R 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ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u1 u4) u2} Nat (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u3, u3, max u1 u4, u2} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 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(Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) (LinearMap.addCommMonoid.{u3, u3, max u1 u4, u2} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u1 u4) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat.semiring (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Pi.module.{u1, max u4 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u4, u2} R R Nat (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))))) (Module.toDistribMulAction.{0, max (max u1 u4) u2} Nat (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u3, u3, max u1 u4, u2} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u4, u2} R R Nat (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (SemilinearMapClass.distribMulActionHomClass.{0, max (max u1 u4) u2, max (max u1 u4) u2, max (max u1 u4) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) 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(_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u4 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u4, u2} R R Nat (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u4, u2} R R Nat (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R 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(Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u4, u2} R R Nat (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))) (SemilinearEquivClass.instSemilinearMapClass.{0, 0, max 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(LinearMap.addCommMonoid.{u3, u3, max u1 u4, u2} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u4 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) 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(Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u1 u5) u2} (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (DistribMulAction.toDistribSMul.{0, max (max u1 u5) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u1 u5) u2} (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Module.toDistribMulAction.{0, max (max u1 u5) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) Nat.semiring (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Pi.module.{u1, max u5 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u5, u2} R R Nat (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))))))) (SMulZeroClass.toSMul.{0, max (max u1 u5) u2} Nat (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (AddMonoid.toZero.{max (max u1 u5) u2} (LinearMap.{u3, u3, max 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(Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (LinearMap.addCommMonoid.{u3, u3, max u1 u5, u2} R R (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (DistribSMul.toSMulZeroClass.{0, max (max u1 u5) u2} Nat (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) 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u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (LinearMap.addCommMonoid.{u3, u3, max u1 u5, u2} R R (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (DistribMulAction.toDistribSMul.{0, max (max u1 u5) u2} Nat (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u1 u5) u2} (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ 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=> β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u5, u2} R R Nat (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u5) u2, 0, max (max u1 u5) u2, max (max u1 u5) u2} (LinearEquiv.{0, 0, max (max u1 u5) u2, max u2 u5 u1} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι 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R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u5 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u5, u2} R R Nat (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u5, u2} R R Nat (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) Nat (forall 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=> _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (LinearMap.addCommMonoid.{u3, u3, max u1 u5, u2} R R (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u1 u5) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) Nat.semiring (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R 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(AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))))) (Module.toDistribMulAction.{0, max (max u1 u5) u2} Nat (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u3, u3, max u1 u5, u2} R R (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) 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_inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (SemilinearMapClass.distribMulActionHomClass.{0, max (max u1 u5) u2, max (max u1 u5) u2, max (max u1 u5) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (LinearEquiv.{0, 0, max (max u1 u5) u2, max u2 u5 u1} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, max u1 u5, u2} R R (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u5 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u5, u2} R R Nat (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u5, u2} R R Nat (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) Nat.semiring 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(fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))) (SemilinearEquivClass.instSemilinearMapClass.{0, 0, max (max u1 u5) u2, max (max u1 u5) u2, max (max u1 u5) u2} Nat Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (LinearEquiv.{0, 0, max (max u1 u5) u2, max u2 u5 u1} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, max u1 u5, u2} R R (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u5 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u5, u2} R R Nat (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u5, u2} R R Nat (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, max u1 u5, u2} R R (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u5 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u5, u2} R R Nat (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u5, u2} R R Nat (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R 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+  forall {ι : Type.{u1}} {R : Type.{u3}} {N : Type.{u2}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u3} R] [_inst_4 : AddCommMonoid.{u2} N] [_inst_5 : Module.{u3, u2} R N _inst_1 _inst_4] {β₁ : ι -> Type.{u5}} {β₂ : ι -> Type.{u4}} [_inst_7 : forall (i : ι), AddCommMonoid.{u5} (β₁ i)] [_inst_8 : forall (i : ι), AddCommMonoid.{u4} (β₂ i)] [_inst_10 : forall (i : ι), Module.{u3, u5} R (β₁ i) _inst_1 (_inst_7 i)] [_inst_11 : forall (i : ι), Module.{u3, u4} R (β₂ i) _inst_1 (_inst_8 i)] [_inst_12 : forall (i : ι) (x : β₁ i), Decidable (Ne.{succ u5} (β₁ i) x (OfNat.ofNat.{u5} (β₁ i) 0 (Zero.toOfNat0.{u5} (β₁ i) (AddMonoid.toZero.{u5} (β₁ i) (AddCommMonoid.toAddMonoid.{u5} (β₁ i) (_inst_7 i))))))] [_inst_13 : forall (i : ι) (x : β₂ i), Decidable (Ne.{succ u4} (β₂ i) x (OfNat.ofNat.{u4} (β₂ i) 0 (Zero.toOfNat0.{u4} (β₂ i) (AddMonoid.toZero.{u4} (β₂ i) (AddCommMonoid.toAddMonoid.{u4} (β₂ i) (_inst_8 i))))))] {f : forall (i : ι), LinearMap.{u3, u3, u5, u4} R R _inst_1 _inst_1 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(LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u4, u2} R R Nat (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (_x : forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) => LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) _x) (SMulHomClass.toFunLike.{max (max u1 u4) u2, 0, max (max u1 u4) u2, max (max u1 u4) u2} (LinearEquiv.{0, 0, max (max u1 u4) u2, max u2 u4 u1} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, max u1 u4, u2} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u4 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u4, u2} R R Nat (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u4, u2} R R Nat (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) Nat (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) (SMulZeroClass.toSMul.{0, max (max u1 u4) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (AddMonoid.toZero.{max (max u1 u4) u2} (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u1 u4) u2} (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{0, max (max u1 u4) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (AddMonoid.toAddZeroClass.{max (max u1 u4) u2} (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u1 u4) u2} (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (DistribMulAction.toDistribSMul.{0, max (max u1 u4) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u1 u4) u2} (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Module.toDistribMulAction.{0, max (max u1 u4) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat.semiring (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Pi.module.{u1, max u4 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => 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(fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) (AddMonoid.toZero.{max (max u1 u4) u2} (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u1 u4) u2} (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun 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(LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) (LinearMap.addCommMonoid.{u3, u3, max u1 u4, u2} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u1 u4) u2} Nat (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u3, u3, max u1 u4, u2} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u4, u2} R R Nat (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u4) u2, 0, max (max u1 u4) u2, max (max u1 u4) u2} (LinearEquiv.{0, 0, max (max u1 u4) u2, max u2 u4 u1} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} 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_inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u4 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u4, u2} R R Nat (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u4, u2} R R Nat (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) Nat (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) 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(Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) (LinearMap.addCommMonoid.{u3, u3, max u1 u4, u2} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u1 u4) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat.semiring (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Pi.module.{u1, max u4 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u4, u2} R R Nat (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))))) (Module.toDistribMulAction.{0, max (max u1 u4) u2} Nat (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => 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(AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u4, u2} R R Nat (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R 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_inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (SMulZeroClass.toSMul.{0, max (max u1 u5) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (AddMonoid.toZero.{max (max u1 u5) u2} (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (AddCommMonoid.toAddMonoid.{max (max 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(Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u1 u5) u2} (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (DistribMulAction.toDistribSMul.{0, max (max u1 u5) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u1 u5) u2} (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Module.toDistribMulAction.{0, max (max u1 u5) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) Nat.semiring (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Pi.module.{u1, max u5 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u5, u2} R R Nat (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))))))) (SMulZeroClass.toSMul.{0, max (max u1 u5) u2} Nat (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (AddMonoid.toZero.{max (max u1 u5) u2} (LinearMap.{u3, u3, max 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(Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (LinearMap.addCommMonoid.{u3, u3, max u1 u5, u2} R R (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (DistribSMul.toSMulZeroClass.{0, max (max u1 u5) u2} Nat (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (AddMonoid.toAddZeroClass.{max (max u1 u5) u2} (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u1 u5) u2} (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (LinearMap.addCommMonoid.{u3, u3, max u1 u5, u2} R R (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (DistribMulAction.toDistribSMul.{0, max (max u1 u5) u2} Nat (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u1 u5) u2} (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ 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_inst_1 _inst_4 _inst_5))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u5) u2, 0, max (max u1 u5) u2, max (max u1 u5) u2} (LinearEquiv.{0, 0, max (max u1 u5) u2, max u2 u5 u1} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι 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(AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))))) (Module.toDistribMulAction.{0, max (max u1 u5) u2} Nat (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u3, u3, max u1 u5, u2} R R (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) 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(fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))) (SemilinearEquivClass.instSemilinearMapClass.{0, 0, max (max u1 u5) u2, max (max u1 u5) u2, max (max u1 u5) u2} Nat Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R 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_inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, max u1 u5, u2} R R (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u5 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 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_inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, max u1 u5, u2} R R (Dfinsupp.{u1, u5} ι (fun 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i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u5, u2} R R Nat (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{0, 0, max (max u1 u5) u2, max (max u1 u5) u2} Nat Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, max u1 u5, u2} R R (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u5 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u5, u2} R R Nat (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u5, u2} R R Nat (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u1, u3, 0, u5, u2} ι R Nat β₁ N (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i) _inst_4 _inst_5 Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))) (fun (i : ι) => LinearMap.comp.{u3, u3, u3, u5, u4, u2} R R R (β₁ i) (β₂ i) N _inst_1 _inst_1 _inst_1 (_inst_7 i) (_inst_8 i) _inst_4 (_inst_10 i) (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomCompTriple.ids.{u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (h i) (f i))) l)
 Case conversion may be inaccurate. Consider using '#align dfinsupp.sum_map_range_index.linear_map Dfinsupp.sum_mapRange_index.linearMapₓ'. -/
 theorem sum_mapRange_index.linearMap [∀ (i : ι) (x : β₁ i), Decidable (x ≠ 0)]
     [∀ (i : ι) (x : β₂ i), Decidable (x ≠ 0)] {f : ∀ i, β₁ i →ₗ[R] β₂ i} {h : ∀ i, β₂ i →ₗ[R] N}
@@ -414,7 +414,7 @@ noncomputable def coprodMap (f : ∀ i : ι, M i →ₗ[R] N) : (Π₀ i, M i) 
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : ι -> Type.{u3}} {N : Type.{u4}} [_inst_1 : Semiring.{u2} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (M i)] [_inst_3 : forall (i : ι), Module.{u2, u3} R (M i) _inst_1 (_inst_2 i)] [_inst_4 : AddCommMonoid.{u4} N] [_inst_5 : Module.{u2, u4} R N _inst_1 _inst_4] [_inst_6 : DecidableEq.{succ u1} ι] [_inst_7 : forall (x : N), Decidable (Ne.{succ u4} N x (OfNat.ofNat.{u4} N 0 (OfNat.mk.{u4} N 0 (Zero.zero.{u4} N (AddZeroClass.toHasZero.{u4} N (AddMonoid.toAddZeroClass.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_4)))))))] (f : forall (i : ι), LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (x : Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} ((fun (i : ι) => M i) i) (AddMonoid.toAddZeroClass.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i))))), Eq.{succ u4} N (coeFn.{max (succ (max u1 u3)) (succ u4), max (succ (max u1 u3)) (succ u4)} (LinearMap.{u2, u2, max u1 u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => M i) i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} ((fun (i : ι) => M i) i) (AddMonoid.toAddZeroClass.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) ((fun (i : ι) => _inst_2 i) i))))) N (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => M i) i) (fun (i : ι) => (fun (i : ι) => _inst_2 i) i)) _inst_4 (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => (fun (i : ι) => M i) i) _inst_1 (fun (i : ι) => (fun (i : ι) => _inst_2 i) i) (fun (i : ι) => (fun (i : ι) => _inst_3 i) i)) _inst_5) (fun (_x : LinearMap.{u2, u2, max u1 u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => M i) i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} ((fun (i : ι) => M i) i) (AddMonoid.toAddZeroClass.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) ((fun (i : ι) => _inst_2 i) i))))) N (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => M i) i) (fun (i : ι) => (fun (i : ι) => _inst_2 i) i)) _inst_4 (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => (fun (i : ι) => M i) i) _inst_1 (fun (i : ι) => (fun (i : ι) => _inst_2 i) i) (fun (i : ι) => (fun (i : ι) => _inst_3 i) i)) _inst_5) => (Dfinsupp.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => M i) i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} ((fun (i : ι) => M i) i) (AddMonoid.toAddZeroClass.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) ((fun (i : ι) => _inst_2 i) i))))) -> N) (LinearMap.hasCoeToFun.{u2, u2, max u1 u3, u4} R R (Dfinsupp.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => M i) i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} ((fun (i : ι) => M i) i) (AddMonoid.toAddZeroClass.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) ((fun (i : ι) => _inst_2 i) i))))) N _inst_1 _inst_1 (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => M i) i) (fun (i : ι) => (fun (i : ι) => _inst_2 i) i)) _inst_4 (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => (fun (i : ι) => M i) i) _inst_1 (fun (i : ι) => (fun (i : ι) => _inst_2 i) i) (fun (i : ι) => (fun (i : ι) => _inst_3 i) i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Dfinsupp.coprodMap.{u1, u2, u3, u4} ι R (fun (i : ι) => M i) N _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) _inst_4 _inst_5 (fun (a : ι) (b : ι) => _inst_6 a b) (fun (x : N) => _inst_7 x) f) x) (Finsupp.sum.{u1, u4, u4} ι N N (AddZeroClass.toHasZero.{u4} N (AddMonoid.toAddZeroClass.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_4))) _inst_4 (Dfinsupp.toFinsupp.{u1, u4} ι N (fun (a : ι) (b : ι) => _inst_6 a b) (AddZeroClass.toHasZero.{u4} N (AddMonoid.toAddZeroClass.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_4))) (fun (x : N) => _inst_7 x) (Dfinsupp.mapRange.{u1, u3, u4} ι (fun (i : ι) => M i) (fun (i : ι) => N) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i)))) (fun (i : ι) => AddZeroClass.toHasZero.{u4} N (AddMonoid.toAddZeroClass.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_4))) (fun (i : ι) => coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (fun (_x : LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) => (M i) -> N) (LinearMap.hasCoeToFun.{u2, u2, u3, u4} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (f i)) (fun (i : ι) => LinearMap.map_zero.{u2, u2, u3, u4} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (f i)) x)) (fun (i : ι) => id.{succ u4} N))
 but is expected to have type
-  forall {ι : Type.{u1}} {R : Type.{u4}} {M : ι -> Type.{u3}} {N : Type.{u2}} [_inst_1 : Semiring.{u4} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (M i)] [_inst_3 : forall (i : ι), Module.{u4, u3} R (M i) _inst_1 (_inst_2 i)] [_inst_4 : AddCommMonoid.{u2} N] [_inst_5 : Module.{u4, u2} R N _inst_1 _inst_4] [_inst_6 : DecidableEq.{succ u1} ι] [_inst_7 : forall (x : N), Decidable (Ne.{succ u2} N x (OfNat.ofNat.{u2} N 0 (Zero.toOfNat0.{u2} N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_4)))))] (f : forall (i : ι), LinearMap.{u4, u4, u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (x : Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) => N) x) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u3), succ u2} (LinearMap.{u4, u4, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u3, u4} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5) (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) (fun (_x : Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) => N) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u1 u3, u2} R R (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u3, u4} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Dfinsupp.coprodMap.{u1, u4, u3, u2} ι R (fun (i : ι) => M i) N _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) _inst_4 _inst_5 (fun (a : ι) (b : ι) => _inst_6 a b) (fun (x : N) => _inst_7 x) f) x) (Finsupp.sum.{u1, u2, u2} ι N N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_4)) _inst_4 (Dfinsupp.toFinsupp.{u1, u2} ι N (fun (a : ι) (b : ι) => _inst_6 a b) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_4)) (fun (x : N) => _inst_7 x) (Dfinsupp.mapRange.{u1, u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => N) (fun (i : ι) => AddMonoid.toZero.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))) (fun (i : ι) => AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_4)) (fun (i : ι) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (LinearMap.{u4, u4, u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (M i) (fun (_x : M i) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M i) => N) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, u2} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (f i)) (fun (i : ι) => LinearMap.map_zero.{u4, u4, u3, u2} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (f i)) x)) (fun (i : ι) => id.{succ u2} N))
+  forall {ι : Type.{u1}} {R : Type.{u4}} {M : ι -> Type.{u3}} {N : Type.{u2}} [_inst_1 : Semiring.{u4} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (M i)] [_inst_3 : forall (i : ι), Module.{u4, u3} R (M i) _inst_1 (_inst_2 i)] [_inst_4 : AddCommMonoid.{u2} N] [_inst_5 : Module.{u4, u2} R N _inst_1 _inst_4] [_inst_6 : DecidableEq.{succ u1} ι] [_inst_7 : forall (x : N), Decidable (Ne.{succ u2} N x (OfNat.ofNat.{u2} N 0 (Zero.toOfNat0.{u2} N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_4)))))] (f : forall (i : ι), LinearMap.{u4, u4, u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (x : Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) => N) x) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u3), succ u2} (LinearMap.{u4, u4, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u3, u4} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5) (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) (fun (_x : Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) => N) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u1 u3, u2} R R (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u3, u4} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Dfinsupp.coprodMap.{u1, u4, u3, u2} ι R (fun (i : ι) => M i) N _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) _inst_4 _inst_5 (fun (a : ι) (b : ι) => _inst_6 a b) (fun (x : N) => _inst_7 x) f) x) (Finsupp.sum.{u1, u2, u2} ι N N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_4)) _inst_4 (Dfinsupp.toFinsupp.{u1, u2} ι N (fun (a : ι) (b : ι) => _inst_6 a b) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_4)) (fun (x : N) => _inst_7 x) (Dfinsupp.mapRange.{u1, u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => N) (fun (i : ι) => AddMonoid.toZero.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))) (fun (i : ι) => AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_4)) (fun (i : ι) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (LinearMap.{u4, u4, u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (M i) (fun (_x : M i) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M i) => N) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, u2} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (f i)) (fun (i : ι) => LinearMap.map_zero.{u4, u4, u3, u2} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (f i)) x)) (fun (i : ι) => id.{succ u2} N))
 Case conversion may be inaccurate. Consider using '#align dfinsupp.coprod_map_apply Dfinsupp.coprodMap_applyₓ'. -/
 theorem coprodMap_apply (f : ∀ i : ι, M i →ₗ[R] N) (x : Π₀ i, M i) :
     coprodMap f x =
@@ -482,7 +482,7 @@ theorem dfinsupp_sumAddHom_mem {β : ι → Type _} [∀ i, AddZeroClass (β i)]
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} N] [_inst_3 : Module.{u2, u3} R N _inst_1 _inst_2] (p : ι -> (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3)), Eq.{succ u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (iSup.{u3, succ u1} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u3} R N _inst_1 _inst_2 _inst_3))) ι p) (LinearMap.range.{u2, u2, max u1 u3, u3, max u1 u3} R R (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (AddMonoid.toAddZeroClass.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (AddCommMonoid.toAddMonoid.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (Submodule.addCommMonoid.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i)))))) N _inst_1 _inst_1 (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (i : ι) => Submodule.addCommMonoid.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_2 (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, max u1 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (AddMonoid.toAddZeroClass.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (AddCommMonoid.toAddMonoid.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 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Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u3} N _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R N (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} N _inst_2) (Module.toDistribMulAction.{u2, u3} R N _inst_1 _inst_2 _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)) (Dfinsupp.lsum.{u1, u2, 0, u3, u3} ι R Nat (fun (i : ι) => coeSort.{succ u3, succ (succ 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 but is expected to have type
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(Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N _inst_1 _inst_1 (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, max u1 u2, u2} R R (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_2 (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N _inst_1 _inst_1 (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u2, u2} R R Nat (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N _inst_1 _inst_1 (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u2, u2} R R Nat (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_2 (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u1, u3, 0, u2, u2} ι R Nat (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 _inst_3 Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3))) (fun (i : ι) => Submodule.subtype.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))
 Case conversion may be inaccurate. Consider using '#align submodule.supr_eq_range_dfinsupp_lsum Submodule.iSup_eq_range_dfinsupp_lsumₓ'. -/
 /-- The supremum of a family of submodules is equal to the range of `dfinsupp.lsum`; that is
 every element in the `supr` can be produced from taking a finite number of non-zero elements
@@ -502,7 +502,7 @@ theorem iSup_eq_range_dfinsupp_lsum (p : ι → Submodule R N) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} N] [_inst_3 : Module.{u2, u3} R N _inst_1 _inst_2] (p : ι -> Prop) [_inst_4 : DecidablePred.{succ u1} ι p] (S : ι -> (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3)), Eq.{succ u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (iSup.{u3, succ u1} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u3} R N _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => iSup.{u3, 0} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u3} R N _inst_1 _inst_2 _inst_3))) (p i) (fun (h : p i) => S i))) (LinearMap.range.{u2, u2, max u1 u3, u3, max u1 u3} R R (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (S i)) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (S i)) (AddMonoid.toAddZeroClass.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (S i)) (AddCommMonoid.toAddMonoid.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (S i)) (Submodule.addCommMonoid.{u2, u3} R N _inst_1 _inst_2 _inst_3 (S i)))))) N _inst_1 _inst_1 (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (S i)) (fun (i : ι) => Submodule.addCommMonoid.{u2, u3} R N _inst_1 _inst_2 _inst_3 (S i))) _inst_2 (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} 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 but is expected to have type
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(Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} N _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R N (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_2) (Module.toDistribMulAction.{u2, u1} R N _inst_1 _inst_2 _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u3, u2, 0, u1, u1} ι R Nat (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) N (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 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(Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) N (Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_2 (Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u1, u1} R R (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) N _inst_1 _inst_1 (Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_2 (Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u3 u1, u1} R R (Dfinsupp.{u3, u1} ι (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) (fun (i : ι) => AddMonoid.toZero.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (AddCommMonoid.toAddMonoid.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u1} ι (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) (fun (i : ι) => Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))) _inst_2 (Dfinsupp.module.{u3, u1, u2} ι R (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) (fun (i : ι) => Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) N (Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_2 (Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_3) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u1, u1} R R (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) N _inst_1 _inst_1 (Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_2 (Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u1, u1} R R Nat (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) N _inst_1 _inst_1 (Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_2 (Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} N _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R N (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_2) (Module.toDistribMulAction.{u2, u1} R N _inst_1 _inst_2 _inst_3)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u3 u1, u1} R R Nat (Dfinsupp.{u3, u1} ι (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) (fun (i : ι) => AddMonoid.toZero.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (AddCommMonoid.toAddMonoid.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u1} ι (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) (fun (i : ι) => Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))) _inst_2 (Dfinsupp.module.{u3, u1, u2} ι R (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) (fun (i : ι) => Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} N _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R N (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_2) (Module.toDistribMulAction.{u2, u1} R N _inst_1 _inst_2 _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u3, u2, 0, u1, u1} ι R Nat (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) N (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) (fun (i : ι) => Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_2 _inst_3 Nat.semiring (AddCommMonoid.natModule.{u1} N _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R N (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_2) (Module.toDistribMulAction.{u2, u1} R N _inst_1 _inst_2 _inst_3))) (fun (i : ι) => Submodule.subtype.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))) (Dfinsupp.filterLinearMap.{u3, u1, u2} ι R (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) (fun (i : ι) => Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) p (fun (a : ι) => _inst_4 a))))
 Case conversion may be inaccurate. Consider using '#align submodule.bsupr_eq_range_dfinsupp_lsum Submodule.biSup_eq_range_dfinsupp_lsumₓ'. -/
 /-- The bounded supremum of a family of commutative additive submonoids is equal to the range of
 `dfinsupp.sum_add_hom` composed with `dfinsupp.filter_add_monoid_hom`; that is, every element in the
@@ -528,7 +528,7 @@ theorem biSup_eq_range_dfinsupp_lsum (p : ι → Prop) [DecidablePred p] (S : ι
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} N] [_inst_3 : Module.{u2, u3} R N _inst_1 _inst_2] (p : ι -> (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (x : N), Iff (Membership.Mem.{u3, u3} N (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) x (iSup.{u3, succ u1} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u3} R N _inst_1 _inst_2 _inst_3))) ι p)) (Exists.{succ (max u1 u3)} (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (i : ι) => Submodule.zero.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i))) (fun (f : Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (i : ι) => Submodule.zero.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i))) => Eq.{succ u3} N (coeFn.{max (succ (max u1 u3)) (succ u3), max (succ (max u1 u3)) (succ u3)} (LinearMap.{u2, u2, max u1 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (AddMonoid.toAddZeroClass.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (AddCommMonoid.toAddMonoid.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (Submodule.addCommMonoid.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i)))))) N 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 but is expected to have type
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(Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_2 (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u1, u3, 0, u2, u2} ι R Nat (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 _inst_3 Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3))) (fun (i : ι) => Submodule.subtype.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) f) x))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_iff_exists_dfinsupp Submodule.mem_iSup_iff_exists_dfinsuppₓ'. -/
 theorem mem_iSup_iff_exists_dfinsupp (p : ι → Submodule R N) (x : N) :
     x ∈ iSup p ↔ ∃ f : Π₀ i, p i, Dfinsupp.lsum ℕ (fun i => (p i).Subtype) f = x :=
@@ -554,7 +554,7 @@ theorem mem_iSup_iff_exists_dfinsupp' (p : ι → Submodule R N) [∀ (i) (x : p
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} N] [_inst_3 : Module.{u2, u3} R N _inst_1 _inst_2] (p : ι -> Prop) [_inst_4 : DecidablePred.{succ u1} ι p] (S : ι -> (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (x : N), Iff (Membership.Mem.{u3, u3} N (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) x (iSup.{u3, succ u1} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u3} R N _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => iSup.{u3, 0} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u3} 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 but is expected to have type
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(Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (AddCommMonoid.toAddMonoid.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u1} ι (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) (fun (i : ι) => Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))) _inst_2 (Dfinsupp.module.{u3, u1, u2} ι R (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) (fun (i : ι) => Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} N _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R N (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_2) (Module.toDistribMulAction.{u2, u1} R N _inst_1 _inst_2 _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u3, u2, 0, u1, u1} ι R Nat (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) N (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) (fun (i : ι) => Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_2 _inst_3 Nat.semiring (AddCommMonoid.natModule.{u1} N _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R N (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_2) (Module.toDistribMulAction.{u2, u1} R N _inst_1 _inst_2 _inst_3))) (fun (i : ι) => Submodule.subtype.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))) (Dfinsupp.filter.{u3, u1} ι (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) (fun (i : ι) => AddMonoid.toZero.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (AddCommMonoid.toAddMonoid.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)))) p (fun (a : ι) => _inst_4 a) f)) x))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_bsupr_iff_exists_dfinsupp Submodule.mem_biSup_iff_exists_dfinsuppₓ'. -/
 theorem mem_biSup_iff_exists_dfinsupp (p : ι → Prop) [DecidablePred p] (S : ι → Submodule R N)
     (x : N) :
@@ -624,7 +624,7 @@ variable [Semiring R] [AddCommMonoid N] [Module R N]
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} N] [_inst_3 : Module.{u2, u3} R N _inst_1 _inst_2] (p : ι -> (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3)), Iff (CompleteLattice.Independent.{succ u1, u3} ι (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u3} R N _inst_1 _inst_2 _inst_3) p) (forall (i : ι) (x : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (v : Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (i : ι) => 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 but is expected to have type
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Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N _inst_1 _inst_1 (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u2, u2} R R Nat (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N _inst_1 _inst_1 (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u2, u2} R R Nat (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_2 (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u1, u3, 0, u2, u2} ι R Nat (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 _inst_3 Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3))) (fun (i : ι) => Submodule.subtype.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) (Dfinsupp.erase.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)))) i v)) (Subtype.val.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Set.{u2} N) (Set.instMembershipSet.{u2} N) x (SetLike.coe.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3) (p i))) x)) -> (Eq.{succ u2} (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) x (OfNat.ofNat.{u2} (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) 0 (Zero.toOfNat0.{u2} (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (Submodule.zero.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))))
 Case conversion may be inaccurate. Consider using '#align complete_lattice.independent_iff_forall_dfinsupp CompleteLattice.independent_iff_forall_dfinsuppₓ'. -/
 /-- Independence of a family of submodules can be expressed as a quantifier over `dfinsupp`s.
 
@@ -648,7 +648,7 @@ theorem independent_iff_forall_dfinsupp (p : ι → Submodule R N) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} N] [_inst_3 : Module.{u2, u3} R N _inst_1 _inst_2] (p : ι -> (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3)), (Function.Injective.{succ (max u1 u3), succ u3} (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (AddMonoid.toAddZeroClass.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (AddCommMonoid.toAddMonoid.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (Submodule.addCommMonoid.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i)))))) N (coeFn.{max (succ (max u1 u3)) (succ u3), max (succ (max u1 u3)) (succ u3)} (LinearMap.{u2, u2, max u1 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (i : ι) => 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 but is expected to have type
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Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_2 (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{0, 0, max u1 u2, max u1 u2} Nat Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3) (LinearMap.{u3, u3, max u2 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_2 (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N _inst_1 _inst_1 (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, max u1 u2, u2} R R (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_2 (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N _inst_1 _inst_1 (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u2, u2} R R Nat (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N _inst_1 _inst_1 (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u2, u2} R R Nat (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_2 (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u1, u3, 0, u2, u2} ι R Nat (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 _inst_3 Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3))) (fun (i : ι) => Submodule.subtype.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))) -> (CompleteLattice.Independent.{succ u1, u2} ι (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u3, u2} R N _inst_1 _inst_2 _inst_3) p)
 Case conversion may be inaccurate. Consider using '#align complete_lattice.independent_of_dfinsupp_lsum_injective CompleteLattice.independent_of_dfinsupp_lsum_injectiveₓ'. -/
 /- If `dfinsupp.lsum` applied with `submodule.subtype` is injective then the submodules are
 independent. -/
@@ -683,7 +683,7 @@ theorem independent_of_dfinsupp_sumAddHom_injective (p : ι → AddSubmonoid N)
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} N] [_inst_3 : Module.{u2, u3} R N _inst_1 _inst_2] [_inst_4 : forall (m : R), Decidable (Ne.{succ u2} R m (OfNat.ofNat.{u2} R 0 (OfNat.mk.{u2} R 0 (Zero.zero.{u2} R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))))] (p : ι -> (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3)) {v : ι -> N} (hv : forall (i : ι), Membership.Mem.{u3, u3} N (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (v i) (p i)), Eq.{max (succ (max u1 u2)) (succ u3)} (LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) N (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_3) (LinearMap.comp.{u2, u2, u2, max u1 u2, max u1 u3, u3} R R R (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (AddMonoid.toAddZeroClass.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (AddCommMonoid.toAddMonoid.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (Submodule.addCommMonoid.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i)))))) N _inst_1 _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (i : ι) => Submodule.addCommMonoid.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_2 (Finsupp.module.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomCompTriple.right_ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (coeFn.{succ (max u1 u3), succ (max u1 u3)} (LinearEquiv.{0, 0, max u1 u3, max u1 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) N (Submodule.addCommMonoid.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3) (LinearMap.{u2, u2, max u1 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (AddMonoid.toAddZeroClass.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (AddCommMonoid.toAddMonoid.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) 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u3} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomCompTriple.right_ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Dfinsupp.mapRange.linearMap.{u1, u2, u2, u3} ι R _inst_1 (fun (i : ι) => R) (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => Submodule.addCommMonoid.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) (fun (i : ι) => Submodule.module.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => LinearMap.toSpanSingleton.{u2, u3} R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) _inst_1 (Submodule.addCommMonoid.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i)) (Submodule.module.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i)) (Subtype.mk.{succ u3} N (fun (x : N) => Membership.Mem.{u3, u3} N (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) x (p i)) (v i) (hv i)))) (LinearEquiv.toLinearMap.{u2, u2, max u1 u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) (Dfinsupp.{u1, u2} ι (fun (i : ι) => R) (fun (i : ι) => AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Dfinsupp.addCommMonoid.{u1, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (Dfinsupp.module.{u1, u2, u2} ι R (fun (i : ι) => R) _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) (finsuppLequivDfinsupp.{u1, u2, u2} ι R R (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (m : R) => _inst_4 m) (Semiring.toModule.{u2} R _inst_1))))) (Finsupp.total.{u1, u3, u2} ι N R _inst_1 _inst_2 _inst_3 v)
 but is expected to have type
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+  forall {ι : Type.{u1}} {R : Type.{u3}} {N : Type.{u2}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} N] [_inst_3 : Module.{u3, u2} R N _inst_1 _inst_2] [_inst_4 : forall (m : R), Decidable (Ne.{succ u3} R m (OfNat.ofNat.{u3} R 0 (Zero.toOfNat0.{u3} R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)))))] (p : ι -> (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) {v : ι -> N} (hv : forall (i : ι), Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) (v i) (p i)), Eq.{max (max (succ u1) (succ u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} ι R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R 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(Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u2, u2} R R Nat (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N _inst_1 _inst_1 (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u2, u2} R R Nat (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_2 (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u1, u3, 0, u2, u2} ι R Nat (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 _inst_3 Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3))) (fun (i : ι) => Submodule.subtype.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) (LinearMap.comp.{u3, u3, u3, max u1 u3, max u1 u3, max u1 u2} R R R (Finsupp.{u1, u3} ι R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (Dfinsupp.{u1, u3} ι (fun (i : ι) => R) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => R) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => R) i) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))) _inst_1 _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u3} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) (Finsupp.module.{u1, u3, u3} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (Dfinsupp.module.{u1, u3, u3} ι R (fun (i : ι) => R) _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => Semiring.toModule.{u3} R _inst_1)) (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomCompTriple.ids.{u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Dfinsupp.mapRange.linearMap.{u1, u3, u3, u2} ι R _inst_1 (fun (i : ι) => R) (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Semiring.toModule.{u3} R _inst_1) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => LinearMap.toSpanSingleton.{u3, u2} R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) _inst_1 (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (Subtype.mk.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i)) (v i) (hv i)))) (LinearEquiv.toLinearMap.{u3, u3, max u1 u3, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.{u1, u3} ι R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (Dfinsupp.{u1, u3} ι (fun (i : ι) => R) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (_i : ι) => R) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (_i : ι) => R) i) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (Finsupp.addCommMonoid.{u1, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u3} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (Dfinsupp.module.{u1, u3, u3} ι R (fun (i : ι) => R) _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => Semiring.toModule.{u3} R _inst_1)) (finsuppLequivDfinsupp.{u1, u3, u3} ι R R (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (m : R) => _inst_4 m) (Semiring.toModule.{u3} R _inst_1))))) (Finsupp.total.{u1, u2, u3} ι N R _inst_1 _inst_2 _inst_3 v)
 Case conversion may be inaccurate. Consider using '#align complete_lattice.lsum_comp_map_range_to_span_singleton CompleteLattice.lsum_comp_mapRange_toSpanSingletonₓ'. -/
 /-- Combining `dfinsupp.lsum` with `linear_map.to_span_singleton` is the same as `finsupp.total` -/
 theorem lsum_comp_mapRange_toSpanSingleton [∀ m : R, Decidable (m ≠ 0)] (p : ι → Submodule R N)
@@ -723,7 +723,7 @@ theorem independent_of_dfinsupp_sumAddHom_injective' (p : ι → AddSubgroup N)
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} N] [_inst_3 : Module.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2)] {p : ι -> (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3)}, (CompleteLattice.Independent.{succ u1, u3} ι (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) (Submodule.completeLattice.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) p) -> (Function.Injective.{succ (max u1 u3), succ u3} (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R 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(AddGroup.toSubNegMonoid.{u3} N (AddCommGroup.toAddGroup.{u3} N _inst_2))) (Module.toDistribMulAction.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3))) (fun (i : ι) => Submodule.subtype.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3 (p i)))))
 but is expected to have type
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(AddCommGroup.toAddCommMonoid.{u2} N _inst_2)) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u2, u2} R R Nat (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) 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u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)))) Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (LinearMap.{u3, u3, max u2 u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (Ring.toSemiring.{u3} R _inst_1) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) _inst_3) (SMulZeroClass.toSMul.{0, max u1 u2} Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (AddMonoid.toZero.{max u1 u2} (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{0, max u1 u2} Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R 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(Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R 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(Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))))))) (DistribMulAction.toDistribSMul.{0, max u1 u2} Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max u1 u2} (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))))) (Module.toDistribMulAction.{0, max u1 u2} Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) Nat.semiring (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) 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R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) Nat.semiring (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N 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u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u1, u3, 0, u2, u2} ι R Nat (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N 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+  forall {ι : Type.{u1}} {R : Type.{u3}} {N : Type.{u2}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u2} N] [_inst_3 : Module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)] {p : ι -> (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)}, (CompleteLattice.Independent.{succ u1, u2} ι (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (Submodule.completeLattice.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) p) -> (Function.Injective.{max (succ u1) (succ u2), succ u2} (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N 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u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)))) Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x 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_inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N 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=> LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))))) (Module.toDistribMulAction.{0, max u1 u2} Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) Nat.semiring (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))))) (Pi.module.{u1, u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u2, u2} R R Nat (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u2} N (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)))))))) (SMulZeroClass.toSMul.{0, max u1 u2} Nat (LinearMap.{u3, u3, max u2 u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} 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_inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (Ring.toSemiring.{u3} R _inst_1) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) _inst_3) (AddMonoid.toZero.{max u1 u2} (LinearMap.{u3, u3, max u2 u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N 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_inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))))) (LinearMap.addCommMonoid.{u3, u3, max u1 u2, u2} R R (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (Ring.toSemiring.{u3} R _inst_1) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) (Pi.module.{u1, u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u2, u2} R R Nat (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u2} N (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u2, u2} R R Nat (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (Ring.toSemiring.{u3} R _inst_1) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u2} N (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u1, u3, 0, u2, u2} ι R Nat (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (fun (a : ι) (b : ι) => dec_ι a b) (Ring.toSemiring.{u3} R _inst_1) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 Nat.semiring (AddCommMonoid.natModule.{u2} N (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3))) (fun (i : ι) => Submodule.subtype.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)))))
 Case conversion may be inaccurate. Consider using '#align complete_lattice.independent.dfinsupp_lsum_injective CompleteLattice.Independent.dfinsupp_lsum_injectiveₓ'. -/
 /-- The canonical map out of a direct sum of a family of submodules is injective when the submodules
 are `complete_lattice.independent`.
@@ -772,7 +772,7 @@ theorem Independent.dfinsupp_sumAddHom_injective {p : ι → AddSubgroup N} (h :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} N] [_inst_3 : Module.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2)] (p : ι -> (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3)), Iff (CompleteLattice.Independent.{succ u1, u3} ι (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) (Submodule.completeLattice.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) p) (Function.Injective.{succ (max u1 u3), succ u3} (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R 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(AddGroup.toSubNegMonoid.{u3} N (AddCommGroup.toAddGroup.{u3} N _inst_2))) (Module.toDistribMulAction.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3))) (fun (i : ι) => Submodule.subtype.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3 (p i)))))
 but is expected to have type
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(AddCommGroup.toAddCommMonoid.{u2} N _inst_2)) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u2, u2} R R Nat (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) 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u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)))) Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (LinearMap.{u3, u3, max u2 u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (Ring.toSemiring.{u3} R _inst_1) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) _inst_3) (SMulZeroClass.toSMul.{0, max u1 u2} Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (AddMonoid.toZero.{max u1 u2} (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{0, max u1 u2} Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R 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(Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R 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(Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))))))) (DistribMulAction.toDistribSMul.{0, max u1 u2} Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max u1 u2} (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))))) (Module.toDistribMulAction.{0, max u1 u2} Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) Nat.semiring (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) 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R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) Nat.semiring (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N 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(AddCommGroup.toAddCommMonoid.{u2} N _inst_2)) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u2, u2} R R Nat (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) 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u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u1, u3, 0, u2, u2} ι R Nat (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N 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+  forall {ι : Type.{u1}} {R : Type.{u3}} {N : Type.{u2}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u2} N] [_inst_3 : Module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)] (p : ι -> (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)), Iff (CompleteLattice.Independent.{succ u1, u2} ι (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (Submodule.completeLattice.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) p) (Function.Injective.{max (succ u1) (succ u2), succ u2} (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N 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u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)))) Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x 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_inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N 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=> LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))))) (Module.toDistribMulAction.{0, max u1 u2} Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) Nat.semiring (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))))) (Pi.module.{u1, u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u2, u2} R R Nat (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u2} N (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)))))))) (SMulZeroClass.toSMul.{0, max u1 u2} Nat (LinearMap.{u3, u3, max u2 u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} 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_inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (Ring.toSemiring.{u3} R _inst_1) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) _inst_3) (AddMonoid.toZero.{max u1 u2} (LinearMap.{u3, u3, max u2 u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N 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_inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N 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(AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (Ring.toSemiring.{u3} R _inst_1) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) (Pi.module.{u1, u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u2, u2} R R Nat (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u2} N (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u2, u2} R R Nat (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (Ring.toSemiring.{u3} R _inst_1) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u2} N (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u1, u3, 0, u2, u2} ι R Nat (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (fun (a : ι) (b : ι) => dec_ι a b) (Ring.toSemiring.{u3} R _inst_1) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 Nat.semiring (AddCommMonoid.natModule.{u2} N (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3))) (fun (i : ι) => Submodule.subtype.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)))))
 Case conversion may be inaccurate. Consider using '#align complete_lattice.independent_iff_dfinsupp_lsum_injective CompleteLattice.independent_iff_dfinsupp_lsum_injectiveₓ'. -/
 /-- A family of submodules over an additive group are independent if and only iff `dfinsupp.lsum`
 applied with `submodule.subtype` is injective.

f4758115

bump to nightly-2023-05-18-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/c89fe2d59ae06402c3f55f978016d1ada444f57e

b46e9d53

Diff

@@ -84,7 +84,7 @@ def lsingle (i) : M i →ₗ[R] Π₀ i, M i :=
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : ι -> Type.{u3}} {N : Type.{u4}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (M i)] [_inst_3 : forall (i : ι), Module.{u2, u3} R (M i) _inst_1 (_inst_2 i)] [_inst_4 : AddCommMonoid.{u4} N] [_inst_5 : Module.{u2, u4} R N _inst_1 _inst_4] {{φ : LinearMap.{u2, u2, max u1 u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))))) N (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5}} {{ψ : LinearMap.{u2, u2, max u1 u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))))) N (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5}}, (forall (i : ι) (x : M i), Eq.{succ u4} N (coeFn.{max (succ (max u1 u3)) (succ u4), max (succ (max u1 u3)) (succ u4)} (LinearMap.{u2, u2, max u1 u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))))) N (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => M i) _inst_1 (fun 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 but is expected to have type
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+  forall {ι : Type.{u2}} {R : Type.{u4}} {M : ι -> Type.{u3}} {N : Type.{u1}} [dec_ι : DecidableEq.{succ u2} ι] [_inst_1 : Semiring.{u4} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (M i)] [_inst_3 : forall (i : ι), Module.{u4, u3} R (M i) _inst_1 (_inst_2 i)] [_inst_4 : AddCommMonoid.{u1} N] [_inst_5 : Module.{u4, u1} R N _inst_1 _inst_4] {{φ : LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Dfinsupp.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u2, u3, u4} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5}} {{ψ : LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R 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(AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i))) i x))) -> (Eq.{max (max (succ u2) (succ u3)) (succ u1)} (LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Dfinsupp.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u2, u3, u4} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5) φ ψ)
 Case conversion may be inaccurate. Consider using '#align dfinsupp.lhom_ext Dfinsupp.lhom_extₓ'. -/
 /-- Two `R`-linear maps from `Π₀ i, M i` which agree on each `single i x` agree everywhere. -/
 theorem lhom_ext ⦃φ ψ : (Π₀ i, M i) →ₗ[R] N⦄ (h : ∀ i x, φ (single i x) = ψ (single i x)) : φ = ψ :=
@@ -129,7 +129,7 @@ include dec_ι
 lean 3 declaration is
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 but is expected to have type
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(Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x (Finset.toSet.{u3} ι s)) i)) R _inst_1 (fun (i : Set.Elem.{u3} ι (Finset.toSet.{u3} ι s)) => _inst_2 (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x (Finset.toSet.{u3} ι s)) i)) (fun (i : Set.Elem.{u3} ι (Finset.toSet.{u3} ι s)) => _inst_3 (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x (Finset.toSet.{u3} ι s)) i))) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Dfinsupp.lmk.{u3, u1, u2} ι R (fun (i : ι) => M i) (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) s) x) (Dfinsupp.mk.{u3, u2} ι M (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => AddMonoid.toZero.{u2} (M i) (AddCommMonoid.toAddMonoid.{u2} (M i) (_inst_2 i))) s x)
+  forall {ι : Type.{u3}} {R : Type.{u1}} {M : ι -> Type.{u2}} [dec_ι : DecidableEq.{succ u3} ι] [_inst_1 : Semiring.{u1} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (M i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (M i) _inst_1 (_inst_2 i)] (s : Finset.{u3} ι) (x : forall (i : Set.Elem.{u3} ι (Finset.toSet.{u3} ι s)), M (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x (Finset.toSet.{u3} ι s)) i)), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : forall (i : Set.Elem.{u3} ι (Finset.toSet.{u3} ι s)), M (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x (Finset.toSet.{u3} ι s)) i)) => Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) x) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ 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 Case conversion may be inaccurate. Consider using '#align dfinsupp.lmk_apply Dfinsupp.lmk_applyₓ'. -/
 @[simp]
 theorem lmk_apply (s : Finset ι) (x) : (lmk s : _ →ₗ[R] Π₀ i, M i) x = mk s x :=
@@ -140,7 +140,7 @@ theorem lmk_apply (s : Finset ι) (x) : (lmk s : _ →ₗ[R] Π₀ i, M i) x = m
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : ι -> Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (M i)] [_inst_3 : forall (i : ι), Module.{u2, u3} R (M i) _inst_1 (_inst_2 i)] (i : ι) (x : M i), Eq.{succ (max u1 u3)} (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))))) (coeFn.{max (succ u3) (succ (max u1 u3)), max (succ u3) (succ (max u1 u3))} (LinearMap.{u2, u2, u3, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (M i) (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))))) (_inst_2 i) (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (fun (_x : LinearMap.{u2, u2, u3, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (M i) (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))))) (_inst_2 i) (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) => (M i) -> (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i)))))) (LinearMap.hasCoeToFun.{u2, u2, u3, max u1 u3} R R (M i) (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))))) _inst_1 _inst_1 (_inst_2 i) (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Dfinsupp.lsingle.{u1, u2, u3} ι R (fun (i : ι) => M i) (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i) x) (Dfinsupp.single.{u1, u3} ι (fun (i : ι) => M i) (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i)))) i x)
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u1}} {M : ι -> Type.{u2}} [dec_ι : DecidableEq.{succ u3} ι] [_inst_1 : Semiring.{u1} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (M i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (M i) _inst_1 (_inst_2 i)] (i : ι) (x : M i), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M i) => Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) x) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (M i) (Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) (_inst_2 i) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (M i) (fun (_x : M i) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M i) => Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u2} R R (M i) (Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) _inst_1 _inst_1 (_inst_2 i) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Dfinsupp.lsingle.{u3, u1, u2} ι R M (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i) x) (Dfinsupp.single.{u3, u2} ι M (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => AddMonoid.toZero.{u2} (M i) (AddCommMonoid.toAddMonoid.{u2} (M i) (_inst_2 i))) i x)
+  forall {ι : Type.{u3}} {R : Type.{u1}} {M : ι -> Type.{u2}} [dec_ι : DecidableEq.{succ u3} ι] [_inst_1 : Semiring.{u1} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (M i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (M i) _inst_1 (_inst_2 i)] (i : ι) (x : M i), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M i) => Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) x) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (M i) (Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) (_inst_2 i) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (M i) (fun (_x : M i) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M i) => Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u2} R R (M i) (Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) _inst_1 _inst_1 (_inst_2 i) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Dfinsupp.lsingle.{u3, u1, u2} ι R M (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i) x) (Dfinsupp.single.{u3, u2} ι M (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => AddMonoid.toZero.{u2} (M i) (AddCommMonoid.toAddMonoid.{u2} (M i) (_inst_2 i))) i x)
 Case conversion may be inaccurate. Consider using '#align dfinsupp.lsingle_apply Dfinsupp.lsingle_applyₓ'. -/
 @[simp]
 theorem lsingle_apply (i : ι) (x : M i) : (lsingle i : _ →ₗ[R] _) x = single i x :=
@@ -153,7 +153,7 @@ omit dec_ι
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : ι -> Type.{u3}} [_inst_1 : Semiring.{u2} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (M i)] [_inst_3 : forall (i : ι), Module.{u2, u3} R (M i) _inst_1 (_inst_2 i)] (i : ι) (f : Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} ((fun (i : ι) => M i) i) (AddMonoid.toAddZeroClass.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i))))), Eq.{succ u3} (M i) (coeFn.{max (succ (max u1 u3)) (succ u3), max (succ (max u1 u3)) (succ u3)} (LinearMap.{u2, u2, max u1 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))))) (M i) (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i)) (fun (_x : LinearMap.{u2, u2, max u1 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))))) (M i) (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i)) => (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))))) -> (M i)) (LinearMap.hasCoeToFun.{u2, u2, max u1 u3, u3} R R (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))))) (M i) _inst_1 _inst_1 (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Dfinsupp.lapply.{u1, u2, u3} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i) f) (coeFn.{succ (max u1 u3), max (succ u1) (succ u3)} (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} ((fun (i : ι) => M i) i) (AddMonoid.toAddZeroClass.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i))))) (fun (_x : Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} ((fun (i : ι) => M i) i) (AddMonoid.toAddZeroClass.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i))))) => forall (i : ι), M i) (Dfinsupp.hasCoeToFun.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} ((fun (i : ι) => M i) i) (AddMonoid.toAddZeroClass.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i))))) f i)
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u1}} {M : ι -> Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (M i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (M i) _inst_1 (_inst_2 i)] (i : ι) (f : Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) => M i) f) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), succ u2} (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) (M i) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i)) (Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) (fun (_x : Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) => M i) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u2, u2} R R (Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) (M i) _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Dfinsupp.lapply.{u3, u1, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i) f) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Dfinsupp.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => M i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => M i) i) _x) (Dfinsupp.funLike.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => M i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i))) i)) f i)
+  forall {ι : Type.{u3}} {R : Type.{u1}} {M : ι -> Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (M i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (M i) _inst_1 (_inst_2 i)] (i : ι) (f : Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) => M i) f) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), succ u2} (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) (M i) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i)) (Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) (fun (_x : Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) => M i) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u2, u2} R R (Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) (M i) _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Dfinsupp.lapply.{u3, u1, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i) f) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Dfinsupp.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => M i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => M i) i) _x) (Dfinsupp.funLike.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => M i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i))) i)) f i)
 Case conversion may be inaccurate. Consider using '#align dfinsupp.lapply_apply Dfinsupp.lapply_applyₓ'. -/
 @[simp]
 theorem lapply_apply (i : ι) (f : Π₀ i, M i) : (lapply i : _ →ₗ[R] _) f = f i :=
@@ -239,7 +239,7 @@ def lsum [Semiring S] [Module S N] [SMulCommClass R S N] :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} (S : Type.{u3}) {M : ι -> Type.{u4}} {N : Type.{u5}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u4} (M i)] [_inst_3 : forall (i : ι), Module.{u2, u4} R (M i) _inst_1 (_inst_2 i)] [_inst_4 : AddCommMonoid.{u5} N] [_inst_5 : Module.{u2, u5} R N _inst_1 _inst_4] [_inst_6 : Semiring.{u3} S] [_inst_7 : Module.{u3, u5} S N _inst_6 _inst_4] [_inst_8 : SMulCommClass.{u2, u3, u5} R S N (SMulZeroClass.toHasSmul.{u2, u5} R N (AddZeroClass.toHasZero.{u5} N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4))) (SMulWithZero.toSmulZeroClass.{u2, u5} R N (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))) (AddZeroClass.toHasZero.{u5} N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4))) (MulActionWithZero.toSMulWithZero.{u2, u5} R N (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddZeroClass.toHasZero.{u5} N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4))) (Module.toMulActionWithZero.{u2, u5} R N _inst_1 _inst_4 _inst_5)))) (SMulZeroClass.toHasSmul.{u3, u5} S N (AddZeroClass.toHasZero.{u5} N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4))) (SMulWithZero.toSmulZeroClass.{u3, u5} S N (MulZeroClass.toHasZero.{u3} S (MulZeroOneClass.toMulZeroClass.{u3} S (MonoidWithZero.toMulZeroOneClass.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_6)))) (AddZeroClass.toHasZero.{u5} N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4))) (MulActionWithZero.toSMulWithZero.{u3, u5} S N (Semiring.toMonoidWithZero.{u3} S _inst_6) (AddZeroClass.toHasZero.{u5} N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4))) (Module.toMulActionWithZero.{u3, u5} S N _inst_6 _inst_4 _inst_7))))] (F : forall (i : ι), LinearMap.{u2, u2, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (i : ι) (x : M i), Eq.{succ u5} N (coeFn.{max (succ (max u1 u4)) (succ u5), max (succ (max u1 u4)) (succ u5)} (LinearMap.{u2, u2, max u1 u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} (M i) (AddMonoid.toAddZeroClass.{u4} (M i) (AddCommMonoid.toAddMonoid.{u4} (M i) (_inst_2 i))))) N (Dfinsupp.addCommMonoid.{u1, u4} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u4, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5) (fun (_x : LinearMap.{u2, u2, max u1 u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} (M i) (AddMonoid.toAddZeroClass.{u4} (M i) (AddCommMonoid.toAddMonoid.{u4} (M i) (_inst_2 i))))) N (Dfinsupp.addCommMonoid.{u1, u4} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u4, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5) => (Dfinsupp.{u1, u4} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} (M i) (AddMonoid.toAddZeroClass.{u4} (M i) (AddCommMonoid.toAddMonoid.{u4} (M i) (_inst_2 i))))) -> N) (LinearMap.hasCoeToFun.{u2, u2, max u1 u4, u5} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} (M i) (AddMonoid.toAddZeroClass.{u4} (M i) (AddCommMonoid.toAddMonoid.{u4} (M i) (_inst_2 i))))) N _inst_1 _inst_1 (Dfinsupp.addCommMonoid.{u1, u4} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u4, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5 (RingHom.id.{u2} R 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 but is expected to have type
-  forall {ι : Type.{u1}} {R : Type.{u3}} (S : Type.{u5}) {M : ι -> Type.{u2}} {N : Type.{u4}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u3} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (M i)] [_inst_3 : forall (i : ι), Module.{u3, u2} R (M i) _inst_1 (_inst_2 i)] [_inst_4 : AddCommMonoid.{u4} N] [_inst_5 : Module.{u3, u4} R N _inst_1 _inst_4] [_inst_6 : Semiring.{u5} S] [_inst_7 : Module.{u5, u4} S N _inst_6 _inst_4] [_inst_8 : SMulCommClass.{u3, u5, u4} R S N (SMulZeroClass.toSMul.{u3, u4} R N (AddMonoid.toZero.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_4)) (SMulWithZero.toSMulZeroClass.{u3, u4} R N (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddMonoid.toZero.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_4)) (MulActionWithZero.toSMulWithZero.{u3, u4} R N (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddMonoid.toZero.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_4)) (Module.toMulActionWithZero.{u3, u4} R N _inst_1 _inst_4 _inst_5)))) 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(forall (i : ι), LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (AddMonoid.toAddZeroClass.{max (max u1 u2) u4} (forall (i : ι), LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u4} (forall (i : ι), LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (Pi.addCommMonoid.{u1, max u2 u4} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u4} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u5, max (max u1 u2) u4} S (forall (i : ι), LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (MonoidWithZero.toMonoid.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u4} (forall (i : ι), LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (Pi.addCommMonoid.{u1, max u2 u4} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u4} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Module.toDistribMulAction.{u5, max (max u1 u2) u4} S (forall (i : ι), LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) _inst_6 (Pi.addCommMonoid.{u1, max u2 u4} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u4} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Pi.module.{u1, max u2 u4, u5} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) S _inst_6 (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u4} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u5, u2, u4} R R S (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) _inst_6 _inst_7 _inst_8)))))) (SMulZeroClass.toSMul.{u5, max (max u1 u2) u4} S (LinearMap.{u3, u3, max u2 u1, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5) (AddMonoid.toZero.{max (max u1 u2) u4} (LinearMap.{u3, u3, max u2 u1, u4} R R _inst_1 _inst_1 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dec_ι a b) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) _inst_4 _inst_5 _inst_6 _inst_7 _inst_8) F) (Dfinsupp.single.{u1, u2} ι (fun (i : ι) => M i) (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i))) i x)) (FunLike.coe.{max (succ u2) (succ u4), succ u2, succ u4} (LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (M i) (fun (_x : M i) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M i) => N) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u4} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (F i) x)
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(forall (i : ι), LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (AddMonoid.toAddZeroClass.{max (max u1 u2) u4} (forall (i : ι), LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u4} (forall (i : ι), LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (Pi.addCommMonoid.{u1, max u2 u4} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u4} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u5, max (max u1 u2) u4} S (forall (i : ι), LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (MonoidWithZero.toMonoid.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u4} (forall (i : ι), LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (Pi.addCommMonoid.{u1, max u2 u4} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u4} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Module.toDistribMulAction.{u5, max (max u1 u2) u4} S (forall (i : ι), LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) _inst_6 (Pi.addCommMonoid.{u1, max u2 u4} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u4} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Pi.module.{u1, max u2 u4, u5} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) S _inst_6 (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u4} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u5, u2, u4} R R S (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) _inst_6 _inst_7 _inst_8)))))) (SMulZeroClass.toSMul.{u5, max (max u1 u2) u4} S (LinearMap.{u3, u3, max u2 u1, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5) (AddMonoid.toZero.{max (max u1 u2) u4} (LinearMap.{u3, u3, max u2 u1, u4} R R _inst_1 _inst_1 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dec_ι a b) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) _inst_4 _inst_5 _inst_6 _inst_7 _inst_8) F) (Dfinsupp.single.{u1, u2} ι (fun (i : ι) => M i) (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i))) i x)) (FunLike.coe.{max (succ u2) (succ u4), succ u2, succ u4} (LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (M i) (fun (_x : M i) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M i) => N) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u4} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (F i) x)
 Case conversion may be inaccurate. Consider using '#align dfinsupp.lsum_single Dfinsupp.lsum_singleₓ'. -/
 /-- While `simp` can prove this, it is often convenient to avoid unfolding `lsum` into `sum_add_hom`
 with `dfinsupp.lsum_apply_apply`. -/
@@ -324,7 +324,7 @@ include dec_ι
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u2, u3} R N _inst_1 _inst_4] {β₁ : ι -> Type.{u4}} {β₂ : ι -> Type.{u5}} [_inst_7 : forall (i : ι), AddCommMonoid.{u4} (β₁ i)] [_inst_8 : forall (i : ι), AddCommMonoid.{u5} (β₂ i)] [_inst_10 : forall (i : ι), Module.{u2, u4} R (β₁ i) _inst_1 (_inst_7 i)] [_inst_11 : forall (i : ι), Module.{u2, u5} R (β₂ i) _inst_1 (_inst_8 i)] [_inst_12 : forall (i : ι) (x : β₁ i), Decidable (Ne.{succ u4} (β₁ i) x (OfNat.ofNat.{u4} (β₁ i) 0 (OfNat.mk.{u4} (β₁ i) 0 (Zero.zero.{u4} (β₁ i) (AddZeroClass.toHasZero.{u4} (β₁ i) (AddMonoid.toAddZeroClass.{u4} (β₁ i) (AddCommMonoid.toAddMonoid.{u4} (β₁ i) (_inst_7 i))))))))] [_inst_13 : forall (i : ι) (x : β₂ i), Decidable (Ne.{succ u5} (β₂ i) x (OfNat.ofNat.{u5} (β₂ i) 0 (OfNat.mk.{u5} (β₂ i) 0 (Zero.zero.{u5} (β₂ i) (AddZeroClass.toHasZero.{u5} (β₂ i) (AddMonoid.toAddZeroClass.{u5} (β₂ i) (AddCommMonoid.toAddMonoid.{u5} (β₂ i) (_inst_8 i))))))))] {f : forall (i : ι), LinearMap.{u2, u2, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (β₁ i) (β₂ i) (_inst_7 i) (_inst_8 i) (_inst_10 i) (_inst_11 i)} {h : forall (i : ι), LinearMap.{u2, u2, u5, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5} {l : Dfinsupp.{u1, u4} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} ((fun (i : ι) => β₁ i) i) (AddMonoid.toAddZeroClass.{u4} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₁ i) i) (_inst_7 i))))}, Eq.{succ u3} N (coeFn.{max (succ (max u1 u5)) (succ u3), max (succ (max u1 u5)) (succ u3)} (LinearMap.{u2, u2, max u1 u5, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddZeroClass.toHasZero.{u5} (β₂ i) 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i) _inst_4 _inst_5 Nat.semiring (AddCommMonoid.natModule.{u3} N _inst_4) (AddMonoid.nat_smulCommClass'.{u2, u3} R N (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} N _inst_4) (Module.toDistribMulAction.{u2, u3} R N _inst_1 _inst_4 _inst_5))) (fun (i : ι) => LinearMap.comp.{u2, u2, u2, u4, u5, u3} R R R (β₁ i) (β₂ i) N _inst_1 _inst_1 _inst_1 (_inst_7 i) (_inst_8 i) _inst_4 (_inst_10 i) (_inst_11 i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomCompTriple.right_ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (h i) (f i))) l)
 but is expected to have type
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_inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) _x) (SMulHomClass.toFunLike.{max (max u1 u4) u2, 0, max (max u1 u4) u2, max (max u1 u4) u2} (LinearEquiv.{0, 0, max (max u1 u4) u2, max u2 u4 u1} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, max u1 u4, u2} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u4 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u4, u2} R R Nat (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u4, u2} R R Nat (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) Nat (forall 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(forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u1 u4) u2} (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{0, max (max u1 u4) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (AddMonoid.toAddZeroClass.{max (max u1 u4) u2} (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u1 u4) u2} (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (DistribMulAction.toDistribSMul.{0, max (max u1 u4) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u1 u4) u2} (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Module.toDistribMulAction.{0, max (max u1 u4) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat.semiring (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Pi.module.{u1, max u4 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u4, u2} R R Nat (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))))))) (SMulZeroClass.toSMul.{0, max (max u1 u4) u2} Nat (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R 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ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u1 u4) u2} Nat (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u3, u3, max u1 u4, u2} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 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(Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) (LinearMap.addCommMonoid.{u3, u3, max u1 u4, u2} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u1 u4) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat.semiring (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Pi.module.{u1, max u4 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u4, u2} R R Nat (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))))) (Module.toDistribMulAction.{0, max (max u1 u4) u2} Nat (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u3, u3, max u1 u4, u2} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u4, u2} R R Nat (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (SemilinearMapClass.distribMulActionHomClass.{0, max (max u1 u4) u2, max (max u1 u4) u2, max (max u1 u4) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) 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(_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u4 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u4, u2} R R Nat (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u4, u2} R R Nat (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R 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(Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u4, u2} R R Nat (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))) (SemilinearEquivClass.instSemilinearMapClass.{0, 0, max 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(LinearMap.addCommMonoid.{u3, u3, max u1 u4, u2} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u4 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) 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(Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u1 u5) u2} (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (DistribMulAction.toDistribSMul.{0, max (max u1 u5) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u1 u5) u2} (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Module.toDistribMulAction.{0, max (max u1 u5) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) Nat.semiring (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Pi.module.{u1, max u5 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u5, u2} R R Nat (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))))))) (SMulZeroClass.toSMul.{0, max (max u1 u5) u2} Nat (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (AddMonoid.toZero.{max (max u1 u5) u2} (LinearMap.{u3, u3, max 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(Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (LinearMap.addCommMonoid.{u3, u3, max u1 u5, u2} R R (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (DistribSMul.toSMulZeroClass.{0, max (max u1 u5) u2} Nat (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) 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u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (LinearMap.addCommMonoid.{u3, u3, max u1 u5, u2} R R (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (DistribMulAction.toDistribSMul.{0, max (max u1 u5) u2} Nat (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u1 u5) u2} (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ 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=> β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u5, u2} R R Nat (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u5) u2, 0, max (max u1 u5) u2, max (max u1 u5) u2} (LinearEquiv.{0, 0, max (max u1 u5) u2, max u2 u5 u1} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι 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R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u5 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u5, u2} R R Nat (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u5, u2} R R Nat (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) Nat (forall 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=> _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (LinearMap.addCommMonoid.{u3, u3, max u1 u5, u2} R R (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u1 u5) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) Nat.semiring (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R 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(AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))))) (Module.toDistribMulAction.{0, max (max u1 u5) u2} Nat (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u3, u3, max u1 u5, u2} R R (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) 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_inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (SemilinearMapClass.distribMulActionHomClass.{0, max (max u1 u5) u2, max (max u1 u5) u2, max (max u1 u5) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (LinearEquiv.{0, 0, max (max u1 u5) u2, max u2 u5 u1} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, max u1 u5, u2} R R (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u5 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u5, u2} R R Nat (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u5, u2} R R Nat (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) Nat.semiring 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(fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))) (SemilinearEquivClass.instSemilinearMapClass.{0, 0, max (max u1 u5) u2, max (max u1 u5) u2, max (max u1 u5) u2} Nat Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (LinearEquiv.{0, 0, max (max u1 u5) u2, max u2 u5 u1} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, max u1 u5, u2} R R (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u5 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u5, u2} R R Nat (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u5, u2} R R Nat (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, max u1 u5, u2} R R (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u5 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u5, u2} R R Nat (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u5, u2} R R Nat (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R 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+  forall {ι : Type.{u1}} {R : Type.{u3}} {N : Type.{u2}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u3} R] [_inst_4 : AddCommMonoid.{u2} N] [_inst_5 : Module.{u3, u2} R N _inst_1 _inst_4] {β₁ : ι -> Type.{u5}} {β₂ : ι -> Type.{u4}} [_inst_7 : forall (i : ι), AddCommMonoid.{u5} (β₁ i)] [_inst_8 : forall (i : ι), AddCommMonoid.{u4} (β₂ i)] [_inst_10 : forall (i : ι), Module.{u3, u5} R (β₁ i) _inst_1 (_inst_7 i)] [_inst_11 : forall (i : ι), Module.{u3, u4} R (β₂ i) _inst_1 (_inst_8 i)] [_inst_12 : forall (i : ι) (x : β₁ i), Decidable (Ne.{succ u5} (β₁ i) x (OfNat.ofNat.{u5} (β₁ i) 0 (Zero.toOfNat0.{u5} (β₁ i) (AddMonoid.toZero.{u5} (β₁ i) (AddCommMonoid.toAddMonoid.{u5} (β₁ i) (_inst_7 i))))))] [_inst_13 : forall (i : ι) (x : β₂ i), Decidable (Ne.{succ u4} (β₂ i) x (OfNat.ofNat.{u4} (β₂ i) 0 (Zero.toOfNat0.{u4} (β₂ i) (AddMonoid.toZero.{u4} (β₂ i) (AddCommMonoid.toAddMonoid.{u4} (β₂ i) (_inst_8 i))))))] {f : forall (i : ι), LinearMap.{u3, u3, u5, u4} R R _inst_1 _inst_1 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(LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u4, u2} R R Nat (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (_x : forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) => LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) _x) (SMulHomClass.toFunLike.{max (max u1 u4) u2, 0, max (max u1 u4) u2, max (max u1 u4) u2} (LinearEquiv.{0, 0, max (max u1 u4) u2, max u2 u4 u1} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, max u1 u4, u2} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u4 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u4, u2} R R Nat (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u4, u2} R R Nat (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) Nat (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) (SMulZeroClass.toSMul.{0, max (max u1 u4) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (AddMonoid.toZero.{max (max u1 u4) u2} (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u1 u4) u2} (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{0, max (max u1 u4) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (AddMonoid.toAddZeroClass.{max (max u1 u4) u2} (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u1 u4) u2} (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (DistribMulAction.toDistribSMul.{0, max (max u1 u4) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u1 u4) u2} (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Module.toDistribMulAction.{0, max (max u1 u4) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat.semiring (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Pi.module.{u1, max u4 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => 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(fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) (AddMonoid.toZero.{max (max u1 u4) u2} (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u1 u4) u2} (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun 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(LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) (LinearMap.addCommMonoid.{u3, u3, max u1 u4, u2} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u1 u4) u2} Nat (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u3, u3, max u1 u4, u2} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u4, u2} R R Nat (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u4) u2, 0, max (max u1 u4) u2, max (max u1 u4) u2} (LinearEquiv.{0, 0, max (max u1 u4) u2, max u2 u4 u1} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} 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_inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u4 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u4, u2} R R Nat (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u4, u2} R R Nat (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) Nat (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) 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(Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) (LinearMap.addCommMonoid.{u3, u3, max u1 u4, u2} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u1 u4) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat.semiring (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Pi.module.{u1, max u4 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u4, u2} R R Nat (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))))) (Module.toDistribMulAction.{0, max (max u1 u4) u2} Nat (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => 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(AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u4, u2} R R Nat (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R 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_inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (SMulZeroClass.toSMul.{0, max (max u1 u5) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (AddMonoid.toZero.{max (max u1 u5) u2} (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (AddCommMonoid.toAddMonoid.{max (max 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(Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u1 u5) u2} (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (DistribMulAction.toDistribSMul.{0, max (max u1 u5) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u1 u5) u2} (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Module.toDistribMulAction.{0, max (max u1 u5) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) Nat.semiring (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Pi.module.{u1, max u5 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u5, u2} R R Nat (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))))))) (SMulZeroClass.toSMul.{0, max (max u1 u5) u2} Nat (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (AddMonoid.toZero.{max (max u1 u5) u2} (LinearMap.{u3, u3, max 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(Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (LinearMap.addCommMonoid.{u3, u3, max u1 u5, u2} R R (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (DistribSMul.toSMulZeroClass.{0, max (max u1 u5) u2} Nat (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (AddMonoid.toAddZeroClass.{max (max u1 u5) u2} (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u1 u5) u2} (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (LinearMap.addCommMonoid.{u3, u3, max u1 u5, u2} R R (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (DistribMulAction.toDistribSMul.{0, max (max u1 u5) u2} Nat (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u1 u5) u2} (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ 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_inst_1 _inst_4 _inst_5))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u5) u2, 0, max (max u1 u5) u2, max (max u1 u5) u2} (LinearEquiv.{0, 0, max (max u1 u5) u2, max u2 u5 u1} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι 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(AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))))) (Module.toDistribMulAction.{0, max (max u1 u5) u2} Nat (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u3, u3, max u1 u5, u2} R R (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) 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(fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))) (SemilinearEquivClass.instSemilinearMapClass.{0, 0, max (max u1 u5) u2, max (max u1 u5) u2, max (max u1 u5) u2} Nat Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R 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_inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, max u1 u5, u2} R R (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u5 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 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_inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, max u1 u5, u2} R R (Dfinsupp.{u1, u5} ι (fun 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i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u5, u2} R R Nat (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{0, 0, max (max u1 u5) u2, max (max u1 u5) u2} Nat Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, max u1 u5, u2} R R (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u5 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u5, u2} R R Nat (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u5, u2} R R Nat (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u1, u3, 0, u5, u2} ι R Nat β₁ N (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i) _inst_4 _inst_5 Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))) (fun (i : ι) => LinearMap.comp.{u3, u3, u3, u5, u4, u2} R R R (β₁ i) (β₂ i) N _inst_1 _inst_1 _inst_1 (_inst_7 i) (_inst_8 i) _inst_4 (_inst_10 i) (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomCompTriple.ids.{u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (h i) (f i))) l)
 Case conversion may be inaccurate. Consider using '#align dfinsupp.sum_map_range_index.linear_map Dfinsupp.sum_mapRange_index.linearMapₓ'. -/
 theorem sum_mapRange_index.linearMap [∀ (i : ι) (x : β₁ i), Decidable (x ≠ 0)]
     [∀ (i : ι) (x : β₂ i), Decidable (x ≠ 0)] {f : ∀ i, β₁ i →ₗ[R] β₂ i} {h : ∀ i, β₂ i →ₗ[R] N}
@@ -414,7 +414,7 @@ noncomputable def coprodMap (f : ∀ i : ι, M i →ₗ[R] N) : (Π₀ i, M i) 
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : ι -> Type.{u3}} {N : Type.{u4}} [_inst_1 : Semiring.{u2} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (M i)] [_inst_3 : forall (i : ι), Module.{u2, u3} R (M i) _inst_1 (_inst_2 i)] [_inst_4 : AddCommMonoid.{u4} N] [_inst_5 : Module.{u2, u4} R N _inst_1 _inst_4] [_inst_6 : DecidableEq.{succ u1} ι] [_inst_7 : forall (x : N), Decidable (Ne.{succ u4} N x (OfNat.ofNat.{u4} N 0 (OfNat.mk.{u4} N 0 (Zero.zero.{u4} N (AddZeroClass.toHasZero.{u4} N (AddMonoid.toAddZeroClass.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_4)))))))] (f : forall (i : ι), LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (x : Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} ((fun (i : ι) => M i) i) (AddMonoid.toAddZeroClass.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i))))), Eq.{succ u4} N (coeFn.{max (succ (max u1 u3)) (succ u4), max (succ (max u1 u3)) (succ u4)} (LinearMap.{u2, u2, max u1 u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => M i) i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} ((fun (i : ι) => M i) i) (AddMonoid.toAddZeroClass.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) ((fun (i : ι) => _inst_2 i) i))))) N (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => M i) i) (fun (i : ι) => (fun (i : ι) => _inst_2 i) i)) _inst_4 (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => (fun (i : ι) => M i) i) _inst_1 (fun (i : ι) => (fun (i : ι) => _inst_2 i) i) (fun (i : ι) => (fun (i : ι) => _inst_3 i) i)) _inst_5) (fun (_x : LinearMap.{u2, u2, max u1 u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => M i) i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} ((fun (i : ι) => M i) i) (AddMonoid.toAddZeroClass.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) ((fun (i : ι) => _inst_2 i) i))))) N (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => M i) i) (fun (i : ι) => (fun (i : ι) => _inst_2 i) i)) _inst_4 (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => (fun (i : ι) => M i) i) _inst_1 (fun (i : ι) => (fun (i : ι) => _inst_2 i) i) (fun (i : ι) => (fun (i : ι) => _inst_3 i) i)) _inst_5) => (Dfinsupp.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => M i) i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} ((fun (i : ι) => M i) i) (AddMonoid.toAddZeroClass.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) ((fun (i : ι) => _inst_2 i) i))))) -> N) (LinearMap.hasCoeToFun.{u2, u2, max u1 u3, u4} R R (Dfinsupp.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => M i) i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} ((fun (i : ι) => M i) i) (AddMonoid.toAddZeroClass.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) ((fun (i : ι) => _inst_2 i) i))))) N _inst_1 _inst_1 (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => M i) i) (fun (i : ι) => (fun (i : ι) => _inst_2 i) i)) _inst_4 (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => (fun (i : ι) => M i) i) _inst_1 (fun (i : ι) => (fun (i : ι) => _inst_2 i) i) (fun (i : ι) => (fun (i : ι) => _inst_3 i) i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Dfinsupp.coprodMap.{u1, u2, u3, u4} ι R (fun (i : ι) => M i) N _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) _inst_4 _inst_5 (fun (a : ι) (b : ι) => _inst_6 a b) (fun (x : N) => _inst_7 x) f) x) (Finsupp.sum.{u1, u4, u4} ι N N (AddZeroClass.toHasZero.{u4} N (AddMonoid.toAddZeroClass.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_4))) _inst_4 (Dfinsupp.toFinsupp.{u1, u4} ι N (fun (a : ι) (b : ι) => _inst_6 a b) (AddZeroClass.toHasZero.{u4} N (AddMonoid.toAddZeroClass.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_4))) (fun (x : N) => _inst_7 x) (Dfinsupp.mapRange.{u1, u3, u4} ι (fun (i : ι) => M i) (fun (i : ι) => N) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i)))) (fun (i : ι) => AddZeroClass.toHasZero.{u4} N (AddMonoid.toAddZeroClass.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_4))) (fun (i : ι) => coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (fun (_x : LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) => (M i) -> N) (LinearMap.hasCoeToFun.{u2, u2, u3, u4} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (f i)) (fun (i : ι) => LinearMap.map_zero.{u2, u2, u3, u4} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (f i)) x)) (fun (i : ι) => id.{succ u4} N))
 but is expected to have type
-  forall {ι : Type.{u1}} {R : Type.{u4}} {M : ι -> Type.{u3}} {N : Type.{u2}} [_inst_1 : Semiring.{u4} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (M i)] [_inst_3 : forall (i : ι), Module.{u4, u3} R (M i) _inst_1 (_inst_2 i)] [_inst_4 : AddCommMonoid.{u2} N] [_inst_5 : Module.{u4, u2} R N _inst_1 _inst_4] [_inst_6 : DecidableEq.{succ u1} ι] [_inst_7 : forall (x : N), Decidable (Ne.{succ u2} N x (OfNat.ofNat.{u2} N 0 (Zero.toOfNat0.{u2} N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_4)))))] (f : forall (i : ι), LinearMap.{u4, u4, u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (x : Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) => N) x) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u3), succ u2} (LinearMap.{u4, u4, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u3, u4} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5) (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) (fun (_x : Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) => N) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u1 u3, u2} R R (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u3, u4} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Dfinsupp.coprodMap.{u1, u4, u3, u2} ι R (fun (i : ι) => M i) N _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) _inst_4 _inst_5 (fun (a : ι) (b : ι) => _inst_6 a b) (fun (x : N) => _inst_7 x) f) x) (Finsupp.sum.{u1, u2, u2} ι N N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_4)) _inst_4 (Dfinsupp.toFinsupp.{u1, u2} ι N (fun (a : ι) (b : ι) => _inst_6 a b) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_4)) (fun (x : N) => _inst_7 x) (Dfinsupp.mapRange.{u1, u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => N) (fun (i : ι) => AddMonoid.toZero.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))) (fun (i : ι) => AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_4)) (fun (i : ι) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (LinearMap.{u4, u4, u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (M i) (fun (_x : M i) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M i) => N) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, u2} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (f i)) (fun (i : ι) => LinearMap.map_zero.{u4, u4, u3, u2} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (f i)) x)) (fun (i : ι) => id.{succ u2} N))
+  forall {ι : Type.{u1}} {R : Type.{u4}} {M : ι -> Type.{u3}} {N : Type.{u2}} [_inst_1 : Semiring.{u4} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (M i)] [_inst_3 : forall (i : ι), Module.{u4, u3} R (M i) _inst_1 (_inst_2 i)] [_inst_4 : AddCommMonoid.{u2} N] [_inst_5 : Module.{u4, u2} R N _inst_1 _inst_4] [_inst_6 : DecidableEq.{succ u1} ι] [_inst_7 : forall (x : N), Decidable (Ne.{succ u2} N x (OfNat.ofNat.{u2} N 0 (Zero.toOfNat0.{u2} N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_4)))))] (f : forall (i : ι), LinearMap.{u4, u4, u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (x : Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) => N) x) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u3), succ u2} (LinearMap.{u4, u4, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u3, u4} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5) (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) (fun (_x : Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) => N) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u1 u3, u2} R R (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u3, u4} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Dfinsupp.coprodMap.{u1, u4, u3, u2} ι R (fun (i : ι) => M i) N _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) _inst_4 _inst_5 (fun (a : ι) (b : ι) => _inst_6 a b) (fun (x : N) => _inst_7 x) f) x) (Finsupp.sum.{u1, u2, u2} ι N N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_4)) _inst_4 (Dfinsupp.toFinsupp.{u1, u2} ι N (fun (a : ι) (b : ι) => _inst_6 a b) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_4)) (fun (x : N) => _inst_7 x) (Dfinsupp.mapRange.{u1, u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => N) (fun (i : ι) => AddMonoid.toZero.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))) (fun (i : ι) => AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_4)) (fun (i : ι) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (LinearMap.{u4, u4, u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (M i) (fun (_x : M i) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M i) => N) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, u2} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (f i)) (fun (i : ι) => LinearMap.map_zero.{u4, u4, u3, u2} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (f i)) x)) (fun (i : ι) => id.{succ u2} N))
 Case conversion may be inaccurate. Consider using '#align dfinsupp.coprod_map_apply Dfinsupp.coprodMap_applyₓ'. -/
 theorem coprodMap_apply (f : ∀ i : ι, M i →ₗ[R] N) (x : Π₀ i, M i) :
     coprodMap f x =
@@ -482,7 +482,7 @@ theorem dfinsupp_sumAddHom_mem {β : ι → Type _} [∀ i, AddZeroClass (β i)]
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} N] [_inst_3 : Module.{u2, u3} R N _inst_1 _inst_2] (p : ι -> (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3)), Eq.{succ u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (iSup.{u3, succ u1} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u3} R N _inst_1 _inst_2 _inst_3))) ι p) (LinearMap.range.{u2, u2, max u1 u3, u3, max u1 u3} R R (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (AddMonoid.toAddZeroClass.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (AddCommMonoid.toAddMonoid.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (Submodule.addCommMonoid.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i)))))) N _inst_1 _inst_1 (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (i : ι) => Submodule.addCommMonoid.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_2 (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, max u1 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (AddMonoid.toAddZeroClass.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (AddCommMonoid.toAddMonoid.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 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Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u3} N _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R N (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} N _inst_2) (Module.toDistribMulAction.{u2, u3} R N _inst_1 _inst_2 _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)) (Dfinsupp.lsum.{u1, u2, 0, u3, u3} ι R Nat (fun (i : ι) => coeSort.{succ u3, succ (succ 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 but is expected to have type
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(Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N _inst_1 _inst_1 (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, max u1 u2, u2} R R (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_2 (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N _inst_1 _inst_1 (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u2, u2} R R Nat (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N _inst_1 _inst_1 (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u2, u2} R R Nat (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_2 (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u1, u3, 0, u2, u2} ι R Nat (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 _inst_3 Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3))) (fun (i : ι) => Submodule.subtype.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))
 Case conversion may be inaccurate. Consider using '#align submodule.supr_eq_range_dfinsupp_lsum Submodule.iSup_eq_range_dfinsupp_lsumₓ'. -/
 /-- The supremum of a family of submodules is equal to the range of `dfinsupp.lsum`; that is
 every element in the `supr` can be produced from taking a finite number of non-zero elements
@@ -502,7 +502,7 @@ theorem iSup_eq_range_dfinsupp_lsum (p : ι → Submodule R N) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} N] [_inst_3 : Module.{u2, u3} R N _inst_1 _inst_2] (p : ι -> Prop) [_inst_4 : DecidablePred.{succ u1} ι p] (S : ι -> (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3)), Eq.{succ u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (iSup.{u3, succ u1} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u3} R N _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => iSup.{u3, 0} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u3} R N _inst_1 _inst_2 _inst_3))) (p i) (fun (h : p i) => S i))) (LinearMap.range.{u2, u2, max u1 u3, u3, max u1 u3} R R (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (S i)) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (S i)) (AddMonoid.toAddZeroClass.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (S i)) (AddCommMonoid.toAddMonoid.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (S i)) (Submodule.addCommMonoid.{u2, u3} R N _inst_1 _inst_2 _inst_3 (S i)))))) N _inst_1 _inst_1 (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (S i)) (fun (i : ι) => Submodule.addCommMonoid.{u2, u3} R N _inst_1 _inst_2 _inst_3 (S i))) _inst_2 (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} 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 but is expected to have type
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(Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} N _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R N (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_2) (Module.toDistribMulAction.{u2, u1} R N _inst_1 _inst_2 _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u3, u2, 0, u1, u1} ι R Nat (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) N (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 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(Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) N (Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_2 (Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u1, u1} R R (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) N _inst_1 _inst_1 (Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_2 (Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u3 u1, u1} R R (Dfinsupp.{u3, u1} ι (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) (fun (i : ι) => AddMonoid.toZero.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (AddCommMonoid.toAddMonoid.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u1} ι (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) (fun (i : ι) => Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))) _inst_2 (Dfinsupp.module.{u3, u1, u2} ι R (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) (fun (i : ι) => Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) N (Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_2 (Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_3) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u1, u1} R R (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) N _inst_1 _inst_1 (Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_2 (Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u1, u1} R R Nat (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) N _inst_1 _inst_1 (Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_2 (Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} N _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R N (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_2) (Module.toDistribMulAction.{u2, u1} R N _inst_1 _inst_2 _inst_3)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u3 u1, u1} R R Nat (Dfinsupp.{u3, u1} ι (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) (fun (i : ι) => AddMonoid.toZero.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (AddCommMonoid.toAddMonoid.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u1} ι (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) (fun (i : ι) => Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))) _inst_2 (Dfinsupp.module.{u3, u1, u2} ι R (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) (fun (i : ι) => Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} N _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R N (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_2) (Module.toDistribMulAction.{u2, u1} R N _inst_1 _inst_2 _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u3, u2, 0, u1, u1} ι R Nat (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) N (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) (fun (i : ι) => Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_2 _inst_3 Nat.semiring (AddCommMonoid.natModule.{u1} N _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R N (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_2) (Module.toDistribMulAction.{u2, u1} R N _inst_1 _inst_2 _inst_3))) (fun (i : ι) => Submodule.subtype.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))) (Dfinsupp.filterLinearMap.{u3, u1, u2} ι R (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) (fun (i : ι) => Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) p (fun (a : ι) => _inst_4 a))))
 Case conversion may be inaccurate. Consider using '#align submodule.bsupr_eq_range_dfinsupp_lsum Submodule.biSup_eq_range_dfinsupp_lsumₓ'. -/
 /-- The bounded supremum of a family of commutative additive submonoids is equal to the range of
 `dfinsupp.sum_add_hom` composed with `dfinsupp.filter_add_monoid_hom`; that is, every element in the
@@ -528,7 +528,7 @@ theorem biSup_eq_range_dfinsupp_lsum (p : ι → Prop) [DecidablePred p] (S : ι
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} N] [_inst_3 : Module.{u2, u3} R N _inst_1 _inst_2] (p : ι -> (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (x : N), Iff (Membership.Mem.{u3, u3} N (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) x (iSup.{u3, succ u1} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u3} R N _inst_1 _inst_2 _inst_3))) ι p)) (Exists.{succ (max u1 u3)} (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (i : ι) => Submodule.zero.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i))) (fun (f : Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (i : ι) => Submodule.zero.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i))) => Eq.{succ u3} N (coeFn.{max (succ (max u1 u3)) (succ u3), max (succ (max u1 u3)) (succ u3)} (LinearMap.{u2, u2, max u1 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (AddMonoid.toAddZeroClass.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (AddCommMonoid.toAddMonoid.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (Submodule.addCommMonoid.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i)))))) N 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 but is expected to have type
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(Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_2 (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u1, u3, 0, u2, u2} ι R Nat (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 _inst_3 Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3))) (fun (i : ι) => Submodule.subtype.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) f) x))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_iff_exists_dfinsupp Submodule.mem_iSup_iff_exists_dfinsuppₓ'. -/
 theorem mem_iSup_iff_exists_dfinsupp (p : ι → Submodule R N) (x : N) :
     x ∈ iSup p ↔ ∃ f : Π₀ i, p i, Dfinsupp.lsum ℕ (fun i => (p i).Subtype) f = x :=
@@ -554,7 +554,7 @@ theorem mem_iSup_iff_exists_dfinsupp' (p : ι → Submodule R N) [∀ (i) (x : p
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} N] [_inst_3 : Module.{u2, u3} R N _inst_1 _inst_2] (p : ι -> Prop) [_inst_4 : DecidablePred.{succ u1} ι p] (S : ι -> (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (x : N), Iff (Membership.Mem.{u3, u3} N (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) x (iSup.{u3, succ u1} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u3} R N _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => iSup.{u3, 0} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u3} 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 but is expected to have type
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(Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (AddCommMonoid.toAddMonoid.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u1} ι (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) (fun (i : ι) => Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))) _inst_2 (Dfinsupp.module.{u3, u1, u2} ι R (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) (fun (i : ι) => Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} N _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R N (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_2) (Module.toDistribMulAction.{u2, u1} R N _inst_1 _inst_2 _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u3, u2, 0, u1, u1} ι R Nat (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) N (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) (fun (i : ι) => Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_2 _inst_3 Nat.semiring (AddCommMonoid.natModule.{u1} N _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R N (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_2) (Module.toDistribMulAction.{u2, u1} R N _inst_1 _inst_2 _inst_3))) (fun (i : ι) => Submodule.subtype.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))) (Dfinsupp.filter.{u3, u1} ι (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) (fun (i : ι) => AddMonoid.toZero.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (AddCommMonoid.toAddMonoid.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)))) p (fun (a : ι) => _inst_4 a) f)) x))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_bsupr_iff_exists_dfinsupp Submodule.mem_biSup_iff_exists_dfinsuppₓ'. -/
 theorem mem_biSup_iff_exists_dfinsupp (p : ι → Prop) [DecidablePred p] (S : ι → Submodule R N)
     (x : N) :
@@ -624,7 +624,7 @@ variable [Semiring R] [AddCommMonoid N] [Module R N]
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} N] [_inst_3 : Module.{u2, u3} R N _inst_1 _inst_2] (p : ι -> (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3)), Iff (CompleteLattice.Independent.{succ u1, u3} ι (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u3} R N _inst_1 _inst_2 _inst_3) p) (forall (i : ι) (x : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (v : Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (i : ι) => 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 but is expected to have type
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Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N _inst_1 _inst_1 (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u2, u2} R R Nat (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N _inst_1 _inst_1 (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u2, u2} R R Nat (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_2 (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u1, u3, 0, u2, u2} ι R Nat (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 _inst_3 Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3))) (fun (i : ι) => Submodule.subtype.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) (Dfinsupp.erase.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)))) i v)) (Subtype.val.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Set.{u2} N) (Set.instMembershipSet.{u2} N) x (SetLike.coe.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3) (p i))) x)) -> (Eq.{succ u2} (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) x (OfNat.ofNat.{u2} (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) 0 (Zero.toOfNat0.{u2} (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (Submodule.zero.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))))
 Case conversion may be inaccurate. Consider using '#align complete_lattice.independent_iff_forall_dfinsupp CompleteLattice.independent_iff_forall_dfinsuppₓ'. -/
 /-- Independence of a family of submodules can be expressed as a quantifier over `dfinsupp`s.
 
@@ -648,7 +648,7 @@ theorem independent_iff_forall_dfinsupp (p : ι → Submodule R N) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} N] [_inst_3 : Module.{u2, u3} R N _inst_1 _inst_2] (p : ι -> (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3)), (Function.Injective.{succ (max u1 u3), succ u3} (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (AddMonoid.toAddZeroClass.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (AddCommMonoid.toAddMonoid.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (Submodule.addCommMonoid.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i)))))) N (coeFn.{max (succ (max u1 u3)) (succ u3), max (succ (max u1 u3)) (succ u3)} (LinearMap.{u2, u2, max u1 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (i : ι) => 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 but is expected to have type
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Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_2 (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{0, 0, max u1 u2, max u1 u2} Nat Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3) (LinearMap.{u3, u3, max u2 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_2 (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N _inst_1 _inst_1 (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, max u1 u2, u2} R R (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_2 (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N _inst_1 _inst_1 (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u2, u2} R R Nat (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N _inst_1 _inst_1 (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u2, u2} R R Nat (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_2 (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u1, u3, 0, u2, u2} ι R Nat (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 _inst_3 Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3))) (fun (i : ι) => Submodule.subtype.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))) -> (CompleteLattice.Independent.{succ u1, u2} ι (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u3, u2} R N _inst_1 _inst_2 _inst_3) p)
 Case conversion may be inaccurate. Consider using '#align complete_lattice.independent_of_dfinsupp_lsum_injective CompleteLattice.independent_of_dfinsupp_lsum_injectiveₓ'. -/
 /- If `dfinsupp.lsum` applied with `submodule.subtype` is injective then the submodules are
 independent. -/
@@ -723,7 +723,7 @@ theorem independent_of_dfinsupp_sumAddHom_injective' (p : ι → AddSubgroup N)
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} N] [_inst_3 : Module.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2)] {p : ι -> (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3)}, (CompleteLattice.Independent.{succ u1, u3} ι (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) (Submodule.completeLattice.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) p) -> (Function.Injective.{succ (max u1 u3), succ u3} (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) N (Submodule.setLike.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3)) (p i)) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) N (Submodule.setLike.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3)) (p i)) (AddMonoid.toAddZeroClass.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) N (Submodule.setLike.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3)) (p i)) (AddCommMonoid.toAddMonoid.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) N (Submodule.setLike.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3)) (p i)) (Submodule.addCommMonoid.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3 (p i)))))) N (coeFn.{max (succ (max u1 u3)) (succ u3), max (succ (max u1 u3)) (succ u3)} (LinearMap.{u2, u2, max u1 u3, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) N (Submodule.setLike.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3)) (p i)) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) N (Submodule.setLike.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3)) (p i)) (AddMonoid.toAddZeroClass.{u3} (coeSort.{succ u3, succ (succ 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(Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) N (Submodule.setLike.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3)) (p i)) (fun (i : ι) => Submodule.addCommMonoid.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3 (p i))) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) N (Submodule.setLike.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3)) (p i)) (Ring.toSemiring.{u2} R _inst_1) (fun (i : ι) => Submodule.addCommMonoid.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3 (p i))) _inst_3) (fun (_x : LinearMap.{u2, u2, max u1 u3, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) N (Submodule.setLike.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3)) (p i)) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) N (Submodule.setLike.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3)) (p i)) (AddMonoid.toAddZeroClass.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) N 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(AddGroup.toSubNegMonoid.{u3} N (AddCommGroup.toAddGroup.{u3} N _inst_2))) (Module.toDistribMulAction.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3))) (fun (i : ι) => Submodule.subtype.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3 (p i)))))
 but is expected to have type
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(AddCommGroup.toAddCommMonoid.{u2} N _inst_2)) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u2, u2} R R Nat (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) 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u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)))) Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (LinearMap.{u3, u3, max u2 u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (Ring.toSemiring.{u3} R _inst_1) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) _inst_3) (SMulZeroClass.toSMul.{0, max u1 u2} Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (AddMonoid.toZero.{max u1 u2} (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{0, max u1 u2} Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R 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(Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R 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(Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))))))) (DistribMulAction.toDistribSMul.{0, max u1 u2} Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max u1 u2} (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))))) (Module.toDistribMulAction.{0, max u1 u2} Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) Nat.semiring (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) 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R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) Nat.semiring (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N 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u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u1, u3, 0, u2, u2} ι R Nat (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N 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+  forall {ι : Type.{u1}} {R : Type.{u3}} {N : Type.{u2}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u2} N] [_inst_3 : Module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)] {p : ι -> (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)}, (CompleteLattice.Independent.{succ u1, u2} ι (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (Submodule.completeLattice.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) p) -> (Function.Injective.{max (succ u1) (succ u2), succ u2} (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N 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u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)))) Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x 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_inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N 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=> LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))))) (Module.toDistribMulAction.{0, max u1 u2} Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) Nat.semiring (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))))) (Pi.module.{u1, u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u2, u2} R R Nat (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u2} N (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)))))))) (SMulZeroClass.toSMul.{0, max u1 u2} Nat (LinearMap.{u3, u3, max u2 u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} 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_inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (Ring.toSemiring.{u3} R _inst_1) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) _inst_3) (AddMonoid.toZero.{max u1 u2} (LinearMap.{u3, u3, max u2 u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N 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_inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))))) (LinearMap.addCommMonoid.{u3, u3, max u1 u2, u2} R R (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (Ring.toSemiring.{u3} R _inst_1) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) (Pi.module.{u1, u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u2, u2} R R Nat (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u2} N (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u2, u2} R R Nat (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (Ring.toSemiring.{u3} R _inst_1) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u2} N (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u1, u3, 0, u2, u2} ι R Nat (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (fun (a : ι) (b : ι) => dec_ι a b) (Ring.toSemiring.{u3} R _inst_1) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 Nat.semiring (AddCommMonoid.natModule.{u2} N (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3))) (fun (i : ι) => Submodule.subtype.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)))))
 Case conversion may be inaccurate. Consider using '#align complete_lattice.independent.dfinsupp_lsum_injective CompleteLattice.Independent.dfinsupp_lsum_injectiveₓ'. -/
 /-- The canonical map out of a direct sum of a family of submodules is injective when the submodules
 are `complete_lattice.independent`.
@@ -772,7 +772,7 @@ theorem Independent.dfinsupp_sumAddHom_injective {p : ι → AddSubgroup N} (h :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} N] [_inst_3 : Module.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2)] (p : ι -> (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3)), Iff (CompleteLattice.Independent.{succ u1, u3} ι (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) (Submodule.completeLattice.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) p) (Function.Injective.{succ (max u1 u3), succ u3} (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R 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(AddGroup.toSubNegMonoid.{u3} N (AddCommGroup.toAddGroup.{u3} N _inst_2))) (Module.toDistribMulAction.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3))) (fun (i : ι) => Submodule.subtype.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3 (p i)))))
 but is expected to have type
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(AddCommGroup.toAddCommMonoid.{u2} N _inst_2)) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u2, u2} R R Nat (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) 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u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)))) Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (LinearMap.{u3, u3, max u2 u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (Ring.toSemiring.{u3} R _inst_1) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) _inst_3) (SMulZeroClass.toSMul.{0, max u1 u2} Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (AddMonoid.toZero.{max u1 u2} (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{0, max u1 u2} Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R 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(Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R 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(Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))))))) (DistribMulAction.toDistribSMul.{0, max u1 u2} Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max u1 u2} (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))))) (Module.toDistribMulAction.{0, max u1 u2} Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) Nat.semiring (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) 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R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) Nat.semiring (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N 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(AddCommGroup.toAddCommMonoid.{u2} N _inst_2)) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u2, u2} R R Nat (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) 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u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u1, u3, 0, u2, u2} ι R Nat (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N 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+  forall {ι : Type.{u1}} {R : Type.{u3}} {N : Type.{u2}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u2} N] [_inst_3 : Module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)] (p : ι -> (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)), Iff (CompleteLattice.Independent.{succ u1, u2} ι (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (Submodule.completeLattice.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) p) (Function.Injective.{max (succ u1) (succ u2), succ u2} (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N 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u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)))) Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x 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_inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N 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=> LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))))) (Module.toDistribMulAction.{0, max u1 u2} Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) Nat.semiring (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))))) (Pi.module.{u1, u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u2, u2} R R Nat (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u2} N (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)))))))) (SMulZeroClass.toSMul.{0, max u1 u2} Nat (LinearMap.{u3, u3, max u2 u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} 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_inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (Ring.toSemiring.{u3} R _inst_1) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) _inst_3) (AddMonoid.toZero.{max u1 u2} (LinearMap.{u3, u3, max u2 u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N 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_inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))))) (LinearMap.addCommMonoid.{u3, u3, max u1 u2, u2} R R (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (Ring.toSemiring.{u3} R _inst_1) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) (Pi.module.{u1, u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u2, u2} R R Nat (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u2} N (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u2, u2} R R Nat (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (Ring.toSemiring.{u3} R _inst_1) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u2} N (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u1, u3, 0, u2, u2} ι R Nat (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (fun (a : ι) (b : ι) => dec_ι a b) (Ring.toSemiring.{u3} R _inst_1) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 Nat.semiring (AddCommMonoid.natModule.{u2} N (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3))) (fun (i : ι) => Submodule.subtype.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)))))
 Case conversion may be inaccurate. Consider using '#align complete_lattice.independent_iff_dfinsupp_lsum_injective CompleteLattice.independent_iff_dfinsupp_lsum_injectiveₓ'. -/
 /-- A family of submodules over an additive group are independent if and only iff `dfinsupp.lsum`
 applied with `submodule.subtype` is injective.

f4758115

bump to nightly-2023-05-16-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

00d01a10

Diff

@@ -298,7 +298,7 @@ def mapRange.linearMap (f : ∀ i, β₁ i →ₗ[R] β₂ i) : (Π₀ i, β₁
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {β₂ : ι -> Type.{u3}} [_inst_8 : forall (i : ι), AddCommMonoid.{u3} (β₂ i)] [_inst_11 : forall (i : ι), Module.{u2, u3} R (β₂ i) _inst_1 (_inst_8 i)], Eq.{succ (max u1 u3)} (LinearMap.{u2, u2, max u1 u3, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (β₂ i) (AddMonoid.toAddZeroClass.{u3} (β₂ i) (AddCommMonoid.toAddMonoid.{u3} (β₂ i) (_inst_8 i))))) (Dfinsupp.{u1, u3} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (β₂ i) (AddMonoid.toAddZeroClass.{u3} (β₂ i) (AddCommMonoid.toAddMonoid.{u3} (β₂ i) (_inst_8 i))))) (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i))) (Dfinsupp.mapRange.linearMap.{u1, u2, u3, u3} ι R _inst_1 (fun (i : ι) => β₂ i) (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i) (fun (i : ι) => _inst_11 i) (fun (i : ι) => LinearMap.id.{u2, u3} R (β₂ i) _inst_1 (_inst_8 i) (_inst_11 i))) (LinearMap.id.{u2, max u1 u3} R (Dfinsupp.{u1, u3} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (β₂ i) (AddMonoid.toAddZeroClass.{u3} (β₂ i) (AddCommMonoid.toAddMonoid.{u3} (β₂ i) (_inst_8 i))))) _inst_1 (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [β₂ : Semiring.{u1} R] {_inst_8 : ι -> Type.{u2}} [_inst_11 : forall (i : ι), AddCommMonoid.{u2} (_inst_8 i)] [inst._@.Mathlib.LinearAlgebra.Dfinsupp._hyg.2485 : forall (i : ι), Module.{u1, u2} R (_inst_8 i) β₂ (_inst_11 i)], Eq.{max (succ u3) (succ u2)} (LinearMap.{u1, u1, max u2 u3, max u2 u3} R R β₂ β₂ (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R β₂)) (Dfinsupp.{u3, u2} ι (fun (i : ι) => _inst_8 i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => _inst_8 i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => _inst_8 i) i) (_inst_11 i)))) (Dfinsupp.{u3, u2} ι (fun (i : ι) => _inst_8 i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => _inst_8 i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => _inst_8 i) i) (_inst_11 i)))) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u2} ι (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u2} ι (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => _inst_8 i) β₂ (fun (i : ι) => _inst_11 i) (fun (i : ι) => inst._@.Mathlib.LinearAlgebra.Dfinsupp._hyg.2485 i)) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => _inst_8 i) β₂ (fun (i : ι) => _inst_11 i) (fun (i : ι) => inst._@.Mathlib.LinearAlgebra.Dfinsupp._hyg.2485 i))) (Dfinsupp.mapRange.linearMap.{u3, u1, u2, u2} ι R β₂ (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i) (fun (i : ι) => _inst_11 i) (fun (i : ι) => inst._@.Mathlib.LinearAlgebra.Dfinsupp._hyg.2485 i) (fun (i : ι) => inst._@.Mathlib.LinearAlgebra.Dfinsupp._hyg.2485 i) (fun (i : ι) => LinearMap.id.{u1, u2} R (_inst_8 i) β₂ (_inst_11 i) (inst._@.Mathlib.LinearAlgebra.Dfinsupp._hyg.2485 i))) (LinearMap.id.{u1, max u3 u2} R (Dfinsupp.{u3, u2} ι (fun (i : ι) => _inst_8 i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => _inst_8 i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => _inst_8 i) i) (_inst_11 i)))) β₂ (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u2} ι (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => _inst_8 i) β₂ (fun (i : ι) => _inst_11 i) (fun (i : ι) => inst._@.Mathlib.LinearAlgebra.Dfinsupp._hyg.2485 i)))
+  forall {ι : Type.{u3}} {R : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [β₂ : Semiring.{u1} R] {_inst_8 : ι -> Type.{u2}} [_inst_11 : forall (i : ι), AddCommMonoid.{u2} (_inst_8 i)] [inst._@.Mathlib.LinearAlgebra.Dfinsupp._hyg.2484 : forall (i : ι), Module.{u1, u2} R (_inst_8 i) β₂ (_inst_11 i)], Eq.{max (succ u3) (succ u2)} (LinearMap.{u1, u1, max u2 u3, max u2 u3} R R β₂ β₂ (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R β₂)) (Dfinsupp.{u3, u2} ι (fun (i : ι) => _inst_8 i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => _inst_8 i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => _inst_8 i) i) (_inst_11 i)))) (Dfinsupp.{u3, u2} ι (fun (i : ι) => _inst_8 i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => _inst_8 i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => _inst_8 i) i) (_inst_11 i)))) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u2} ι (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u2} ι (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => _inst_8 i) β₂ (fun (i : ι) => _inst_11 i) (fun (i : ι) => inst._@.Mathlib.LinearAlgebra.Dfinsupp._hyg.2484 i)) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => _inst_8 i) β₂ (fun (i : ι) => _inst_11 i) (fun (i : ι) => inst._@.Mathlib.LinearAlgebra.Dfinsupp._hyg.2484 i))) (Dfinsupp.mapRange.linearMap.{u3, u1, u2, u2} ι R β₂ (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i) (fun (i : ι) => _inst_11 i) (fun (i : ι) => inst._@.Mathlib.LinearAlgebra.Dfinsupp._hyg.2484 i) (fun (i : ι) => inst._@.Mathlib.LinearAlgebra.Dfinsupp._hyg.2484 i) (fun (i : ι) => LinearMap.id.{u1, u2} R (_inst_8 i) β₂ (_inst_11 i) (inst._@.Mathlib.LinearAlgebra.Dfinsupp._hyg.2484 i))) (LinearMap.id.{u1, max u3 u2} R (Dfinsupp.{u3, u2} ι (fun (i : ι) => _inst_8 i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => _inst_8 i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => _inst_8 i) i) (_inst_11 i)))) β₂ (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u2} ι (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => _inst_8 i) β₂ (fun (i : ι) => _inst_11 i) (fun (i : ι) => inst._@.Mathlib.LinearAlgebra.Dfinsupp._hyg.2484 i)))
 Case conversion may be inaccurate. Consider using '#align dfinsupp.map_range.linear_map_id Dfinsupp.mapRange.linearMap_idₓ'. -/
 @[simp]
 theorem mapRange.linearMap_id :
@@ -571,7 +571,7 @@ omit dec_ι
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} N] [_inst_3 : Module.{u2, u3} R N _inst_1 _inst_2] {s : Finset.{u1} ι} (p : ι -> (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (a : N), Iff (Membership.Mem.{u3, u3} N (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) a (iSup.{u3, succ u1} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u3} R N _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => iSup.{u3, 0} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u3} R N _inst_1 _inst_2 _inst_3))) (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i s) (fun (H : Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i s) => p i)))) (Exists.{max (succ u1) (succ u3)} (forall (i : ι), coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (μ : forall (i : ι), coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) => Eq.{succ u3} N (Finset.sum.{u3, u1} N ι _inst_2 s (fun (i : ι) => (fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) N (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) N (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) N (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) N (coeSubtype.{succ u3} N (fun (x : N) => Membership.Mem.{u3, u3} N (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) x (p i)))))) (μ i))) a))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {N : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} N] [s : Module.{u2, u1} R N _inst_2 _inst_3] {p : Finset.{u3} ι} (a : ι -> (Submodule.{u2, u1} R N _inst_2 _inst_3 s)) (a_1 : N), Iff (Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.setLike.{u2, u1} R N _inst_2 _inst_3 s)) a_1 (iSup.{u1, succ u3} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (Submodule.completeLattice.{u2, u1} R N _inst_2 _inst_3 s))) ι (fun (i : ι) => iSup.{u1, 0} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (Submodule.completeLattice.{u2, u1} R N _inst_2 _inst_3 s))) (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i p) (fun (h._@.Mathlib.LinearAlgebra.Dfinsupp._hyg.5224 : Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i p) => a i)))) (Exists.{max (succ u3) (succ u1)} (forall (i : ι), Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.setLike.{u2, u1} R N _inst_2 _inst_3 s)) x (a i))) (fun (μ : forall (i : ι), Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.setLike.{u2, u1} R N _inst_2 _inst_3 s)) x (a i))) => Eq.{succ u1} N (Finset.sum.{u1, u3} N ι _inst_3 p (fun (i : ι) => Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.setLike.{u2, u1} R N _inst_2 _inst_3 s) (a i))) (μ i))) a_1))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {N : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} N] [s : Module.{u2, u1} R N _inst_2 _inst_3] {p : Finset.{u3} ι} (a : ι -> (Submodule.{u2, u1} R N _inst_2 _inst_3 s)) (a_1 : N), Iff (Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.setLike.{u2, u1} R N _inst_2 _inst_3 s)) a_1 (iSup.{u1, succ u3} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (Submodule.completeLattice.{u2, u1} R N _inst_2 _inst_3 s))) ι (fun (i : ι) => iSup.{u1, 0} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (Submodule.completeLattice.{u2, u1} R N _inst_2 _inst_3 s))) (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i p) (fun (h._@.Mathlib.LinearAlgebra.Dfinsupp._hyg.5223 : Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i p) => a i)))) (Exists.{max (succ u3) (succ u1)} (forall (i : ι), Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.setLike.{u2, u1} R N _inst_2 _inst_3 s)) x (a i))) (fun (μ : forall (i : ι), Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.setLike.{u2, u1} R N _inst_2 _inst_3 s)) x (a i))) => Eq.{succ u1} N (Finset.sum.{u1, u3} N ι _inst_3 p (fun (i : ι) => Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.setLike.{u2, u1} R N _inst_2 _inst_3 s) (a i))) (μ i))) a_1))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_finset_iff_exists_sum Submodule.mem_iSup_finset_iff_exists_sumₓ'. -/
 theorem mem_iSup_finset_iff_exists_sum {s : Finset ι} (p : ι → Submodule R N) (a : N) :
     (a ∈ ⨆ i ∈ s, p i) ↔ ∃ μ : ∀ i, p i, (∑ i in s, (μ i : N)) = a := by

f4758115

bump to nightly-2023-05-14-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee

d31da313

Diff

@@ -478,42 +478,42 @@ theorem dfinsupp_sumAddHom_mem {β : ι → Type _} [∀ i, AddZeroClass (β i)]
   dfinsupp_sumAddHom_mem S f g h
 #align submodule.dfinsupp_sum_add_hom_mem Submodule.dfinsupp_sumAddHom_mem
 
-/- warning: submodule.supr_eq_range_dfinsupp_lsum -> Submodule.supᵢ_eq_range_dfinsupp_lsum is a dubious translation:
+/- warning: submodule.supr_eq_range_dfinsupp_lsum -> Submodule.iSup_eq_range_dfinsupp_lsum is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align submodule.supr_eq_range_dfinsupp_lsum Submodule.supᵢ_eq_range_dfinsupp_lsumₓ'. -/
+  forall {ι : Type.{u1}} {R : Type.{u3}} {N : Type.{u2}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} N] [_inst_3 : Module.{u3, u2} R N _inst_1 _inst_2] (p : ι -> (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (iSup.{u2, succ u1} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u3, u2} R N _inst_1 _inst_2 _inst_3))) ι p) (LinearMap.range.{u3, u3, max u1 u2, u2, max u1 u2} R R (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 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+Case conversion may be inaccurate. Consider using '#align submodule.supr_eq_range_dfinsupp_lsum Submodule.iSup_eq_range_dfinsupp_lsumₓ'. -/
 /-- The supremum of a family of submodules is equal to the range of `dfinsupp.lsum`; that is
 every element in the `supr` can be produced from taking a finite number of non-zero elements
 of `p i`, coercing them to `N`, and summing them. -/
-theorem supᵢ_eq_range_dfinsupp_lsum (p : ι → Submodule R N) :
-    supᵢ p = (Dfinsupp.lsum ℕ fun i => (p i).Subtype).range :=
+theorem iSup_eq_range_dfinsupp_lsum (p : ι → Submodule R N) :
+    iSup p = (Dfinsupp.lsum ℕ fun i => (p i).Subtype).range :=
   by
   apply le_antisymm
-  · apply supᵢ_le _
+  · apply iSup_le _
     intro i y hy
     exact ⟨Dfinsupp.single i ⟨y, hy⟩, Dfinsupp.sumAddHom_single _ _ _⟩
   · rintro x ⟨v, rfl⟩
-    exact dfinsupp_sumAddHom_mem _ v _ fun i _ => (le_supᵢ p i : p i ≤ _) (v i).Prop
-#align submodule.supr_eq_range_dfinsupp_lsum Submodule.supᵢ_eq_range_dfinsupp_lsum
+    exact dfinsupp_sumAddHom_mem _ v _ fun i _ => (le_iSup p i : p i ≤ _) (v i).Prop
+#align submodule.supr_eq_range_dfinsupp_lsum Submodule.iSup_eq_range_dfinsupp_lsum
 
-/- warning: submodule.bsupr_eq_range_dfinsupp_lsum -> Submodule.bsupᵢ_eq_range_dfinsupp_lsum is a dubious translation:
+/- warning: submodule.bsupr_eq_range_dfinsupp_lsum -> Submodule.biSup_eq_range_dfinsupp_lsum is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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(Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) N (Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_2 (Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u1, u1} R R (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) N _inst_1 _inst_1 (Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_2 (Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u3 u1, u1} R R (Dfinsupp.{u3, u1} ι (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) (fun (i : ι) => AddMonoid.toZero.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (AddCommMonoid.toAddMonoid.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u1} ι (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => 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(Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) N (Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_2 (Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_3) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u1, u1} R R (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) N _inst_1 _inst_1 (Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_2 (Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_3 (RingHom.id.{u2} R 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_inst_3 (S i)) (fun (i : ι) => Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_2 _inst_3 Nat.semiring (AddCommMonoid.natModule.{u1} N _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R N (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_2) (Module.toDistribMulAction.{u2, u1} R N _inst_1 _inst_2 _inst_3))) (fun (i : ι) => Submodule.subtype.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))) (Dfinsupp.filterLinearMap.{u3, u1, u2} ι R (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) (fun (i : ι) => Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) p (fun (a : ι) => _inst_4 a))))
-Case conversion may be inaccurate. Consider using '#align submodule.bsupr_eq_range_dfinsupp_lsum Submodule.bsupᵢ_eq_range_dfinsupp_lsumₓ'. -/
+  forall {ι : Type.{u3}} {R : Type.{u2}} {N : Type.{u1}} [dec_ι : DecidableEq.{succ u3} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} N] [_inst_3 : Module.{u2, u1} R N _inst_1 _inst_2] (p : ι -> Prop) [_inst_4 : DecidablePred.{succ u3} ι p] (S : ι -> (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3)), Eq.{succ u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (iSup.{u1, succ u3} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R N _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => iSup.{u1, 0} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R N _inst_1 _inst_2 _inst_3))) (p i) (fun (h : p i) => S i))) (LinearMap.range.{u2, u2, max u3 u1, u1, max u1 u3} R R (Dfinsupp.{u3, u1} ι (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) (fun (i : ι) => AddMonoid.toZero.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (AddCommMonoid.toAddMonoid.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 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+Case conversion may be inaccurate. Consider using '#align submodule.bsupr_eq_range_dfinsupp_lsum Submodule.biSup_eq_range_dfinsupp_lsumₓ'. -/
 /-- The bounded supremum of a family of commutative additive submonoids is equal to the range of
 `dfinsupp.sum_add_hom` composed with `dfinsupp.filter_add_monoid_hom`; that is, every element in the
 bounded `supr` can be produced from taking a finite number of non-zero elements from the `S i` that
 satisfy `p i`, coercing them to `γ`, and summing them. -/
-theorem bsupᵢ_eq_range_dfinsupp_lsum (p : ι → Prop) [DecidablePred p] (S : ι → Submodule R N) :
+theorem biSup_eq_range_dfinsupp_lsum (p : ι → Prop) [DecidablePred p] (S : ι → Submodule R N) :
     (⨆ (i) (h : p i), S i) =
       ((Dfinsupp.lsum ℕ fun i => (S i).Subtype).comp (Dfinsupp.filterLinearMap R _ p)).range :=
   by
   apply le_antisymm
-  · refine' supᵢ₂_le fun i hi y hy => ⟨Dfinsupp.single i ⟨y, hy⟩, _⟩
+  · refine' iSup₂_le fun i hi y hy => ⟨Dfinsupp.single i ⟨y, hy⟩, _⟩
     rw [LinearMap.comp_apply, filter_linear_map_apply, filter_single_pos _ _ hi]
     exact Dfinsupp.sumAddHom_single _ _ _
   · rintro x ⟨v, rfl⟩
@@ -522,63 +522,63 @@ theorem bsupᵢ_eq_range_dfinsupp_lsum (p : ι → Prop) [DecidablePred p] (S :
     by_cases hp : p i
     · simp [hp]
     · simp [hp]
-#align submodule.bsupr_eq_range_dfinsupp_lsum Submodule.bsupᵢ_eq_range_dfinsupp_lsum
+#align submodule.bsupr_eq_range_dfinsupp_lsum Submodule.biSup_eq_range_dfinsupp_lsum
 
-/- warning: submodule.mem_supr_iff_exists_dfinsupp -> Submodule.mem_supᵢ_iff_exists_dfinsupp is a dubious translation:
+/- warning: submodule.mem_supr_iff_exists_dfinsupp -> Submodule.mem_iSup_iff_exists_dfinsupp is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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_inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N _inst_1 _inst_1 (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, max u1 u2, u2} R R (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => 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(Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N _inst_1 _inst_1 (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u2, u2} R R Nat (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N _inst_1 _inst_1 (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u2, u2} R R Nat (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_2 (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u1, u3, 0, u2, u2} ι R Nat (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 _inst_3 Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3))) (fun (i : ι) => Submodule.subtype.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) f) x))
-Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_iff_exists_dfinsupp Submodule.mem_supᵢ_iff_exists_dfinsuppₓ'. -/
-theorem mem_supᵢ_iff_exists_dfinsupp (p : ι → Submodule R N) (x : N) :
-    x ∈ supᵢ p ↔ ∃ f : Π₀ i, p i, Dfinsupp.lsum ℕ (fun i => (p i).Subtype) f = x :=
-  SetLike.ext_iff.mp (supᵢ_eq_range_dfinsupp_lsum p) x
-#align submodule.mem_supr_iff_exists_dfinsupp Submodule.mem_supᵢ_iff_exists_dfinsupp
+  forall {ι : Type.{u1}} {R : Type.{u3}} {N : Type.{u2}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} N] [_inst_3 : Module.{u3, u2} R N _inst_1 _inst_2] (p : ι -> (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) (x : N), Iff (Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (iSup.{u2, succ u1} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u3, u2} R N _inst_1 _inst_2 _inst_3))) ι p)) (Exists.{max (succ u1) (succ u2)} (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => Submodule.zero.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) (fun (f : Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => Submodule.zero.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) => Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))) => N) f) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : forall (i : ι), LinearMap.{u3, u3, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Subtype.{succ u2} N 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_inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 _inst_3 Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3))) (fun (i : ι) => Submodule.subtype.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) f) x))
+Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_iff_exists_dfinsupp Submodule.mem_iSup_iff_exists_dfinsuppₓ'. -/
+theorem mem_iSup_iff_exists_dfinsupp (p : ι → Submodule R N) (x : N) :
+    x ∈ iSup p ↔ ∃ f : Π₀ i, p i, Dfinsupp.lsum ℕ (fun i => (p i).Subtype) f = x :=
+  SetLike.ext_iff.mp (iSup_eq_range_dfinsupp_lsum p) x
+#align submodule.mem_supr_iff_exists_dfinsupp Submodule.mem_iSup_iff_exists_dfinsupp
 
-/- warning: submodule.mem_supr_iff_exists_dfinsupp' -> Submodule.mem_supᵢ_iff_exists_dfinsupp' is a dubious translation:
+/- warning: submodule.mem_supr_iff_exists_dfinsupp' -> Submodule.mem_iSup_iff_exists_dfinsupp' is a dubious translation:
 lean 3 declaration is
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+  forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} N] [_inst_3 : Module.{u2, u3} R N _inst_1 _inst_2] (p : ι -> (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3)) [_inst_4 : forall (i : ι) (x : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)), Decidable (Ne.{succ u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) x (OfNat.ofNat.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N 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(Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) N (coeSubtype.{succ u3} N (fun (x : N) => Membership.Mem.{u3, u3} N (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) x (p i)))))) xi)) x))
 but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_iff_exists_dfinsupp' Submodule.mem_supᵢ_iff_exists_dfinsupp'ₓ'. -/
+  forall {ι : Type.{u1}} {R : Type.{u3}} {N : Type.{u2}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} N] [_inst_3 : Module.{u3, u2} R N _inst_1 _inst_2] (p : ι -> (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) [_inst_4 : forall (i : ι) (x : Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))), Decidable (Ne.{succ u2} (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) x (OfNat.ofNat.{u2} (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) 0 (Zero.toOfNat0.{u2} (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (Submodule.zero.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)))))] (x : N), Iff (Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (iSup.{u2, succ u1} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u3, u2} R N _inst_1 _inst_2 _inst_3))) ι p)) (Exists.{max (succ u1) (succ u2)} (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => Submodule.zero.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) (fun (f : Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => Submodule.zero.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) => Eq.{succ u2} N (Dfinsupp.sum.{u1, u2, u2} ι N (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => Submodule.zero.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) (x : Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) => _inst_4 i x) _inst_2 f (fun (i : ι) (xi : Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) => Subtype.val.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Set.{u2} N) (Set.instMembershipSet.{u2} N) x (SetLike.coe.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3) (p i))) xi)) x))
+Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_iff_exists_dfinsupp' Submodule.mem_iSup_iff_exists_dfinsupp'ₓ'. -/
 /-- A variant of `submodule.mem_supr_iff_exists_dfinsupp` with the RHS fully unfolded. -/
-theorem mem_supᵢ_iff_exists_dfinsupp' (p : ι → Submodule R N) [∀ (i) (x : p i), Decidable (x ≠ 0)]
-    (x : N) : x ∈ supᵢ p ↔ ∃ f : Π₀ i, p i, (f.Sum fun i xi => ↑xi) = x :=
+theorem mem_iSup_iff_exists_dfinsupp' (p : ι → Submodule R N) [∀ (i) (x : p i), Decidable (x ≠ 0)]
+    (x : N) : x ∈ iSup p ↔ ∃ f : Π₀ i, p i, (f.Sum fun i xi => ↑xi) = x :=
   by
   rw [mem_supr_iff_exists_dfinsupp]
   simp_rw [Dfinsupp.lsum_apply_apply, Dfinsupp.sumAddHom_apply]
   congr
-#align submodule.mem_supr_iff_exists_dfinsupp' Submodule.mem_supᵢ_iff_exists_dfinsupp'
+#align submodule.mem_supr_iff_exists_dfinsupp' Submodule.mem_iSup_iff_exists_dfinsupp'
 
-/- warning: submodule.mem_bsupr_iff_exists_dfinsupp -> Submodule.mem_bsupᵢ_iff_exists_dfinsupp is a dubious translation:
+/- warning: submodule.mem_bsupr_iff_exists_dfinsupp -> Submodule.mem_biSup_iff_exists_dfinsupp is a dubious translation:
 lean 3 declaration is
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_inst_2 _inst_3 (S i))) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u3} N _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R N (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} N _inst_2) (Module.toDistribMulAction.{u2, u3} R N _inst_1 _inst_2 _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)) (Dfinsupp.lsum.{u1, u2, 0, u3, u3} ι R Nat (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (S i)) N (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u2, u3} R N _inst_1 _inst_2 _inst_3 (S i)) (fun (i : ι) => Submodule.module.{u2, u3} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_2 _inst_3 Nat.semiring (AddCommMonoid.natModule.{u3} N _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R N (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} N _inst_2) (Module.toDistribMulAction.{u2, u3} R N _inst_1 _inst_2 _inst_3))) (fun (i : ι) => Submodule.subtype.{u2, u3} R N _inst_1 _inst_2 _inst_3 (S i))) (Dfinsupp.filter.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (S i)) (fun (i : ι) => Submodule.zero.{u2, u3} R N _inst_1 _inst_2 _inst_3 (S i)) p (fun (a : ι) => _inst_4 a) f)) x))
 but is expected to have type
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(Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (AddCommMonoid.toAddMonoid.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u1} ι (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) (fun (i : ι) => Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))) _inst_2 (Dfinsupp.module.{u3, u1, u2} ι R (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) (fun (i : ι) => Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} N _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R N (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_2) (Module.toDistribMulAction.{u2, u1} R N _inst_1 _inst_2 _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u3, u2, 0, u1, u1} ι R Nat (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) N (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) (fun (i : ι) => Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_2 _inst_3 Nat.semiring (AddCommMonoid.natModule.{u1} N _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R N (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_2) (Module.toDistribMulAction.{u2, u1} R N _inst_1 _inst_2 _inst_3))) (fun (i : ι) => Submodule.subtype.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))) (Dfinsupp.filter.{u3, u1} ι (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) (fun (i : ι) => AddMonoid.toZero.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (AddCommMonoid.toAddMonoid.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)))) p (fun (a : ι) => _inst_4 a) f)) x))
-Case conversion may be inaccurate. Consider using '#align submodule.mem_bsupr_iff_exists_dfinsupp Submodule.mem_bsupᵢ_iff_exists_dfinsuppₓ'. -/
-theorem mem_bsupᵢ_iff_exists_dfinsupp (p : ι → Prop) [DecidablePred p] (S : ι → Submodule R N)
+  forall {ι : Type.{u3}} {R : Type.{u2}} {N : Type.{u1}} [dec_ι : DecidableEq.{succ u3} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} N] [_inst_3 : Module.{u2, u1} R N _inst_1 _inst_2] (p : ι -> Prop) [_inst_4 : DecidablePred.{succ u3} ι p] (S : ι -> (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3)) (x : N), Iff (Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (iSup.{u1, succ u3} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R N _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => iSup.{u1, 0} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R N _inst_1 _inst_2 _inst_3))) (p i) (fun (h : p i) => S i)))) (Exists.{max (succ u3) (succ u1)} (Dfinsupp.{u3, u1} ι (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) (fun (i : ι) => Submodule.zero.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))) (fun (f : Dfinsupp.{u3, u1} ι (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) (fun (i : ι) => Submodule.zero.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))) => Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Dfinsupp.{u3, u1} ι (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) (fun (i : ι) => AddMonoid.toZero.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (AddCommMonoid.toAddMonoid.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))))) => N) (Dfinsupp.filter.{u3, u1} ι (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) (fun (i : ι) => AddMonoid.toZero.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (AddCommMonoid.toAddMonoid.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)))) p (fun (a : ι) => _inst_4 a) f)) (FunLike.coe.{max (succ u3) (succ u1), max (succ u3) (succ u1), succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : forall (i : ι), LinearMap.{u2, u2, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) N (Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_2 (Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_3) => LinearMap.{u2, u2, max u1 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u3, u1} ι (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) (fun (i : ι) => AddMonoid.toZero.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (AddCommMonoid.toAddMonoid.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u1} ι (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) (fun (i : ι) => Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))) _inst_2 (Dfinsupp.module.{u3, u1, u2} ι R (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) (fun (i : ι) => Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))) _inst_3) (fun (i : ι) => Submodule.subtype.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))) (Dfinsupp.{u3, u1} ι (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) (fun (i : ι) => AddMonoid.toZero.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (AddCommMonoid.toAddMonoid.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 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(Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u3, u2, 0, u1, u1} ι R Nat (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) N (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) (fun (i : ι) => Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_2 _inst_3 Nat.semiring (AddCommMonoid.natModule.{u1} N _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R N (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_2) (Module.toDistribMulAction.{u2, u1} R N _inst_1 _inst_2 _inst_3))) (fun (i : ι) => Submodule.subtype.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))) (Dfinsupp.filter.{u3, u1} ι (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) (fun (i : ι) => AddMonoid.toZero.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (AddCommMonoid.toAddMonoid.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)))) p (fun (a : ι) => _inst_4 a) f)) x))
+Case conversion may be inaccurate. Consider using '#align submodule.mem_bsupr_iff_exists_dfinsupp Submodule.mem_biSup_iff_exists_dfinsuppₓ'. -/
+theorem mem_biSup_iff_exists_dfinsupp (p : ι → Prop) [DecidablePred p] (S : ι → Submodule R N)
     (x : N) :
     (x ∈ ⨆ (i) (h : p i), S i) ↔
       ∃ f : Π₀ i, S i, Dfinsupp.lsum ℕ (fun i => (S i).Subtype) (f.filterₓ p) = x :=
-  SetLike.ext_iff.mp (bsupᵢ_eq_range_dfinsupp_lsum p S) x
-#align submodule.mem_bsupr_iff_exists_dfinsupp Submodule.mem_bsupᵢ_iff_exists_dfinsupp
+  SetLike.ext_iff.mp (biSup_eq_range_dfinsupp_lsum p S) x
+#align submodule.mem_bsupr_iff_exists_dfinsupp Submodule.mem_biSup_iff_exists_dfinsupp
 
 open BigOperators
 
 omit dec_ι
 
-/- warning: submodule.mem_supr_finset_iff_exists_sum -> Submodule.mem_supᵢ_finset_iff_exists_sum is a dubious translation:
+/- warning: submodule.mem_supr_finset_iff_exists_sum -> Submodule.mem_iSup_finset_iff_exists_sum is a dubious translation:
 lean 3 declaration is
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+  forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} N] [_inst_3 : Module.{u2, u3} R N _inst_1 _inst_2] {s : Finset.{u1} ι} (p : ι -> (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (a : N), Iff (Membership.Mem.{u3, u3} N (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) a (iSup.{u3, succ u1} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u3} R N _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => iSup.{u3, 0} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u3} R N _inst_1 _inst_2 _inst_3))) (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i s) (fun (H : Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i s) => p i)))) (Exists.{max (succ u1) (succ u3)} (forall (i : ι), coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (μ : forall (i : ι), coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) => Eq.{succ u3} N (Finset.sum.{u3, u1} N ι _inst_2 s (fun (i : ι) => (fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) N (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) N (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) N (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) N (coeSubtype.{succ u3} N (fun (x : N) => Membership.Mem.{u3, u3} N (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) x (p i)))))) (μ i))) a))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {N : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} N] [s : Module.{u2, u1} R N _inst_2 _inst_3] {p : Finset.{u3} ι} (a : ι -> (Submodule.{u2, u1} R N _inst_2 _inst_3 s)) (a_1 : N), Iff (Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.setLike.{u2, u1} R N _inst_2 _inst_3 s)) a_1 (supᵢ.{u1, succ u3} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (Submodule.completeLattice.{u2, u1} R N _inst_2 _inst_3 s))) ι (fun (i : ι) => supᵢ.{u1, 0} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (Submodule.completeLattice.{u2, u1} R N _inst_2 _inst_3 s))) (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i p) (fun (h._@.Mathlib.LinearAlgebra.Dfinsupp._hyg.5224 : Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i p) => a i)))) (Exists.{max (succ u3) (succ u1)} (forall (i : ι), Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.setLike.{u2, u1} R N _inst_2 _inst_3 s)) x (a i))) (fun (μ : forall (i : ι), Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.setLike.{u2, u1} R N _inst_2 _inst_3 s)) x (a i))) => Eq.{succ u1} N (Finset.sum.{u1, u3} N ι _inst_3 p (fun (i : ι) => Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.setLike.{u2, u1} R N _inst_2 _inst_3 s) (a i))) (μ i))) a_1))
-Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_finset_iff_exists_sum Submodule.mem_supᵢ_finset_iff_exists_sumₓ'. -/
-theorem mem_supᵢ_finset_iff_exists_sum {s : Finset ι} (p : ι → Submodule R N) (a : N) :
+  forall {ι : Type.{u3}} {R : Type.{u2}} {N : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} N] [s : Module.{u2, u1} R N _inst_2 _inst_3] {p : Finset.{u3} ι} (a : ι -> (Submodule.{u2, u1} R N _inst_2 _inst_3 s)) (a_1 : N), Iff (Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.setLike.{u2, u1} R N _inst_2 _inst_3 s)) a_1 (iSup.{u1, succ u3} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (Submodule.completeLattice.{u2, u1} R N _inst_2 _inst_3 s))) ι (fun (i : ι) => iSup.{u1, 0} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (Submodule.completeLattice.{u2, u1} R N _inst_2 _inst_3 s))) (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i p) (fun (h._@.Mathlib.LinearAlgebra.Dfinsupp._hyg.5224 : Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i p) => a i)))) (Exists.{max (succ u3) (succ u1)} (forall (i : ι), Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.setLike.{u2, u1} R N _inst_2 _inst_3 s)) x (a i))) (fun (μ : forall (i : ι), Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.setLike.{u2, u1} R N _inst_2 _inst_3 s)) x (a i))) => Eq.{succ u1} N (Finset.sum.{u1, u3} N ι _inst_3 p (fun (i : ι) => Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.setLike.{u2, u1} R N _inst_2 _inst_3 s) (a i))) (μ i))) a_1))
+Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_finset_iff_exists_sum Submodule.mem_iSup_finset_iff_exists_sumₓ'. -/
+theorem mem_iSup_finset_iff_exists_sum {s : Finset ι} (p : ι → Submodule R N) (a : N) :
     (a ∈ ⨆ i ∈ s, p i) ↔ ∃ μ : ∀ i, p i, (∑ i in s, (μ i : N)) = a := by
   classical
-    rw [Submodule.mem_supᵢ_iff_exists_dfinsupp']
+    rw [Submodule.mem_iSup_iff_exists_dfinsupp']
     constructor <;> rintro ⟨μ, hμ⟩
-    · use fun i => ⟨μ i, (supᵢ_const_le : _ ≤ p i) (coe_mem <| μ i)⟩
+    · use fun i => ⟨μ i, (iSup_const_le : _ ≤ p i) (coe_mem <| μ i)⟩
       rw [← hμ]
       symm
       apply Finset.sum_subset
@@ -590,7 +590,7 @@ theorem mem_supᵢ_finset_iff_exists_sum {s : Finset ι} (p : ι → Submodule R
         rw [coe_zero, ← mem_bot R]
         convert coe_mem (μ x)
         symm
-        exact supᵢ_neg hx
+        exact iSup_neg hx
       · intro x _ hx
         rw [mem_support_iff, not_ne_iff] at hx
         rw [hx]
@@ -598,7 +598,7 @@ theorem mem_supᵢ_finset_iff_exists_sum {s : Finset ι} (p : ι → Submodule R
     · refine' ⟨Dfinsupp.mk s _, _⟩
       · rintro ⟨i, hi⟩
         refine' ⟨μ i, _⟩
-        rw [supᵢ_pos]
+        rw [iSup_pos]
         · exact coe_mem _
         · exact hi
       simp only [Dfinsupp.sum]
@@ -608,7 +608,7 @@ theorem mem_supᵢ_finset_iff_exists_sum {s : Finset ι} (p : ι → Submodule R
         rw [mem_support_iff, not_ne_iff] at hx
         rw [hx]
         rfl
-#align submodule.mem_supr_finset_iff_exists_sum Submodule.mem_supᵢ_finset_iff_exists_sum
+#align submodule.mem_supr_finset_iff_exists_sum Submodule.mem_iSup_finset_iff_exists_sum
 
 end Submodule
 
@@ -637,7 +637,7 @@ theorem independent_iff_forall_dfinsupp (p : ι → Submodule R N) :
         lsum ℕ (fun i => (p i).Subtype) (erase i v) = x → x = 0 :=
   by
   simp_rw [CompleteLattice.independent_def, Submodule.disjoint_def,
-    Submodule.mem_bsupᵢ_iff_exists_dfinsupp, exists_imp, filter_ne_eq_erase]
+    Submodule.mem_biSup_iff_exists_dfinsupp, exists_imp, filter_ne_eq_erase]
   apply forall_congr' fun i => _
   refine' subtype.forall'.trans _
   simp_rw [Submodule.coe_eq_zero]

f4758115

bump to nightly-2023-05-03-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/36b8aa61ea7c05727161f96a0532897bd72aedab

aa7b8e08

Diff

@@ -571,7 +571,7 @@ omit dec_ι
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} N] [_inst_3 : Module.{u2, u3} R N _inst_1 _inst_2] {s : Finset.{u1} ι} (p : ι -> (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (a : N), Iff (Membership.Mem.{u3, u3} N (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) a (supᵢ.{u3, succ u1} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u3} R N _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => supᵢ.{u3, 0} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u3} R N _inst_1 _inst_2 _inst_3))) (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i s) (fun (H : Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i s) => p i)))) (Exists.{max (succ u1) (succ u3)} (forall (i : ι), coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (μ : forall (i : ι), coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) => Eq.{succ u3} N (Finset.sum.{u3, u1} N ι _inst_2 s (fun (i : ι) => (fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) N (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) N (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) N (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) N (coeSubtype.{succ u3} N (fun (x : N) => Membership.Mem.{u3, u3} N (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) x (p i)))))) (μ i))) a))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {N : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} N] [s : Module.{u2, u1} R N _inst_2 _inst_3] {p : Finset.{u3} ι} (a : ι -> (Submodule.{u2, u1} R N _inst_2 _inst_3 s)) (a_1 : N), Iff (Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.setLike.{u2, u1} R N _inst_2 _inst_3 s)) a_1 (supᵢ.{u1, succ u3} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (Submodule.completeLattice.{u2, u1} R N _inst_2 _inst_3 s))) ι (fun (i : ι) => supᵢ.{u1, 0} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (Submodule.completeLattice.{u2, u1} R N _inst_2 _inst_3 s))) (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i p) (fun (h._@.Mathlib.LinearAlgebra.Dfinsupp._hyg.5226 : Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i p) => a i)))) (Exists.{max (succ u3) (succ u1)} (forall (i : ι), Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.setLike.{u2, u1} R N _inst_2 _inst_3 s)) x (a i))) (fun (μ : forall (i : ι), Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.setLike.{u2, u1} R N _inst_2 _inst_3 s)) x (a i))) => Eq.{succ u1} N (Finset.sum.{u1, u3} N ι _inst_3 p (fun (i : ι) => Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.setLike.{u2, u1} R N _inst_2 _inst_3 s) (a i))) (μ i))) a_1))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {N : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} N] [s : Module.{u2, u1} R N _inst_2 _inst_3] {p : Finset.{u3} ι} (a : ι -> (Submodule.{u2, u1} R N _inst_2 _inst_3 s)) (a_1 : N), Iff (Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.setLike.{u2, u1} R N _inst_2 _inst_3 s)) a_1 (supᵢ.{u1, succ u3} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (Submodule.completeLattice.{u2, u1} R N _inst_2 _inst_3 s))) ι (fun (i : ι) => supᵢ.{u1, 0} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (Submodule.completeLattice.{u2, u1} R N _inst_2 _inst_3 s))) (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i p) (fun (h._@.Mathlib.LinearAlgebra.Dfinsupp._hyg.5224 : Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i p) => a i)))) (Exists.{max (succ u3) (succ u1)} (forall (i : ι), Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.setLike.{u2, u1} R N _inst_2 _inst_3 s)) x (a i))) (fun (μ : forall (i : ι), Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.setLike.{u2, u1} R N _inst_2 _inst_3 s)) x (a i))) => Eq.{succ u1} N (Finset.sum.{u1, u3} N ι _inst_3 p (fun (i : ι) => Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.setLike.{u2, u1} R N _inst_2 _inst_3 s) (a i))) (μ i))) a_1))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_finset_iff_exists_sum Submodule.mem_supᵢ_finset_iff_exists_sumₓ'. -/
 theorem mem_supᵢ_finset_iff_exists_sum {s : Finset ι} (p : ι → Submodule R N) (a : N) :
     (a ∈ ⨆ i ∈ s, p i) ↔ ∃ μ : ∀ i, p i, (∑ i in s, (μ i : N)) = a := by

f4758115

bump to nightly-2023-04-29-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/a4f99eae998680d3a2c240da4a2b16354c85ee49

742d9611

Diff

@@ -803,7 +803,7 @@ omit dec_ι
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} N] [_inst_3 : Module.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2)] [_inst_4 : NoZeroSMulDivisors.{u2, u3} R N (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (SubNegMonoid.toAddMonoid.{u3} N (AddGroup.toSubNegMonoid.{u3} N (AddCommGroup.toAddGroup.{u3} N _inst_2))))) (SMulZeroClass.toHasSmul.{u2, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N _inst_2)))) (SMulWithZero.toSmulZeroClass.{u2, u3} R N (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N _inst_2)))) (MulActionWithZero.toSMulWithZero.{u2, u3} R N (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N _inst_2)))) (Module.toMulActionWithZero.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3))))] (p : ι -> (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3)), (CompleteLattice.Independent.{succ u1, u3} ι (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) (Submodule.completeLattice.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) p) -> (forall {v : ι -> N}, (forall (i : ι), Membership.Mem.{u3, u3} N (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) N (Submodule.setLike.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3)) (v i) (p i)) -> (forall (i : ι), Ne.{succ u3} N (v i) (OfNat.ofNat.{u3} N 0 (OfNat.mk.{u3} N 0 (Zero.zero.{u3} N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (SubNegMonoid.toAddMonoid.{u3} N (AddGroup.toSubNegMonoid.{u3} N (AddCommGroup.toAddGroup.{u3} N _inst_2))))))))) -> (LinearIndependent.{u1, u2, u3} ι R N v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3))
 but is expected to have type
-  forall {ι : Type.{u1}} {R : Type.{u3}} {N : Type.{u2}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : Ring.{u3} R] [_inst_3 : AddCommGroup.{u2} N] [_inst_4 : Module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3)] [p : NoZeroSMulDivisors.{u3, u2} R N (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_2))) (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N _inst_3))))) (SMulZeroClass.toSMul.{u3, u2} R N (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N _inst_3))))) (SMulWithZero.toSMulZeroClass.{u3, u2} R N (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_2))) (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N _inst_3))))) (MulActionWithZero.toSMulWithZero.{u3, u2} R N (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_2)) (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N _inst_3))))) (Module.toMulActionWithZero.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4))))] (hp : ι -> (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4)), (CompleteLattice.Independent.{succ u1, u2} ι (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4) (Submodule.completeLattice.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4) hp) -> (forall {hv : ι -> N}, (forall (i : ι), Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4)) (hv i) (hp i)) -> (forall (i : ι), Ne.{succ u2} N (hv i) (OfNat.ofNat.{u2} N 0 (Zero.toOfNat0.{u2} N (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N _inst_3)))))))) -> (LinearIndependent.{u1, u3, u2} ι R N hv (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4))
+  forall {ι : Type.{u1}} {R : Type.{u3}} {N : Type.{u2}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u2} N] [_inst_3 : Module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)] [_inst_4 : NoZeroSMulDivisors.{u3, u2} R N (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N _inst_2))))) (SMulZeroClass.toSMul.{u3, u2} R N (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} R N (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} R N (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1)) (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N _inst_2))))) (Module.toMulActionWithZero.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3))))] (p : ι -> (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)), (CompleteLattice.Independent.{succ u1, u2} ι (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (Submodule.completeLattice.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) p) -> (forall {v : ι -> N}, (forall (i : ι), Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) (v i) (p i)) -> (forall (i : ι), Ne.{succ u2} N (v i) (OfNat.ofNat.{u2} N 0 (Zero.toOfNat0.{u2} N (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N _inst_2)))))))) -> (LinearIndependent.{u1, u3, u2} ι R N v (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3))
 Case conversion may be inaccurate. Consider using '#align complete_lattice.independent.linear_independent CompleteLattice.Independent.linearIndependentₓ'. -/
 /-- If a family of submodules is `independent`, then a choice of nonzero vector from each submodule
 forms a linearly independent family.
@@ -831,7 +831,7 @@ theorem Independent.linearIndependent [NoZeroSMulDivisors R N] (p : ι → Submo
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} N] [_inst_3 : Module.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2)] [_inst_4 : NoZeroSMulDivisors.{u2, u3} R N (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (SubNegMonoid.toAddMonoid.{u3} N (AddGroup.toSubNegMonoid.{u3} N (AddCommGroup.toAddGroup.{u3} N _inst_2))))) (SMulZeroClass.toHasSmul.{u2, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N _inst_2)))) (SMulWithZero.toSmulZeroClass.{u2, u3} R N (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N _inst_2)))) (MulActionWithZero.toSMulWithZero.{u2, u3} R N (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N _inst_2)))) (Module.toMulActionWithZero.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3))))] {v : ι -> N}, (forall (i : ι), Ne.{succ u3} N (v i) (OfNat.ofNat.{u3} N 0 (OfNat.mk.{u3} N 0 (Zero.zero.{u3} N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (SubNegMonoid.toAddMonoid.{u3} N (AddGroup.toSubNegMonoid.{u3} N (AddCommGroup.toAddGroup.{u3} N _inst_2))))))))) -> (Iff (CompleteLattice.Independent.{succ u1, u3} ι (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) (Submodule.completeLattice.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) (fun (i : ι) => Submodule.span.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3 (Singleton.singleton.{u3, u3} N (Set.{u3} N) (Set.hasSingleton.{u3} N) (v i)))) (LinearIndependent.{u1, u2, u3} ι R N v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3))
 but is expected to have type
-  forall {ι : Type.{u1}} {R : Type.{u3}} {N : Type.{u2}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : Ring.{u3} R] [_inst_3 : AddCommGroup.{u2} N] [_inst_4 : Module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3)] [v : NoZeroSMulDivisors.{u3, u2} R N (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_2))) (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N _inst_3))))) (SMulZeroClass.toSMul.{u3, u2} R N (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N _inst_3))))) (SMulWithZero.toSMulZeroClass.{u3, u2} R N (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_2))) (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N _inst_3))))) (MulActionWithZero.toSMulWithZero.{u3, u2} R N (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_2)) (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N _inst_3))))) (Module.toMulActionWithZero.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4))))] {h_ne_zero : ι -> N}, (forall (i : ι), Ne.{succ u2} N (h_ne_zero i) (OfNat.ofNat.{u2} N 0 (Zero.toOfNat0.{u2} N (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N _inst_3)))))))) -> (Iff (CompleteLattice.Independent.{succ u1, u2} ι (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4) (Submodule.completeLattice.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4) (fun (i : ι) => Submodule.span.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4 (Singleton.singleton.{u2, u2} N (Set.{u2} N) (Set.instSingletonSet.{u2} N) (h_ne_zero i)))) (LinearIndependent.{u1, u3, u2} ι R N h_ne_zero (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4))
+  forall {ι : Type.{u1}} {R : Type.{u3}} {N : Type.{u2}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u2} N] [_inst_3 : Module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)] [_inst_4 : NoZeroSMulDivisors.{u3, u2} R N (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N _inst_2))))) (SMulZeroClass.toSMul.{u3, u2} R N (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} R N (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} R N (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1)) (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N _inst_2))))) (Module.toMulActionWithZero.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3))))] {v : ι -> N}, (forall (i : ι), Ne.{succ u2} N (v i) (OfNat.ofNat.{u2} N 0 (Zero.toOfNat0.{u2} N (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N _inst_2)))))))) -> (Iff (CompleteLattice.Independent.{succ u1, u2} ι (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (Submodule.completeLattice.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (fun (i : ι) => Submodule.span.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (Singleton.singleton.{u2, u2} N (Set.{u2} N) (Set.instSingletonSet.{u2} N) (v i)))) (LinearIndependent.{u1, u3, u2} ι R N v (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3))
 Case conversion may be inaccurate. Consider using '#align complete_lattice.independent_iff_linear_independent_of_ne_zero CompleteLattice.independent_iff_linearIndependent_of_ne_zeroₓ'. -/
 theorem independent_iff_linearIndependent_of_ne_zero [NoZeroSMulDivisors R N] {v : ι → N}
     (h_ne_zero : ∀ i, v i ≠ 0) : (Independent fun i => R ∙ v i) ↔ LinearIndependent R v :=

f4758115

bump to nightly-2023-04-10-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/e05ead7993520a432bec94ac504842d90707ad63

72a0e1ef

Diff

@@ -298,7 +298,7 @@ def mapRange.linearMap (f : ∀ i, β₁ i →ₗ[R] β₂ i) : (Π₀ i, β₁
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {β₂ : ι -> Type.{u3}} [_inst_8 : forall (i : ι), AddCommMonoid.{u3} (β₂ i)] [_inst_11 : forall (i : ι), Module.{u2, u3} R (β₂ i) _inst_1 (_inst_8 i)], Eq.{succ (max u1 u3)} (LinearMap.{u2, u2, max u1 u3, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (β₂ i) (AddMonoid.toAddZeroClass.{u3} (β₂ i) (AddCommMonoid.toAddMonoid.{u3} (β₂ i) (_inst_8 i))))) (Dfinsupp.{u1, u3} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (β₂ i) (AddMonoid.toAddZeroClass.{u3} (β₂ i) (AddCommMonoid.toAddMonoid.{u3} (β₂ i) (_inst_8 i))))) (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i))) (Dfinsupp.mapRange.linearMap.{u1, u2, u3, u3} ι R _inst_1 (fun (i : ι) => β₂ i) (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i) (fun (i : ι) => _inst_11 i) (fun (i : ι) => LinearMap.id.{u2, u3} R (β₂ i) _inst_1 (_inst_8 i) (_inst_11 i))) (LinearMap.id.{u2, max u1 u3} R (Dfinsupp.{u1, u3} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (β₂ i) (AddMonoid.toAddZeroClass.{u3} (β₂ i) (AddCommMonoid.toAddMonoid.{u3} (β₂ i) (_inst_8 i))))) _inst_1 (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {β₂ : ι -> Type.{u2}} [_inst_8 : forall (i : ι), AddCommMonoid.{u2} (β₂ i)] [_inst_11 : forall (i : ι), Module.{u1, u2} R (β₂ i) _inst_1 (_inst_8 i)], Eq.{max (succ u3) (succ u2)} (LinearMap.{u1, u1, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Dfinsupp.{u3, u2} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) (Dfinsupp.{u3, u2} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u2} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u2} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i))) (Dfinsupp.mapRange.linearMap.{u3, u1, u2, u2} ι R _inst_1 (fun (i : ι) => β₂ i) (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i) (fun (i : ι) => _inst_11 i) (fun (i : ι) => LinearMap.id.{u1, u2} R (β₂ i) _inst_1 (_inst_8 i) (_inst_11 i))) (LinearMap.id.{u1, max u3 u2} R (Dfinsupp.{u3, u2} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u2} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)))
+  forall {ι : Type.{u3}} {R : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [β₂ : Semiring.{u1} R] {_inst_8 : ι -> Type.{u2}} [_inst_11 : forall (i : ι), AddCommMonoid.{u2} (_inst_8 i)] [inst._@.Mathlib.LinearAlgebra.Dfinsupp._hyg.2485 : forall (i : ι), Module.{u1, u2} R (_inst_8 i) β₂ (_inst_11 i)], Eq.{max (succ u3) (succ u2)} (LinearMap.{u1, u1, max u2 u3, max u2 u3} R R β₂ β₂ (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R β₂)) (Dfinsupp.{u3, u2} ι (fun (i : ι) => _inst_8 i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => _inst_8 i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => _inst_8 i) i) (_inst_11 i)))) (Dfinsupp.{u3, u2} ι (fun (i : ι) => _inst_8 i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => _inst_8 i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => _inst_8 i) i) (_inst_11 i)))) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u2} ι (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u2} ι (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => _inst_8 i) β₂ (fun (i : ι) => _inst_11 i) (fun (i : ι) => inst._@.Mathlib.LinearAlgebra.Dfinsupp._hyg.2485 i)) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => _inst_8 i) β₂ (fun (i : ι) => _inst_11 i) (fun (i : ι) => inst._@.Mathlib.LinearAlgebra.Dfinsupp._hyg.2485 i))) (Dfinsupp.mapRange.linearMap.{u3, u1, u2, u2} ι R β₂ (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i) (fun (i : ι) => _inst_11 i) (fun (i : ι) => inst._@.Mathlib.LinearAlgebra.Dfinsupp._hyg.2485 i) (fun (i : ι) => inst._@.Mathlib.LinearAlgebra.Dfinsupp._hyg.2485 i) (fun (i : ι) => LinearMap.id.{u1, u2} R (_inst_8 i) β₂ (_inst_11 i) (inst._@.Mathlib.LinearAlgebra.Dfinsupp._hyg.2485 i))) (LinearMap.id.{u1, max u3 u2} R (Dfinsupp.{u3, u2} ι (fun (i : ι) => _inst_8 i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => _inst_8 i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => _inst_8 i) i) (_inst_11 i)))) β₂ (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u2} ι (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => _inst_8 i) β₂ (fun (i : ι) => _inst_11 i) (fun (i : ι) => inst._@.Mathlib.LinearAlgebra.Dfinsupp._hyg.2485 i)))
 Case conversion may be inaccurate. Consider using '#align dfinsupp.map_range.linear_map_id Dfinsupp.mapRange.linearMap_idₓ'. -/
 @[simp]
 theorem mapRange.linearMap_id :
@@ -571,7 +571,7 @@ omit dec_ι
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} N] [_inst_3 : Module.{u2, u3} R N _inst_1 _inst_2] {s : Finset.{u1} ι} (p : ι -> (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (a : N), Iff (Membership.Mem.{u3, u3} N (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) a (supᵢ.{u3, succ u1} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u3} R N _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => supᵢ.{u3, 0} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u3} R N _inst_1 _inst_2 _inst_3))) (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i s) (fun (H : Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i s) => p i)))) (Exists.{max (succ u1) (succ u3)} (forall (i : ι), coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (μ : forall (i : ι), coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) => Eq.{succ u3} N (Finset.sum.{u3, u1} N ι _inst_2 s (fun (i : ι) => (fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) N (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) N (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) N (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) N (coeSubtype.{succ u3} N (fun (x : N) => Membership.Mem.{u3, u3} N (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) x (p i)))))) (μ i))) a))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {N : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} N] [s : Module.{u2, u1} R N _inst_2 _inst_3] {p : Finset.{u3} ι} (a : ι -> (Submodule.{u2, u1} R N _inst_2 _inst_3 s)) (a_1 : N), Iff (Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.setLike.{u2, u1} R N _inst_2 _inst_3 s)) a_1 (supᵢ.{u1, succ u3} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (Submodule.completeLattice.{u2, u1} R N _inst_2 _inst_3 s))) ι (fun (i : ι) => supᵢ.{u1, 0} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (Submodule.completeLattice.{u2, u1} R N _inst_2 _inst_3 s))) (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i p) (fun (h._@.Mathlib.LinearAlgebra.Dfinsupp._hyg.5132 : Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i p) => a i)))) (Exists.{max (succ u3) (succ u1)} (forall (i : ι), Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.setLike.{u2, u1} R N _inst_2 _inst_3 s)) x (a i))) (fun (μ : forall (i : ι), Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.setLike.{u2, u1} R N _inst_2 _inst_3 s)) x (a i))) => Eq.{succ u1} N (Finset.sum.{u1, u3} N ι _inst_3 p (fun (i : ι) => Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.setLike.{u2, u1} R N _inst_2 _inst_3 s) (a i))) (μ i))) a_1))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {N : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} N] [s : Module.{u2, u1} R N _inst_2 _inst_3] {p : Finset.{u3} ι} (a : ι -> (Submodule.{u2, u1} R N _inst_2 _inst_3 s)) (a_1 : N), Iff (Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.setLike.{u2, u1} R N _inst_2 _inst_3 s)) a_1 (supᵢ.{u1, succ u3} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (Submodule.completeLattice.{u2, u1} R N _inst_2 _inst_3 s))) ι (fun (i : ι) => supᵢ.{u1, 0} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (Submodule.completeLattice.{u2, u1} R N _inst_2 _inst_3 s))) (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i p) (fun (h._@.Mathlib.LinearAlgebra.Dfinsupp._hyg.5226 : Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i p) => a i)))) (Exists.{max (succ u3) (succ u1)} (forall (i : ι), Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.setLike.{u2, u1} R N _inst_2 _inst_3 s)) x (a i))) (fun (μ : forall (i : ι), Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.setLike.{u2, u1} R N _inst_2 _inst_3 s)) x (a i))) => Eq.{succ u1} N (Finset.sum.{u1, u3} N ι _inst_3 p (fun (i : ι) => Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.setLike.{u2, u1} R N _inst_2 _inst_3 s) (a i))) (μ i))) a_1))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_finset_iff_exists_sum Submodule.mem_supᵢ_finset_iff_exists_sumₓ'. -/
 theorem mem_supᵢ_finset_iff_exists_sum {s : Finset ι} (p : ι → Submodule R N) (a : N) :
     (a ∈ ⨆ i ∈ s, p i) ↔ ∃ μ : ∀ i, p i, (∑ i in s, (μ i : N)) = a := by

f4758115

bump to nightly-2023-04-01-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/172bf2812857f5e56938cc148b7a539f52f84ca9

bfc4190c

Diff

@@ -550,18 +550,18 @@ theorem mem_supᵢ_iff_exists_dfinsupp' (p : ι → Submodule R N) [∀ (i) (x :
   congr
 #align submodule.mem_supr_iff_exists_dfinsupp' Submodule.mem_supᵢ_iff_exists_dfinsupp'
 
-/- warning: submodule.mem_bsupr_iff_exists_dfinsupp -> Submodule.mem_bsupr_iff_exists_dfinsupp is a dubious translation:
+/- warning: submodule.mem_bsupr_iff_exists_dfinsupp -> Submodule.mem_bsupᵢ_iff_exists_dfinsupp is a dubious translation:
 lean 3 declaration is
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_inst_2 _inst_3 (S i))) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u3} N _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R N (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} N _inst_2) (Module.toDistribMulAction.{u2, u3} R N _inst_1 _inst_2 _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)) (Dfinsupp.lsum.{u1, u2, 0, u3, u3} ι R Nat (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (S i)) N (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u2, u3} R N _inst_1 _inst_2 _inst_3 (S i)) (fun (i : ι) => Submodule.module.{u2, u3} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_2 _inst_3 Nat.semiring (AddCommMonoid.natModule.{u3} N _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R N (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} N _inst_2) (Module.toDistribMulAction.{u2, u3} R N _inst_1 _inst_2 _inst_3))) (fun (i : ι) => Submodule.subtype.{u2, u3} R N _inst_1 _inst_2 _inst_3 (S i))) (Dfinsupp.filter.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (S i)) (fun (i : ι) => Submodule.zero.{u2, u3} R N _inst_1 _inst_2 _inst_3 (S i)) p (fun (a : ι) => _inst_4 a) f)) x))
 but is expected to have type
   forall {ι : Type.{u3}} {R : Type.{u2}} {N : Type.{u1}} [dec_ι : DecidableEq.{succ u3} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} N] [_inst_3 : Module.{u2, u1} R N _inst_1 _inst_2] (p : ι -> Prop) [_inst_4 : DecidablePred.{succ u3} ι p] (S : ι -> (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3)) (x : N), Iff (Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (supᵢ.{u1, succ u3} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R N _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => supᵢ.{u1, 0} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) 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(Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u1} ι (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) (fun (i : ι) => Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))) _inst_2 (Dfinsupp.module.{u3, u1, u2} ι R (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) (fun (i : ι) => Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))) 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(Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_2 (Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_3) (LinearMap.{u2, u2, max u1 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u3, u1} ι (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) (fun (i : ι) => AddMonoid.toZero.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (AddCommMonoid.toAddMonoid.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N 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(Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (AddCommMonoid.toAddMonoid.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u1} ι (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) (fun (i : ι) => Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))) _inst_2 (Dfinsupp.module.{u3, u1, u2} ι R (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => 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i))) i) (Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)))) p (fun (a : ι) => _inst_4 a) f)) x))
-Case conversion may be inaccurate. Consider using '#align submodule.mem_bsupr_iff_exists_dfinsupp Submodule.mem_bsupr_iff_exists_dfinsuppₓ'. -/
-theorem mem_bsupr_iff_exists_dfinsupp (p : ι → Prop) [DecidablePred p] (S : ι → Submodule R N)
+Case conversion may be inaccurate. Consider using '#align submodule.mem_bsupr_iff_exists_dfinsupp Submodule.mem_bsupᵢ_iff_exists_dfinsuppₓ'. -/
+theorem mem_bsupᵢ_iff_exists_dfinsupp (p : ι → Prop) [DecidablePred p] (S : ι → Submodule R N)
     (x : N) :
     (x ∈ ⨆ (i) (h : p i), S i) ↔
       ∃ f : Π₀ i, S i, Dfinsupp.lsum ℕ (fun i => (S i).Subtype) (f.filterₓ p) = x :=
   SetLike.ext_iff.mp (bsupᵢ_eq_range_dfinsupp_lsum p S) x
-#align submodule.mem_bsupr_iff_exists_dfinsupp Submodule.mem_bsupr_iff_exists_dfinsupp
+#align submodule.mem_bsupr_iff_exists_dfinsupp Submodule.mem_bsupᵢ_iff_exists_dfinsupp
 
 open BigOperators
 
@@ -637,7 +637,7 @@ theorem independent_iff_forall_dfinsupp (p : ι → Submodule R N) :
         lsum ℕ (fun i => (p i).Subtype) (erase i v) = x → x = 0 :=
   by
   simp_rw [CompleteLattice.independent_def, Submodule.disjoint_def,
-    Submodule.mem_bsupr_iff_exists_dfinsupp, exists_imp, filter_ne_eq_erase]
+    Submodule.mem_bsupᵢ_iff_exists_dfinsupp, exists_imp, filter_ne_eq_erase]
   apply forall_congr' fun i => _
   refine' subtype.forall'.trans _
   simp_rw [Submodule.coe_eq_zero]

f4758115

bump to nightly-2023-03-23-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/57e09a1296bfb4330ddf6624f1028ba186117d82

53b827ba

Diff

@@ -438,7 +438,7 @@ Case conversion may be inaccurate. Consider using '#align dfinsupp.basis Dfinsup
 Note that while this is stated for `dfinsupp` not `direct_sum`, the types are defeq. -/
 noncomputable def basis {η : ι → Type _} (b : ∀ i, Basis (η i) R (M i)) :
     Basis (Σi, η i) R (Π₀ i, M i) :=
-  Basis.of_repr
+  Basis.ofRepr
     ((mapRange.linearEquiv fun i => (b i).repr).trans (sigmaFinsuppLequivDfinsupp R).symm)
 #align dfinsupp.basis Dfinsupp.basis

f4758115

bump to nightly-2023-03-18-14

mathlib commit https://github.com/leanprover-community/mathlib/commit/02ba8949f486ebecf93fe7460f1ed0564b5e442c

73d15350

Diff

@@ -458,7 +458,7 @@ open Dfinsupp
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} N] [_inst_3 : Module.{u2, u3} R N _inst_1 _inst_2] {β : ι -> Type.{u4}} [_inst_4 : forall (i : ι), Zero.{u4} (β i)] [_inst_5 : forall (i : ι) (x : β i), Decidable (Ne.{succ u4} (β i) x (OfNat.ofNat.{u4} (β i) 0 (OfNat.mk.{u4} (β i) 0 (Zero.zero.{u4} (β i) (_inst_4 i)))))] (S : Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (f : Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => _inst_4 i)) (g : forall (i : ι), (β i) -> N), (forall (c : ι), (Ne.{succ u4} (β c) (coeFn.{succ (max u1 u4), max (succ u1) (succ u4)} (Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => _inst_4 i)) (fun (_x : Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => _inst_4 i)) => forall (i : ι), β i) (Dfinsupp.hasCoeToFun.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => _inst_4 i)) f c) (OfNat.ofNat.{u4} (β c) 0 (OfNat.mk.{u4} (β c) 0 (Zero.zero.{u4} (β c) (_inst_4 c))))) -> (Membership.Mem.{u3, u3} N (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (g c (coeFn.{succ (max u1 u4), max (succ u1) (succ u4)} (Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => _inst_4 i)) (fun (_x : Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => _inst_4 i)) => forall (i : ι), β i) (Dfinsupp.hasCoeToFun.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => _inst_4 i)) f c)) S)) -> (Membership.Mem.{u3, u3} N (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (Dfinsupp.sum.{u1, u4, u3} ι N (fun (i : ι) => β i) (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => _inst_4 i) (fun (i : ι) (x : β i) => _inst_5 i x) _inst_2 f g) S)
 but is expected to have type
-  forall {ι : Type.{u1}} {R : Type.{u3}} {N : Type.{u2}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} N] [_inst_3 : Module.{u3, u2} R N _inst_1 _inst_2] {β : ι -> Type.{u4}} [_inst_4 : forall (i : ι), Zero.{u4} (β i)] [_inst_5 : forall (i : ι) (x : β i), Decidable (Ne.{succ u4} (β i) x (OfNat.ofNat.{u4} (β i) 0 (Zero.toOfNat0.{u4} (β i) (_inst_4 i))))] (S : Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (f : Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => _inst_4 i)) (g : forall (i : ι), (β i) -> N), (forall (c : ι), (Ne.{succ u4} ((fun (i : ι) => (fun (i : ι) => β i) i) c) (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (Dfinsupp.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => (fun (i : ι) => _inst_4 i) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => β i) i) _x) (Dfinsupp.funLike.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => (fun (i : ι) => _inst_4 i) i)) f c) (OfNat.ofNat.{u4} ((fun (i : ι) => (fun (i : ι) => β i) i) c) 0 (Zero.toOfNat0.{u4} ((fun (i : ι) => (fun (i : ι) => β i) i) c) (_inst_4 c)))) -> (Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) (g c (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (Dfinsupp.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => (fun (i : ι) => _inst_4 i) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => β i) i) _x) (Dfinsupp.funLike.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => (fun (i : ι) => _inst_4 i) i)) f c)) S)) -> (Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) (Dfinsupp.sum.{u1, u4, u2} ι N (fun (i : ι) => β i) (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => _inst_4 i) (fun (i : ι) (x : β i) => _inst_5 i x) _inst_2 f g) S)
+  forall {ι : Type.{u1}} {R : Type.{u3}} {N : Type.{u2}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} N] [_inst_3 : Module.{u3, u2} R N _inst_1 _inst_2] {β : ι -> Type.{u4}} [_inst_4 : forall (i : ι), Zero.{u4} (β i)] [_inst_5 : forall (i : ι) (x : β i), Decidable (Ne.{succ u4} (β i) x (OfNat.ofNat.{u4} (β i) 0 (Zero.toOfNat0.{u4} (β i) (_inst_4 i))))] (S : Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (f : Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => _inst_4 i)) (g : forall (i : ι), (β i) -> N), (forall (c : ι), (Ne.{succ u4} ((fun (i : ι) => (fun (i : ι) => β i) i) c) (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (Dfinsupp.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => (fun (i : ι) => _inst_4 i) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => β i) i) _x) (Dfinsupp.funLike.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => (fun (i : ι) => _inst_4 i) i)) f c) (OfNat.ofNat.{u4} ((fun (i : ι) => (fun (i : ι) => β i) i) c) 0 (Zero.toOfNat0.{u4} ((fun (i : ι) => (fun (i : ι) => β i) i) c) (_inst_4 c)))) -> (Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) (g c (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (Dfinsupp.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => (fun (i : ι) => _inst_4 i) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => β i) i) _x) (Dfinsupp.funLike.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => (fun (i : ι) => _inst_4 i) i)) f c)) S)) -> (Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) (Dfinsupp.sum.{u1, u4, u2} ι N (fun (i : ι) => β i) (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => _inst_4 i) (fun (i : ι) (x : β i) => _inst_5 i x) _inst_2 f g) S)
 Case conversion may be inaccurate. Consider using '#align submodule.dfinsupp_sum_mem Submodule.dfinsupp_sum_memₓ'. -/
 theorem dfinsupp_sum_mem {β : ι → Type _} [∀ i, Zero (β i)] [∀ (i) (x : β i), Decidable (x ≠ 0)]
     (S : Submodule R N) (f : Π₀ i, β i) (g : ∀ i, β i → N) (h : ∀ c, f c ≠ 0 → g c (f c) ∈ S) :
@@ -470,7 +470,7 @@ theorem dfinsupp_sum_mem {β : ι → Type _} [∀ i, Zero (β i)] [∀ (i) (x :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} N] [_inst_3 : Module.{u2, u3} R N _inst_1 _inst_2] {β : ι -> Type.{u4}} [_inst_4 : forall (i : ι), AddZeroClass.{u4} (β i)] (S : Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (f : Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) (g : forall (i : ι), AddMonoidHom.{u4, u3} (β i) N (_inst_4 i) (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_2))), (forall (c : ι), (Ne.{succ u4} (β c) (coeFn.{succ (max u1 u4), max (succ u1) (succ u4)} (Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) (fun (_x : Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) => forall (i : ι), β i) (Dfinsupp.hasCoeToFun.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) f c) (OfNat.ofNat.{u4} (β c) 0 (OfNat.mk.{u4} (β c) 0 (Zero.zero.{u4} (β c) (AddZeroClass.toHasZero.{u4} (β c) (_inst_4 c)))))) -> (Membership.Mem.{u3, u3} N (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (coeFn.{max (succ u3) (succ u4), max (succ u4) (succ u3)} (AddMonoidHom.{u4, u3} (β c) N (_inst_4 c) (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_2))) (fun (_x : AddMonoidHom.{u4, u3} (β c) N (_inst_4 c) (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_2))) => (β c) -> N) (AddMonoidHom.hasCoeToFun.{u4, u3} (β c) N (_inst_4 c) (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_2))) (g c) (coeFn.{succ (max u1 u4), max (succ u1) (succ u4)} (Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) (fun (_x : Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) => forall (i : ι), β i) (Dfinsupp.hasCoeToFun.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) f c)) S)) -> (Membership.Mem.{u3, u3} N (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (coeFn.{max (succ u3) (succ (max u1 u4)), max (succ (max u1 u4)) (succ u3)} (AddMonoidHom.{max u1 u4, u3} (Dfinsupp.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} ((fun (i : ι) => β i) i) ((fun (i : ι) => _inst_4 i) i))) N (Dfinsupp.addZeroClass.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => (fun (i : ι) => _inst_4 i) i)) (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_2))) (fun (_x : AddMonoidHom.{max u1 u4, u3} (Dfinsupp.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} ((fun (i : ι) => β i) i) ((fun (i : ι) => _inst_4 i) i))) N (Dfinsupp.addZeroClass.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => (fun (i : ι) => _inst_4 i) i)) (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_2))) => (Dfinsupp.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} ((fun (i : ι) => β i) i) ((fun (i : ι) => _inst_4 i) i))) -> N) (AddMonoidHom.hasCoeToFun.{max u1 u4, u3} (Dfinsupp.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} ((fun (i : ι) => β i) i) ((fun (i : ι) => _inst_4 i) i))) N (Dfinsupp.addZeroClass.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => (fun (i : ι) => _inst_4 i) i)) (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_2))) (Dfinsupp.sumAddHom.{u1, u4, u3} ι N (fun (i : ι) => β i) (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => _inst_4 i) _inst_2 g) f) S)
 but is expected to have type
-  forall {ι : Type.{u1}} {R : Type.{u3}} {N : Type.{u2}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} N] [_inst_3 : Module.{u3, u2} R N _inst_1 _inst_2] {β : ι -> Type.{u4}} [_inst_4 : forall (i : ι), AddZeroClass.{u4} (β i)] (S : Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (f : Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) (g : forall (i : ι), AddMonoidHom.{u4, u2} (β i) N (_inst_4 i) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))), (forall (c : ι), (Ne.{succ u4} ((fun (i : ι) => (fun (i : ι) => β i) i) c) (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (Dfinsupp.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i)) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => β i) i) _x) (Dfinsupp.funLike.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i)) i)) f c) (OfNat.ofNat.{u4} ((fun (i : ι) => (fun (i : ι) => β i) i) c) 0 (Zero.toOfNat0.{u4} ((fun (i : ι) => (fun (i : ι) => β i) i) c) (AddZeroClass.toZero.{u4} ((fun (i : ι) => (fun (i : ι) => β i) i) c) (_inst_4 c))))) -> (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : β c) => N) (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (Dfinsupp.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i)) i)) ι (fun (a : ι) => (fun (i : ι) => (fun (i : ι) => β i) i) a) (Dfinsupp.funLike.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i)) i)) f c)) (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) (FunLike.coe.{max (succ u2) (succ u4), succ u4, succ u2} (AddMonoidHom.{u4, u2} (β c) N (_inst_4 c) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) (β c) (fun (_x : β c) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : β c) => N) _x) (AddHomClass.toFunLike.{max u2 u4, u4, u2} (AddMonoidHom.{u4, u2} (β c) N (_inst_4 c) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) (β c) N (AddZeroClass.toAdd.{u4} (β c) (_inst_4 c)) (AddZeroClass.toAdd.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) (AddMonoidHomClass.toAddHomClass.{max u2 u4, u4, u2} (AddMonoidHom.{u4, u2} (β c) N (_inst_4 c) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) (β c) N (_inst_4 c) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2)) (AddMonoidHom.addMonoidHomClass.{u4, u2} (β c) N (_inst_4 c) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))))) (g c) (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (Dfinsupp.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i)) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => β i) i) _x) (Dfinsupp.funLike.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i)) i)) f c)) S)) -> (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) => N) f) (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u4), max (succ u1) (succ u4), succ u2} (AddMonoidHom.{max u4 u1, u2} (Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) N (Dfinsupp.addZeroClass.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => _inst_4 i)) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) (fun (_x : Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) => N) _x) (AddHomClass.toFunLike.{max (max u1 u2) u4, max u1 u4, u2} (AddMonoidHom.{max u4 u1, u2} (Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) N (Dfinsupp.addZeroClass.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => _inst_4 i)) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) N (AddZeroClass.toAdd.{max u1 u4} (Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) (Dfinsupp.addZeroClass.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => _inst_4 i))) (AddZeroClass.toAdd.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) (AddMonoidHomClass.toAddHomClass.{max (max u1 u2) u4, max u1 u4, u2} (AddMonoidHom.{max u4 u1, u2} (Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) N (Dfinsupp.addZeroClass.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => _inst_4 i)) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) N (Dfinsupp.addZeroClass.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => _inst_4 i)) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2)) (AddMonoidHom.addMonoidHomClass.{max u1 u4, u2} (Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) N (Dfinsupp.addZeroClass.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => _inst_4 i)) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))))) (Dfinsupp.sumAddHom.{u1, u4, u2} ι N (fun (i : ι) => β i) (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => _inst_4 i) _inst_2 g) f) S)
+  forall {ι : Type.{u1}} {R : Type.{u3}} {N : Type.{u2}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} N] [_inst_3 : Module.{u3, u2} R N _inst_1 _inst_2] {β : ι -> Type.{u4}} [_inst_4 : forall (i : ι), AddZeroClass.{u4} (β i)] (S : Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (f : Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) (g : forall (i : ι), AddMonoidHom.{u4, u2} (β i) N (_inst_4 i) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))), (forall (c : ι), (Ne.{succ u4} ((fun (i : ι) => (fun (i : ι) => β i) i) c) (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (Dfinsupp.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i)) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => β i) i) _x) (Dfinsupp.funLike.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i)) i)) f c) (OfNat.ofNat.{u4} ((fun (i : ι) => (fun (i : ι) => β i) i) c) 0 (Zero.toOfNat0.{u4} ((fun (i : ι) => (fun (i : ι) => β i) i) c) (AddZeroClass.toZero.{u4} ((fun (i : ι) => (fun (i : ι) => β i) i) c) (_inst_4 c))))) -> (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : β c) => N) (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (Dfinsupp.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i)) i)) ι (fun (a : ι) => (fun (i : ι) => (fun (i : ι) => β i) i) a) (Dfinsupp.funLike.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i)) i)) f c)) (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) (FunLike.coe.{max (succ u2) (succ u4), succ u4, succ u2} (AddMonoidHom.{u4, u2} (β c) N (_inst_4 c) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) (β c) (fun (_x : β c) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : β c) => N) _x) (AddHomClass.toFunLike.{max u2 u4, u4, u2} (AddMonoidHom.{u4, u2} (β c) N (_inst_4 c) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) (β c) N (AddZeroClass.toAdd.{u4} (β c) (_inst_4 c)) (AddZeroClass.toAdd.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) (AddMonoidHomClass.toAddHomClass.{max u2 u4, u4, u2} (AddMonoidHom.{u4, u2} (β c) N (_inst_4 c) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) (β c) N (_inst_4 c) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2)) (AddMonoidHom.addMonoidHomClass.{u4, u2} (β c) N (_inst_4 c) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))))) (g c) (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (Dfinsupp.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i)) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => β i) i) _x) (Dfinsupp.funLike.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i)) i)) f c)) S)) -> (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) => N) f) (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u4), max (succ u1) (succ u4), succ u2} (AddMonoidHom.{max u4 u1, u2} (Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) N (Dfinsupp.addZeroClass.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => _inst_4 i)) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) (fun (_x : Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) => N) _x) (AddHomClass.toFunLike.{max (max u1 u2) u4, max u1 u4, u2} (AddMonoidHom.{max u4 u1, u2} (Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) N (Dfinsupp.addZeroClass.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => _inst_4 i)) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) N (AddZeroClass.toAdd.{max u1 u4} (Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) (Dfinsupp.addZeroClass.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => _inst_4 i))) (AddZeroClass.toAdd.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) (AddMonoidHomClass.toAddHomClass.{max (max u1 u2) u4, max u1 u4, u2} (AddMonoidHom.{max u4 u1, u2} (Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) N (Dfinsupp.addZeroClass.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => _inst_4 i)) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) N (Dfinsupp.addZeroClass.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => _inst_4 i)) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2)) (AddMonoidHom.addMonoidHomClass.{max u1 u4, u2} (Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) N (Dfinsupp.addZeroClass.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => _inst_4 i)) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))))) (Dfinsupp.sumAddHom.{u1, u4, u2} ι N (fun (i : ι) => β i) (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => _inst_4 i) _inst_2 g) f) S)
 Case conversion may be inaccurate. Consider using '#align submodule.dfinsupp_sum_add_hom_mem Submodule.dfinsupp_sumAddHom_memₓ'. -/
 theorem dfinsupp_sumAddHom_mem {β : ι → Type _} [∀ i, AddZeroClass (β i)] (S : Submodule R N)
     (f : Π₀ i, β i) (g : ∀ i, β i →+ N) (h : ∀ c, f c ≠ 0 → g c (f c) ∈ S) :
@@ -482,7 +482,7 @@ theorem dfinsupp_sumAddHom_mem {β : ι → Type _} [∀ i, AddZeroClass (β i)]
 lean 3 declaration is
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 but is expected to have type
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i)) _inst_2 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N _inst_1 _inst_1 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) 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_inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{0, 0, max u1 u2, max u1 u2} Nat Nat 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((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_2 (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N _inst_1 _inst_1 (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, max u1 u2, u2} R R (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_2 (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N _inst_1 _inst_1 (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u2, u2} R R Nat (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N _inst_1 _inst_1 (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u2, u2} R R Nat (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_2 (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u1, u3, 0, u2, u2} ι R Nat (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 _inst_3 Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3))) (fun (i : ι) => Submodule.subtype.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))
 Case conversion may be inaccurate. Consider using '#align submodule.supr_eq_range_dfinsupp_lsum Submodule.supᵢ_eq_range_dfinsupp_lsumₓ'. -/
 /-- The supremum of a family of submodules is equal to the range of `dfinsupp.lsum`; that is
 every element in the `supr` can be produced from taking a finite number of non-zero elements
@@ -502,7 +502,7 @@ theorem supᵢ_eq_range_dfinsupp_lsum (p : ι → Submodule R N) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} N] [_inst_3 : Module.{u2, u3} R N _inst_1 _inst_2] (p : ι -> Prop) [_inst_4 : DecidablePred.{succ u1} ι p] (S : ι -> (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3)), Eq.{succ u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (supᵢ.{u3, succ u1} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u3} R N _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => supᵢ.{u3, 0} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) 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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align submodule.bsupr_eq_range_dfinsupp_lsum Submodule.bsupᵢ_eq_range_dfinsupp_lsumₓ'. -/
 /-- The bounded supremum of a family of commutative additive submonoids is equal to the range of
 `dfinsupp.sum_add_hom` composed with `dfinsupp.filter_add_monoid_hom`; that is, every element in the
@@ -526,9 +526,9 @@ theorem bsupᵢ_eq_range_dfinsupp_lsum (p : ι → Prop) [DecidablePred p] (S :
 
 /- warning: submodule.mem_supr_iff_exists_dfinsupp -> Submodule.mem_supᵢ_iff_exists_dfinsupp is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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_inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 _inst_3 Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3))) (fun (i : ι) => Submodule.subtype.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) f) x))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_iff_exists_dfinsupp Submodule.mem_supᵢ_iff_exists_dfinsuppₓ'. -/
 theorem mem_supᵢ_iff_exists_dfinsupp (p : ι → Submodule R N) (x : N) :
     x ∈ supᵢ p ↔ ∃ f : Π₀ i, p i, Dfinsupp.lsum ℕ (fun i => (p i).Subtype) f = x :=
@@ -537,9 +537,9 @@ theorem mem_supᵢ_iff_exists_dfinsupp (p : ι → Submodule R N) (x : N) :
 
 /- warning: submodule.mem_supr_iff_exists_dfinsupp' -> Submodule.mem_supᵢ_iff_exists_dfinsupp' is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} N] [_inst_3 : Module.{u2, u3} R N _inst_1 _inst_2] (p : ι -> (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3)) [_inst_4 : forall (i : ι) (x : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)), Decidable (Ne.{succ u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) x (OfNat.ofNat.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N 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+  forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} N] [_inst_3 : Module.{u2, u3} R N _inst_1 _inst_2] (p : ι -> (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3)) [_inst_4 : forall (i : ι) (x : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)), Decidable (Ne.{succ u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) x (OfNat.ofNat.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N 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 but is expected to have type
-  forall {ι : Type.{u1}} {R : Type.{u3}} {N : Type.{u2}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} N] [_inst_3 : Module.{u3, u2} R N _inst_1 _inst_2] (p : ι -> (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) [_inst_4 : forall (i : ι) (x : Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))), Decidable (Ne.{succ u2} (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) x (OfNat.ofNat.{u2} (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) 0 (Zero.toOfNat0.{u2} (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (Submodule.instZeroSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)))))] (x : N), Iff (Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (supᵢ.{u2, succ u1} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u3, u2} R N _inst_1 _inst_2 _inst_3))) ι p)) (Exists.{max (succ u1) (succ u2)} (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => Submodule.instZeroSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) (fun (f : Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => Submodule.instZeroSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) => Eq.{succ u2} N (Dfinsupp.sum.{u1, u2, u2} ι N (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => Submodule.instZeroSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) (x : Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) => _inst_4 i x) _inst_2 f (fun (i : ι) (xi : Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) => Subtype.val.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Set.{u2} N) (Set.instMembershipSet.{u2} N) x (SetLike.coe.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (p i))) xi)) x))
+  forall {ι : Type.{u1}} {R : Type.{u3}} {N : Type.{u2}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} N] [_inst_3 : Module.{u3, u2} R N _inst_1 _inst_2] (p : ι -> (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) [_inst_4 : forall (i : ι) (x : Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))), Decidable (Ne.{succ u2} (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) x (OfNat.ofNat.{u2} (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) 0 (Zero.toOfNat0.{u2} (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (Submodule.zero.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)))))] (x : N), Iff (Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (supᵢ.{u2, succ u1} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u3, u2} R N _inst_1 _inst_2 _inst_3))) ι p)) (Exists.{max (succ u1) (succ u2)} (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => Submodule.zero.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) (fun (f : Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => Submodule.zero.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) => Eq.{succ u2} N (Dfinsupp.sum.{u1, u2, u2} ι N (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => Submodule.zero.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) (x : Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) => _inst_4 i x) _inst_2 f (fun (i : ι) (xi : Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) => Subtype.val.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Set.{u2} N) (Set.instMembershipSet.{u2} N) x (SetLike.coe.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3) (p i))) xi)) x))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_iff_exists_dfinsupp' Submodule.mem_supᵢ_iff_exists_dfinsupp'ₓ'. -/
 /-- A variant of `submodule.mem_supr_iff_exists_dfinsupp` with the RHS fully unfolded. -/
 theorem mem_supᵢ_iff_exists_dfinsupp' (p : ι → Submodule R N) [∀ (i) (x : p i), Decidable (x ≠ 0)]
@@ -552,9 +552,9 @@ theorem mem_supᵢ_iff_exists_dfinsupp' (p : ι → Submodule R N) [∀ (i) (x :
 
 /- warning: submodule.mem_bsupr_iff_exists_dfinsupp -> Submodule.mem_bsupr_iff_exists_dfinsupp is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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(Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u1, u1} R R Nat (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) N _inst_1 _inst_1 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_2 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_3 (RingHom.id.{u2} R 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Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))) _inst_2 (Dfinsupp.module.{u3, u1, u2} ι R (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) _inst_1 (fun (i : ι) => Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) (fun (i : ι) => Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} N _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R N 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Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_2 _inst_3 Nat.semiring (AddCommMonoid.natModule.{u1} N _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R N (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_2) (Module.toDistribMulAction.{u2, u1} R N _inst_1 _inst_2 _inst_3))) (fun (i : ι) => Submodule.subtype.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))) (Dfinsupp.filter.{u3, u1} ι (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) (fun (i : ι) => AddMonoid.toZero.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} 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+  forall {ι : Type.{u3}} {R : Type.{u2}} {N : Type.{u1}} [dec_ι : DecidableEq.{succ u3} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} N] [_inst_3 : Module.{u2, u1} R N _inst_1 _inst_2] (p : ι -> Prop) [_inst_4 : DecidablePred.{succ u3} ι p] (S : ι -> (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3)) (x : N), Iff (Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (supᵢ.{u1, succ u3} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R N _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => supᵢ.{u1, 0} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) 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(Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u1} ι (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) (fun (i : ι) => Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))) _inst_2 (Dfinsupp.module.{u3, u1, u2} ι R (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) (fun (i : ι) => Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))) _inst_3) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u3, u1} ι (fun (i : ι) => LinearMap.{u2, u2, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) N (Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_2 (Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u1, u1} R R (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) N _inst_1 _inst_1 (Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_2 (Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u3 u1, u1} R R (Dfinsupp.{u3, u1} ι (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) (fun (i : ι) => AddMonoid.toZero.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (AddCommMonoid.toAddMonoid.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u1} ι (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) (fun (i : ι) => Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))) _inst_2 (Dfinsupp.module.{u3, u1, u2} ι R (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) (fun (i : ι) => Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) N (Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_2 (Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_3) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u1, u1} R R (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) N _inst_1 _inst_1 (Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_2 (Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u1, u1} R R Nat (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) N _inst_1 _inst_1 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R N _inst_1 _inst_2 _inst_3 (S i))) _inst_2 (Dfinsupp.module.{u3, u1, u2} ι R (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) (fun (i : ι) => Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} N _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R N (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_2) (Module.toDistribMulAction.{u2, u1} R N _inst_1 _inst_2 _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u3, u2, 0, u1, u1} ι R Nat (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) N (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) (fun (i : ι) => Submodule.module.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_2 _inst_3 Nat.semiring (AddCommMonoid.natModule.{u1} N _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R N (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_2) (Module.toDistribMulAction.{u2, u1} R N _inst_1 _inst_2 _inst_3))) (fun (i : ι) => Submodule.subtype.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))) (Dfinsupp.filter.{u3, u1} ι (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) (fun (i : ι) => AddMonoid.toZero.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (AddCommMonoid.toAddMonoid.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (Submodule.addCommMonoid.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)))) p (fun (a : ι) => _inst_4 a) f)) x))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_bsupr_iff_exists_dfinsupp Submodule.mem_bsupr_iff_exists_dfinsuppₓ'. -/
 theorem mem_bsupr_iff_exists_dfinsupp (p : ι → Prop) [DecidablePred p] (S : ι → Submodule R N)
     (x : N) :
@@ -571,7 +571,7 @@ omit dec_ι
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} N] [_inst_3 : Module.{u2, u3} R N _inst_1 _inst_2] {s : Finset.{u1} ι} (p : ι -> (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (a : N), Iff (Membership.Mem.{u3, u3} N (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) a (supᵢ.{u3, succ u1} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u3} R N _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => supᵢ.{u3, 0} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u3} R N _inst_1 _inst_2 _inst_3))) (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i s) (fun (H : Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i s) => p i)))) (Exists.{max (succ u1) (succ u3)} (forall (i : ι), coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (μ : forall (i : ι), coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) => Eq.{succ u3} N (Finset.sum.{u3, u1} N ι _inst_2 s (fun (i : ι) => (fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) N (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) N (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) N (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) N (coeSubtype.{succ u3} N (fun (x : N) => Membership.Mem.{u3, u3} N (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) x (p i)))))) (μ i))) a))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {N : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} N] [s : Module.{u2, u1} R N _inst_2 _inst_3] {p : Finset.{u3} ι} (a : ι -> (Submodule.{u2, u1} R N _inst_2 _inst_3 s)) (a_1 : N), Iff (Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.instSetLikeSubmodule.{u2, u1} R N _inst_2 _inst_3 s)) a_1 (supᵢ.{u1, succ u3} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (Submodule.completeLattice.{u2, u1} R N _inst_2 _inst_3 s))) ι (fun (i : ι) => supᵢ.{u1, 0} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (Submodule.completeLattice.{u2, u1} R N _inst_2 _inst_3 s))) (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i p) (fun (h._@.Mathlib.LinearAlgebra.Dfinsupp._hyg.5132 : Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i p) => a i)))) (Exists.{max (succ u3) (succ u1)} (forall (i : ι), Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.instSetLikeSubmodule.{u2, u1} R N _inst_2 _inst_3 s)) x (a i))) (fun (μ : forall (i : ι), Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.instSetLikeSubmodule.{u2, u1} R N _inst_2 _inst_3 s)) x (a i))) => Eq.{succ u1} N (Finset.sum.{u1, u3} N ι _inst_3 p (fun (i : ι) => Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.instSetLikeSubmodule.{u2, u1} R N _inst_2 _inst_3 s) (a i))) (μ i))) a_1))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {N : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} N] [s : Module.{u2, u1} R N _inst_2 _inst_3] {p : Finset.{u3} ι} (a : ι -> (Submodule.{u2, u1} R N _inst_2 _inst_3 s)) (a_1 : N), Iff (Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.setLike.{u2, u1} R N _inst_2 _inst_3 s)) a_1 (supᵢ.{u1, succ u3} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (Submodule.completeLattice.{u2, u1} R N _inst_2 _inst_3 s))) ι (fun (i : ι) => supᵢ.{u1, 0} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (Submodule.completeLattice.{u2, u1} R N _inst_2 _inst_3 s))) (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i p) (fun (h._@.Mathlib.LinearAlgebra.Dfinsupp._hyg.5132 : Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i p) => a i)))) (Exists.{max (succ u3) (succ u1)} (forall (i : ι), Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.setLike.{u2, u1} R N _inst_2 _inst_3 s)) x (a i))) (fun (μ : forall (i : ι), Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.setLike.{u2, u1} R N _inst_2 _inst_3 s)) x (a i))) => Eq.{succ u1} N (Finset.sum.{u1, u3} N ι _inst_3 p (fun (i : ι) => Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.setLike.{u2, u1} R N _inst_2 _inst_3 s) (a i))) (μ i))) a_1))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_finset_iff_exists_sum Submodule.mem_supᵢ_finset_iff_exists_sumₓ'. -/
 theorem mem_supᵢ_finset_iff_exists_sum {s : Finset ι} (p : ι → Submodule R N) (a : N) :
     (a ∈ ⨆ i ∈ s, p i) ↔ ∃ μ : ∀ i, p i, (∑ i in s, (μ i : N)) = a := by
@@ -622,9 +622,9 @@ variable [Semiring R] [AddCommMonoid N] [Module R N]
 
 /- warning: complete_lattice.independent_iff_forall_dfinsupp -> CompleteLattice.independent_iff_forall_dfinsupp is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} N] [_inst_3 : Module.{u2, u3} R N _inst_1 _inst_2] (p : ι -> (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3)), Iff (CompleteLattice.Independent.{succ u1, u3} ι (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u3} R N _inst_1 _inst_2 _inst_3) p) (forall (i : ι) (x : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (v : Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (i : ι) => 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 but is expected to have type
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(Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u1, u3, 0, u2, u2} ι R Nat (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 _inst_3 Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3))) (fun (i : ι) => Submodule.subtype.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) (Dfinsupp.erase.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)))) i v)) (Subtype.val.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Set.{u2} N) (Set.instMembershipSet.{u2} N) x (SetLike.coe.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3) (p i))) x)) -> (Eq.{succ u2} (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) x (OfNat.ofNat.{u2} (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) 0 (Zero.toOfNat0.{u2} (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (Submodule.zero.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))))
 Case conversion may be inaccurate. Consider using '#align complete_lattice.independent_iff_forall_dfinsupp CompleteLattice.independent_iff_forall_dfinsuppₓ'. -/
 /-- Independence of a family of submodules can be expressed as a quantifier over `dfinsupp`s.
 
@@ -648,7 +648,7 @@ theorem independent_iff_forall_dfinsupp (p : ι → Submodule R N) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} N] [_inst_3 : Module.{u2, u3} R N _inst_1 _inst_2] (p : ι -> (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3)), (Function.Injective.{succ (max u1 u3), succ u3} (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (AddMonoid.toAddZeroClass.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (AddCommMonoid.toAddMonoid.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (Submodule.addCommMonoid.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i)))))) N (coeFn.{max (succ (max u1 u3)) (succ u3), max (succ (max u1 u3)) (succ u3)} (LinearMap.{u2, u2, max u1 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (i : ι) => 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_inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (i : ι) => Submodule.addCommMonoid.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_2 (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3) (fun (_x : LinearMap.{u2, u2, max u1 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) 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(Submodule.addCommMonoid.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i)))))) N (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (i : ι) => Submodule.addCommMonoid.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_2 (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3) => (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ 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 but is expected to have type
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(Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3) (LinearMap.{u3, u3, max u2 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_2 (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N _inst_1 _inst_1 (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, max u1 u2, u2} R R (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_2 (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N _inst_1 _inst_1 (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u2, u2} R R Nat (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N _inst_1 _inst_1 (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u2, u2} R R Nat (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_2 (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u1, u3, 0, u2, u2} ι R Nat (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 _inst_3 Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3))) (fun (i : ι) => Submodule.subtype.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))) -> (CompleteLattice.Independent.{succ u1, u2} ι (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u3, u2} R N _inst_1 _inst_2 _inst_3) p)
 Case conversion may be inaccurate. Consider using '#align complete_lattice.independent_of_dfinsupp_lsum_injective CompleteLattice.independent_of_dfinsupp_lsum_injectiveₓ'. -/
 /- If `dfinsupp.lsum` applied with `submodule.subtype` is injective then the submodules are
 independent. -/
@@ -683,7 +683,7 @@ theorem independent_of_dfinsupp_sumAddHom_injective (p : ι → AddSubmonoid N)
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} N] [_inst_3 : Module.{u2, u3} R N _inst_1 _inst_2] [_inst_4 : forall (m : R), Decidable (Ne.{succ u2} R m (OfNat.ofNat.{u2} R 0 (OfNat.mk.{u2} R 0 (Zero.zero.{u2} R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))))] (p : ι -> (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3)) {v : ι -> N} (hv : forall (i : ι), Membership.Mem.{u3, u3} N (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (v i) (p i)), Eq.{max (succ (max u1 u2)) (succ u3)} (LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} ι R 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 but is expected to have type
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i)) _inst_2 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N _inst_1 _inst_1 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) 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i))))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_2 (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u1, u3, 0, u2, u2} ι R Nat (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 _inst_3 Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3))) (fun (i : ι) => Submodule.subtype.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) (LinearMap.comp.{u3, u3, u3, max u1 u3, max u1 u3, max u1 u2} R R R (Finsupp.{u1, u3} ι R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (Dfinsupp.{u1, u3} ι (fun (i : ι) => R) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => R) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => R) i) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))) _inst_1 _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u3} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) (Finsupp.module.{u1, u3, u3} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (Dfinsupp.module.{u1, u3, u3} ι R (fun (i : ι) => R) _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => Semiring.toModule.{u3} R _inst_1)) (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomCompTriple.ids.{u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Dfinsupp.mapRange.linearMap.{u1, u3, u3, u2} ι R _inst_1 (fun (i : ι) => R) (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Semiring.toModule.{u3} R _inst_1) (fun (i : ι) => Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => LinearMap.toSpanSingleton.{u3, u2} R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) _inst_1 (Submodule.addCommMonoid.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (Submodule.module.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (Subtype.mk.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i)) (v i) (hv i)))) (LinearEquiv.toLinearMap.{u3, u3, max u1 u3, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.{u1, u3} ι R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (Dfinsupp.{u1, u3} ι (fun (i : ι) => R) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (_i : ι) => R) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (_i : ι) => R) i) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (Finsupp.addCommMonoid.{u1, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u3} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (Dfinsupp.module.{u1, u3, u3} ι R (fun (i : ι) => R) _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => Semiring.toModule.{u3} R _inst_1)) (finsuppLequivDfinsupp.{u1, u3, u3} ι R R (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (m : R) => _inst_4 m) (Semiring.toModule.{u3} R _inst_1))))) (Finsupp.total.{u1, u2, u3} ι N R _inst_1 _inst_2 _inst_3 v)
 Case conversion may be inaccurate. Consider using '#align complete_lattice.lsum_comp_map_range_to_span_singleton CompleteLattice.lsum_comp_mapRange_toSpanSingletonₓ'. -/
 /-- Combining `dfinsupp.lsum` with `linear_map.to_span_singleton` is the same as `finsupp.total` -/
 theorem lsum_comp_mapRange_toSpanSingleton [∀ m : R, Decidable (m ≠ 0)] (p : ι → Submodule R N)
@@ -723,7 +723,7 @@ theorem independent_of_dfinsupp_sumAddHom_injective' (p : ι → AddSubgroup N)
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} N] [_inst_3 : Module.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2)] {p : ι -> (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3)}, (CompleteLattice.Independent.{succ u1, u3} ι (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) (Submodule.completeLattice.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) p) -> (Function.Injective.{succ (max u1 u3), succ u3} (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) N (Submodule.setLike.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3)) (p i)) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) N (Submodule.setLike.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3)) (p i)) (AddMonoid.toAddZeroClass.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) N 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 but is expected to have type
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u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)))) Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (LinearMap.{u3, u3, max u2 u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (Ring.toSemiring.{u3} R _inst_1) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) _inst_3) (SMulZeroClass.toSMul.{0, max u1 u2} Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (AddMonoid.toZero.{max u1 u2} (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{0, max u1 u2} Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (AddMonoid.toAddZeroClass.{max u1 u2} (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))))))) (DistribMulAction.toDistribSMul.{0, max u1 u2} Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max u1 u2} (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))))) (Module.toDistribMulAction.{0, max u1 u2} Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) Nat.semiring (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))))) (Pi.module.{u1, 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(i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) (fun (i : ι) => 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R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u2, u2} R R Nat (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u2} N (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u2, u2} R R Nat (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (Ring.toSemiring.{u3} R _inst_1) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u2} N (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u1, u3, 0, u2, u2} ι R Nat (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (fun (a : ι) (b : ι) => dec_ι a b) (Ring.toSemiring.{u3} R _inst_1) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 Nat.semiring (AddCommMonoid.natModule.{u2} N (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3))) (fun (i : ι) => Submodule.subtype.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)))))
 Case conversion may be inaccurate. Consider using '#align complete_lattice.independent.dfinsupp_lsum_injective CompleteLattice.Independent.dfinsupp_lsum_injectiveₓ'. -/
 /-- The canonical map out of a direct sum of a family of submodules is injective when the submodules
 are `complete_lattice.independent`.
@@ -772,7 +772,7 @@ theorem Independent.dfinsupp_sumAddHom_injective {p : ι → AddSubgroup N} (h :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} N] [_inst_3 : Module.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2)] (p : ι -> (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3)), Iff (CompleteLattice.Independent.{succ u1, u3} ι (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) (Submodule.completeLattice.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) p) (Function.Injective.{succ (max u1 u3), succ u3} (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) N (Submodule.setLike.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3)) (p i)) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) N (Submodule.setLike.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3)) (p i)) (AddMonoid.toAddZeroClass.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) N (Submodule.setLike.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3)) (p i)) (AddCommMonoid.toAddMonoid.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) N (Submodule.setLike.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3)) (p i)) (Submodule.addCommMonoid.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3 (p i)))))) N (coeFn.{max (succ (max u1 u3)) (succ u3), max (succ (max u1 u3)) (succ u3)} (LinearMap.{u2, u2, max u1 u3, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) 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 but is expected to have type
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u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)))) Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (LinearMap.{u3, u3, max u2 u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (Ring.toSemiring.{u3} R _inst_1) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) _inst_3) (SMulZeroClass.toSMul.{0, max u1 u2} Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (AddMonoid.toZero.{max u1 u2} (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{0, max u1 u2} Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (AddMonoid.toAddZeroClass.{max u1 u2} (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))))))) (DistribMulAction.toDistribSMul.{0, max u1 u2} Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max u1 u2} (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))))) (Module.toDistribMulAction.{0, max u1 u2} Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) Nat.semiring (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))))) (Pi.module.{u1, 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(i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) (fun (i : ι) => 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R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) (AddCommGroup.toAddCommMonoid.{u2} N 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R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u2, u2} R R Nat (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u2} N (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u2, u2} R R Nat (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (Ring.toSemiring.{u3} R _inst_1) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u2} N (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u1, u3, 0, u2, u2} ι R Nat (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (fun (a : ι) (b : ι) => dec_ι a b) (Ring.toSemiring.{u3} R _inst_1) (fun (i : ι) => Submodule.addCommMonoid.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 Nat.semiring (AddCommMonoid.natModule.{u2} N (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3))) (fun (i : ι) => Submodule.subtype.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)))))
 Case conversion may be inaccurate. Consider using '#align complete_lattice.independent_iff_dfinsupp_lsum_injective CompleteLattice.independent_iff_dfinsupp_lsum_injectiveₓ'. -/
 /-- A family of submodules over an additive group are independent if and only iff `dfinsupp.lsum`
 applied with `submodule.subtype` is injective.
@@ -803,7 +803,7 @@ omit dec_ι
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} N] [_inst_3 : Module.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2)] [_inst_4 : NoZeroSMulDivisors.{u2, u3} R N (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (SubNegMonoid.toAddMonoid.{u3} N (AddGroup.toSubNegMonoid.{u3} N (AddCommGroup.toAddGroup.{u3} N _inst_2))))) (SMulZeroClass.toHasSmul.{u2, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N _inst_2)))) (SMulWithZero.toSmulZeroClass.{u2, u3} R N (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N _inst_2)))) (MulActionWithZero.toSMulWithZero.{u2, u3} R N (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N _inst_2)))) (Module.toMulActionWithZero.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3))))] (p : ι -> (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3)), (CompleteLattice.Independent.{succ u1, u3} ι (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) (Submodule.completeLattice.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) p) -> (forall {v : ι -> N}, (forall (i : ι), Membership.Mem.{u3, u3} N (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) N (Submodule.setLike.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3)) (v i) (p i)) -> (forall (i : ι), Ne.{succ u3} N (v i) (OfNat.ofNat.{u3} N 0 (OfNat.mk.{u3} N 0 (Zero.zero.{u3} N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (SubNegMonoid.toAddMonoid.{u3} N (AddGroup.toSubNegMonoid.{u3} N (AddCommGroup.toAddGroup.{u3} N _inst_2))))))))) -> (LinearIndependent.{u1, u2, u3} ι R N v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3))
 but is expected to have type
-  forall {ι : Type.{u1}} {R : Type.{u3}} {N : Type.{u2}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : Ring.{u3} R] [_inst_3 : AddCommGroup.{u2} N] [_inst_4 : Module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3)] [p : NoZeroSMulDivisors.{u3, u2} R N (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_2))) (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N _inst_3))))) (SMulZeroClass.toSMul.{u3, u2} R N (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N _inst_3))))) (SMulWithZero.toSMulZeroClass.{u3, u2} R N (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_2))) (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N _inst_3))))) (MulActionWithZero.toSMulWithZero.{u3, u2} R N (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_2)) (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N _inst_3))))) (Module.toMulActionWithZero.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4))))] (hp : ι -> (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4)), (CompleteLattice.Independent.{succ u1, u2} ι (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4) (Submodule.completeLattice.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4) hp) -> (forall {hv : ι -> N}, (forall (i : ι), Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4) N (Submodule.instSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4)) (hv i) (hp i)) -> (forall (i : ι), Ne.{succ u2} N (hv i) (OfNat.ofNat.{u2} N 0 (Zero.toOfNat0.{u2} N (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N _inst_3)))))))) -> (LinearIndependent.{u1, u3, u2} ι R N hv (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4))
+  forall {ι : Type.{u1}} {R : Type.{u3}} {N : Type.{u2}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : Ring.{u3} R] [_inst_3 : AddCommGroup.{u2} N] [_inst_4 : Module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3)] [p : NoZeroSMulDivisors.{u3, u2} R N (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_2))) (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N _inst_3))))) (SMulZeroClass.toSMul.{u3, u2} R N (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N _inst_3))))) (SMulWithZero.toSMulZeroClass.{u3, u2} R N (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_2))) (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N _inst_3))))) (MulActionWithZero.toSMulWithZero.{u3, u2} R N (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_2)) (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N _inst_3))))) (Module.toMulActionWithZero.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4))))] (hp : ι -> (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4)), (CompleteLattice.Independent.{succ u1, u2} ι (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4) (Submodule.completeLattice.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4) hp) -> (forall {hv : ι -> N}, (forall (i : ι), Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4) N (Submodule.setLike.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4)) (hv i) (hp i)) -> (forall (i : ι), Ne.{succ u2} N (hv i) (OfNat.ofNat.{u2} N 0 (Zero.toOfNat0.{u2} N (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N _inst_3)))))))) -> (LinearIndependent.{u1, u3, u2} ι R N hv (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4))
 Case conversion may be inaccurate. Consider using '#align complete_lattice.independent.linear_independent CompleteLattice.Independent.linearIndependentₓ'. -/
 /-- If a family of submodules is `independent`, then a choice of nonzero vector from each submodule
 forms a linearly independent family.

f4758115

bump to nightly-2023-03-11-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

a8ee822f

Diff

@@ -84,7 +84,7 @@ def lsingle (i) : M i →ₗ[R] Π₀ i, M i :=
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : ι -> Type.{u3}} {N : Type.{u4}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (M i)] [_inst_3 : forall (i : ι), Module.{u2, u3} R (M i) _inst_1 (_inst_2 i)] [_inst_4 : AddCommMonoid.{u4} N] [_inst_5 : Module.{u2, u4} R N _inst_1 _inst_4] {{φ : LinearMap.{u2, u2, max u1 u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))))) N (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5}} {{ψ : LinearMap.{u2, u2, max u1 u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))))) N (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5}}, (forall (i : ι) (x : M i), Eq.{succ u4} N (coeFn.{max (succ (max u1 u3)) (succ u4), max (succ (max u1 u3)) (succ u4)} (LinearMap.{u2, u2, max u1 u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))))) N (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5) (fun (_x : LinearMap.{u2, u2, max u1 u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))))) N (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5) => (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))))) -> N) (LinearMap.hasCoeToFun.{u2, u2, max u1 u3, u4} R R (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))))) N _inst_1 _inst_1 (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) φ (Dfinsupp.single.{u1, u3} ι (fun (i : ι) => M i) (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i)))) i x)) (coeFn.{max (succ (max u1 u3)) (succ u4), max (succ (max u1 u3)) (succ u4)} (LinearMap.{u2, u2, max u1 u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))))) N (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5) (fun (_x : LinearMap.{u2, u2, max u1 u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))))) N (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5) => (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))))) -> N) (LinearMap.hasCoeToFun.{u2, u2, max u1 u3, u4} R R (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))))) N _inst_1 _inst_1 (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) ψ (Dfinsupp.single.{u1, u3} ι (fun (i : ι) => M i) (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i)))) i x))) -> (Eq.{max (succ (max u1 u3)) (succ u4)} (LinearMap.{u2, u2, max u1 u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))))) N (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5) φ ψ)
 but is expected to have type
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: ι) => M i) i) (_inst_2 i)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Dfinsupp.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) => N) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u2 u3, u1} R R (Dfinsupp.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u2, u3, u4} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) ψ (Dfinsupp.single.{u2, u3} ι (fun (i : ι) => M i) (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i))) i x))) -> (Eq.{max (max (succ u2) (succ u3)) (succ u1)} (LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Dfinsupp.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u2, u3, u4} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5) φ ψ)
+  forall {ι : Type.{u2}} {R : Type.{u4}} {M : ι -> Type.{u3}} {N : Type.{u1}} [dec_ι : DecidableEq.{succ u2} ι] [_inst_1 : Semiring.{u4} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (M i)] [_inst_3 : forall (i : ι), Module.{u4, u3} R (M i) _inst_1 (_inst_2 i)] [_inst_4 : AddCommMonoid.{u1} N] [_inst_5 : Module.{u4, u1} R N _inst_1 _inst_4] {{φ : LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Dfinsupp.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u2, u3, u4} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5}} {{ψ : LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Dfinsupp.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u2, u3, u4} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5}}, (forall (i : ι) (x : M i), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Dfinsupp.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) => N) (Dfinsupp.single.{u2, u3} ι (fun (i : ι) => M i) (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i))) i x)) (FunLike.coe.{max (max 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=> M i) i) (_inst_2 i))) i x)) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u3), succ u1} (LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Dfinsupp.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u2, u3, u4} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5) (Dfinsupp.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) (fun (_x : Dfinsupp.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Dfinsupp.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) => N) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u2 u3, u1} R R (Dfinsupp.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u2, u3, u4} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) ψ (Dfinsupp.single.{u2, u3} ι (fun (i : ι) => M i) (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i))) i x))) -> (Eq.{max (max (succ u2) (succ u3)) (succ u1)} (LinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Dfinsupp.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u2, u3, u4} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5) φ ψ)
 Case conversion may be inaccurate. Consider using '#align dfinsupp.lhom_ext Dfinsupp.lhom_extₓ'. -/
 /-- Two `R`-linear maps from `Π₀ i, M i` which agree on each `single i x` agree everywhere. -/
 theorem lhom_ext ⦃φ ψ : (Π₀ i, M i) →ₗ[R] N⦄ (h : ∀ i x, φ (single i x) = ψ (single i x)) : φ = ψ :=
@@ -129,7 +129,7 @@ include dec_ι
 lean 3 declaration is
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+  forall {ι : Type.{u3}} {R : Type.{u1}} {M : ι -> Type.{u2}} [dec_ι : DecidableEq.{succ u3} ι] [_inst_1 : Semiring.{u1} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (M i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (M i) _inst_1 (_inst_2 i)] (s : Finset.{u3} ι) (x : forall (i : Set.Elem.{u3} ι (Finset.toSet.{u3} ι s)), M (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x (Finset.toSet.{u3} ι s)) i)), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : forall (i : Set.Elem.{u3} ι (Finset.toSet.{u3} ι s)), M (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x (Finset.toSet.{u3} ι s)) i)) => Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) x) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ 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i))) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} (Set.Elem.{u3} ι (Finset.toSet.{u3} ι s)) (fun (i : Set.Elem.{u3} ι (Finset.toSet.{u3} ι s)) => M (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x (Finset.toSet.{u3} ι s)) i)) R _inst_1 (fun (i : Set.Elem.{u3} ι (Finset.toSet.{u3} ι s)) => _inst_2 (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x (Finset.toSet.{u3} ι s)) i)) (fun (i : Set.Elem.{u3} ι (Finset.toSet.{u3} ι s)) => _inst_3 (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x (Finset.toSet.{u3} ι s)) i))) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (forall (i : Set.Elem.{u3} ι (Finset.toSet.{u3} ι s)), M (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x (Finset.toSet.{u3} ι s)) i)) (fun (_x : forall (i : Set.Elem.{u3} ι (Finset.toSet.{u3} ι s)), M (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x (Finset.toSet.{u3} ι s)) i)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : forall (i : Set.Elem.{u3} ι (Finset.toSet.{u3} ι s)), M (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x (Finset.toSet.{u3} ι s)) i)) => Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u2, max u3 u2} R R (forall (i : Set.Elem.{u3} ι (Finset.toSet.{u3} ι s)), M (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x (Finset.toSet.{u3} ι s)) i)) (Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} (Set.Elem.{u3} ι (Finset.toSet.{u3} ι s)) (fun (i : Set.Elem.{u3} ι (Finset.toSet.{u3} ι s)) => M (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x (Finset.toSet.{u3} ι s)) i)) (fun (i : Set.Elem.{u3} ι (Finset.toSet.{u3} ι s)) => _inst_2 (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x (Finset.toSet.{u3} ι s)) i))) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} (Set.Elem.{u3} ι (Finset.toSet.{u3} ι s)) (fun (i : Set.Elem.{u3} ι (Finset.toSet.{u3} ι s)) => M (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x (Finset.toSet.{u3} ι s)) i)) R _inst_1 (fun (i : Set.Elem.{u3} ι (Finset.toSet.{u3} ι s)) => _inst_2 (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x (Finset.toSet.{u3} ι s)) i)) (fun (i : Set.Elem.{u3} ι (Finset.toSet.{u3} ι s)) => _inst_3 (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x (Finset.toSet.{u3} ι s)) i))) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Dfinsupp.lmk.{u3, u1, u2} ι R (fun (i : ι) => M i) (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) s) x) (Dfinsupp.mk.{u3, u2} ι M (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => AddMonoid.toZero.{u2} (M i) (AddCommMonoid.toAddMonoid.{u2} (M i) (_inst_2 i))) s x)
 Case conversion may be inaccurate. Consider using '#align dfinsupp.lmk_apply Dfinsupp.lmk_applyₓ'. -/
 @[simp]
 theorem lmk_apply (s : Finset ι) (x) : (lmk s : _ →ₗ[R] Π₀ i, M i) x = mk s x :=
@@ -140,7 +140,7 @@ theorem lmk_apply (s : Finset ι) (x) : (lmk s : _ →ₗ[R] Π₀ i, M i) x = m
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : ι -> Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (M i)] [_inst_3 : forall (i : ι), Module.{u2, u3} R (M i) _inst_1 (_inst_2 i)] (i : ι) (x : M i), Eq.{succ (max u1 u3)} (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))))) (coeFn.{max (succ u3) (succ (max u1 u3)), max (succ u3) (succ (max u1 u3))} (LinearMap.{u2, u2, u3, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (M i) (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))))) (_inst_2 i) (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (fun (_x : LinearMap.{u2, u2, u3, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (M i) (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))))) (_inst_2 i) (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) => (M i) -> (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i)))))) (LinearMap.hasCoeToFun.{u2, u2, u3, max u1 u3} R R (M i) (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))))) _inst_1 _inst_1 (_inst_2 i) (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Dfinsupp.lsingle.{u1, u2, u3} ι R (fun (i : ι) => M i) (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i) x) (Dfinsupp.single.{u1, u3} ι (fun (i : ι) => M i) (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i)))) i x)
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u1}} {M : ι -> Type.{u2}} [dec_ι : DecidableEq.{succ u3} ι] [_inst_1 : Semiring.{u1} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (M i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (M i) _inst_1 (_inst_2 i)] (i : ι) (x : M i), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M i) => Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) x) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (M i) (Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) (_inst_2 i) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (M i) (fun (_x : M i) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M i) => Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u2} R R (M i) (Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) _inst_1 _inst_1 (_inst_2 i) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Dfinsupp.lsingle.{u3, u1, u2} ι R M (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i) x) (Dfinsupp.single.{u3, u2} ι M (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => AddMonoid.toZero.{u2} (M i) (AddCommMonoid.toAddMonoid.{u2} (M i) (_inst_2 i))) i x)
+  forall {ι : Type.{u3}} {R : Type.{u1}} {M : ι -> Type.{u2}} [dec_ι : DecidableEq.{succ u3} ι] [_inst_1 : Semiring.{u1} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (M i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (M i) _inst_1 (_inst_2 i)] (i : ι) (x : M i), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M i) => Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) x) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (M i) (Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) (_inst_2 i) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (M i) (fun (_x : M i) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M i) => Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u2} R R (M i) (Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) _inst_1 _inst_1 (_inst_2 i) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Dfinsupp.lsingle.{u3, u1, u2} ι R M (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i) x) (Dfinsupp.single.{u3, u2} ι M (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => AddMonoid.toZero.{u2} (M i) (AddCommMonoid.toAddMonoid.{u2} (M i) (_inst_2 i))) i x)
 Case conversion may be inaccurate. Consider using '#align dfinsupp.lsingle_apply Dfinsupp.lsingle_applyₓ'. -/
 @[simp]
 theorem lsingle_apply (i : ι) (x : M i) : (lsingle i : _ →ₗ[R] _) x = single i x :=
@@ -153,7 +153,7 @@ omit dec_ι
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : ι -> Type.{u3}} [_inst_1 : Semiring.{u2} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (M i)] [_inst_3 : forall (i : ι), Module.{u2, u3} R (M i) _inst_1 (_inst_2 i)] (i : ι) (f : Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} ((fun (i : ι) => M i) i) (AddMonoid.toAddZeroClass.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i))))), Eq.{succ u3} (M i) (coeFn.{max (succ (max u1 u3)) (succ u3), max (succ (max u1 u3)) (succ u3)} (LinearMap.{u2, u2, max u1 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))))) (M i) (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i)) (fun (_x : LinearMap.{u2, u2, max u1 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))))) (M i) (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i)) => (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))))) -> (M i)) (LinearMap.hasCoeToFun.{u2, u2, max u1 u3, u3} R R (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))))) (M i) _inst_1 _inst_1 (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Dfinsupp.lapply.{u1, u2, u3} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i) f) (coeFn.{succ (max u1 u3), max (succ u1) (succ u3)} (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} ((fun (i : ι) => M i) i) (AddMonoid.toAddZeroClass.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i))))) (fun (_x : Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} ((fun (i : ι) => M i) i) (AddMonoid.toAddZeroClass.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i))))) => forall (i : ι), M i) (Dfinsupp.hasCoeToFun.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} ((fun (i : ι) => M i) i) (AddMonoid.toAddZeroClass.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i))))) f i)
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u1}} {M : ι -> Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (M i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (M i) _inst_1 (_inst_2 i)] (i : ι) (f : Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) => M i) f) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), succ u2} (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) (M i) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i)) (Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) (fun (_x : Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) => M i) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u2, u2} R R (Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) (M i) _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Dfinsupp.lapply.{u3, u1, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i) f) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Dfinsupp.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => M i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => M i) i) _x) (Dfinsupp.funLike.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => M i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i))) i)) f i)
+  forall {ι : Type.{u3}} {R : Type.{u1}} {M : ι -> Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (M i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (M i) _inst_1 (_inst_2 i)] (i : ι) (f : Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) => M i) f) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), succ u2} (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) (M i) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i)) (Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) (fun (_x : Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) => M i) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u2, u2} R R (Dfinsupp.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) (M i) _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Dfinsupp.lapply.{u3, u1, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i) f) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Dfinsupp.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => M i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => M i) i) _x) (Dfinsupp.funLike.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => M i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i))) i)) f i)
 Case conversion may be inaccurate. Consider using '#align dfinsupp.lapply_apply Dfinsupp.lapply_applyₓ'. -/
 @[simp]
 theorem lapply_apply (i : ι) (f : Π₀ i, M i) : (lapply i : _ →ₗ[R] _) f = f i :=
@@ -239,7 +239,7 @@ def lsum [Semiring S] [Module S N] [SMulCommClass R S N] :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} (S : Type.{u3}) {M : ι -> Type.{u4}} {N : Type.{u5}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u4} (M i)] [_inst_3 : forall (i : ι), Module.{u2, u4} R (M i) _inst_1 (_inst_2 i)] [_inst_4 : AddCommMonoid.{u5} N] [_inst_5 : Module.{u2, u5} R N _inst_1 _inst_4] [_inst_6 : Semiring.{u3} S] [_inst_7 : Module.{u3, u5} S N _inst_6 _inst_4] [_inst_8 : SMulCommClass.{u2, u3, u5} R S N (SMulZeroClass.toHasSmul.{u2, u5} R N (AddZeroClass.toHasZero.{u5} N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4))) (SMulWithZero.toSmulZeroClass.{u2, u5} R N (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))) (AddZeroClass.toHasZero.{u5} N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4))) (MulActionWithZero.toSMulWithZero.{u2, u5} R N (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddZeroClass.toHasZero.{u5} N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4))) (Module.toMulActionWithZero.{u2, u5} R N _inst_1 _inst_4 _inst_5)))) (SMulZeroClass.toHasSmul.{u3, u5} S N (AddZeroClass.toHasZero.{u5} N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4))) (SMulWithZero.toSmulZeroClass.{u3, u5} S N (MulZeroClass.toHasZero.{u3} S (MulZeroOneClass.toMulZeroClass.{u3} S (MonoidWithZero.toMulZeroOneClass.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_6)))) (AddZeroClass.toHasZero.{u5} N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4))) (MulActionWithZero.toSMulWithZero.{u3, u5} S N (Semiring.toMonoidWithZero.{u3} S _inst_6) (AddZeroClass.toHasZero.{u5} N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4))) (Module.toMulActionWithZero.{u3, u5} S N _inst_6 _inst_4 _inst_7))))] (F : forall (i : ι), LinearMap.{u2, u2, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (i : ι) (x : M i), Eq.{succ u5} N (coeFn.{max (succ (max u1 u4)) (succ u5), max (succ (max u1 u4)) (succ u5)} (LinearMap.{u2, u2, max u1 u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} (M i) (AddMonoid.toAddZeroClass.{u4} (M i) (AddCommMonoid.toAddMonoid.{u4} (M i) (_inst_2 i))))) N (Dfinsupp.addCommMonoid.{u1, u4} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u4, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5) (fun (_x : LinearMap.{u2, u2, max u1 u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} (M i) 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(RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) => (M i) -> N) (LinearMap.hasCoeToFun.{u2, u2, u4, u5} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (F i) x)
 but is expected to have type
-  forall {ι : Type.{u1}} {R : Type.{u3}} (S : Type.{u5}) {M : ι -> Type.{u2}} {N : Type.{u4}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u3} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (M i)] [_inst_3 : forall (i : ι), Module.{u3, u2} R (M i) _inst_1 (_inst_2 i)] [_inst_4 : AddCommMonoid.{u4} N] [_inst_5 : Module.{u3, u4} R N _inst_1 _inst_4] [_inst_6 : Semiring.{u5} S] [_inst_7 : Module.{u5, u4} S N _inst_6 _inst_4] [_inst_8 : SMulCommClass.{u3, u5, u4} R S N (SMulZeroClass.toSMul.{u3, u4} R N (AddMonoid.toZero.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_4)) (SMulWithZero.toSMulZeroClass.{u3, u4} R N (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddMonoid.toZero.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_4)) (MulActionWithZero.toSMulWithZero.{u3, u4} R N (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddMonoid.toZero.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_4)) (Module.toMulActionWithZero.{u3, u4} R N _inst_1 _inst_4 _inst_5)))) 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(RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u5, max u1 u2, u4} R R S (Dfinsupp.{u1, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) _inst_6 _inst_7 _inst_8))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u4, u5, max (max u1 u2) u4, max (max u1 u2) u4} (LinearEquiv.{u5, u5, max (max u1 u2) u4, max u4 u2 u1} S S _inst_6 _inst_6 (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_6)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_6)) 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dec_ι a b) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) _inst_4 _inst_5 _inst_6 _inst_7 _inst_8) F) (Dfinsupp.single.{u1, u2} ι (fun (i : ι) => M i) (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i))) i x)) (FunLike.coe.{max (succ u2) (succ u4), succ u2, succ u4} (LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (M i) (fun (_x : M i) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M i) => N) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u4} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (F i) x)
+  forall {ι : Type.{u1}} {R : Type.{u3}} (S : Type.{u5}) {M : ι -> Type.{u2}} {N : Type.{u4}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u3} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (M i)] [_inst_3 : forall (i : ι), Module.{u3, u2} R (M i) _inst_1 (_inst_2 i)] [_inst_4 : AddCommMonoid.{u4} N] [_inst_5 : Module.{u3, u4} R N _inst_1 _inst_4] [_inst_6 : Semiring.{u5} S] [_inst_7 : Module.{u5, u4} S N _inst_6 _inst_4] [_inst_8 : SMulCommClass.{u3, u5, u4} R S N (SMulZeroClass.toSMul.{u3, u4} R N (AddMonoid.toZero.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_4)) (SMulWithZero.toSMulZeroClass.{u3, u4} R N (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddMonoid.toZero.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_4)) (MulActionWithZero.toSMulWithZero.{u3, u4} R N (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddMonoid.toZero.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_4)) (Module.toMulActionWithZero.{u3, u4} R N _inst_1 _inst_4 _inst_5)))) 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(RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u5, max u1 u2, u4} R R S (Dfinsupp.{u1, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) _inst_6 _inst_7 _inst_8))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u4, u5, max (max u1 u2) u4, max (max u1 u2) u4} (LinearEquiv.{u5, u5, max (max u1 u2) u4, max u4 u2 u1} S S _inst_6 _inst_6 (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_6)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_6)) 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dec_ι a b) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) _inst_4 _inst_5 _inst_6 _inst_7 _inst_8) F) (Dfinsupp.single.{u1, u2} ι (fun (i : ι) => M i) (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i))) i x)) (FunLike.coe.{max (succ u2) (succ u4), succ u2, succ u4} (LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (M i) (fun (_x : M i) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M i) => N) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u4} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (F i) x)
 Case conversion may be inaccurate. Consider using '#align dfinsupp.lsum_single Dfinsupp.lsum_singleₓ'. -/
 /-- While `simp` can prove this, it is often convenient to avoid unfolding `lsum` into `sum_add_hom`
 with `dfinsupp.lsum_apply_apply`. -/
@@ -324,7 +324,7 @@ include dec_ι
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u2, u3} R N _inst_1 _inst_4] {β₁ : ι -> Type.{u4}} {β₂ : ι -> Type.{u5}} [_inst_7 : forall (i : ι), AddCommMonoid.{u4} (β₁ i)] [_inst_8 : forall (i : ι), AddCommMonoid.{u5} (β₂ i)] [_inst_10 : forall (i : ι), Module.{u2, u4} R (β₁ i) _inst_1 (_inst_7 i)] [_inst_11 : forall (i : ι), Module.{u2, u5} R (β₂ i) _inst_1 (_inst_8 i)] [_inst_12 : forall (i : ι) (x : β₁ i), Decidable (Ne.{succ u4} (β₁ i) x (OfNat.ofNat.{u4} (β₁ i) 0 (OfNat.mk.{u4} (β₁ i) 0 (Zero.zero.{u4} (β₁ i) (AddZeroClass.toHasZero.{u4} (β₁ i) (AddMonoid.toAddZeroClass.{u4} (β₁ i) (AddCommMonoid.toAddMonoid.{u4} (β₁ i) (_inst_7 i))))))))] [_inst_13 : forall (i : ι) (x : β₂ i), Decidable (Ne.{succ u5} (β₂ i) x (OfNat.ofNat.{u5} (β₂ i) 0 (OfNat.mk.{u5} (β₂ i) 0 (Zero.zero.{u5} (β₂ i) (AddZeroClass.toHasZero.{u5} (β₂ i) (AddMonoid.toAddZeroClass.{u5} (β₂ i) 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: ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5)) (LinearEquiv.hasCoeToFun.{0, 0, max u1 u4 u3, max (max u1 u4) u3} Nat Nat (forall (i : ι), LinearMap.{u2, u2, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (LinearMap.{u2, u2, max u1 u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} (β₁ i) (AddMonoid.toAddZeroClass.{u4} (β₁ i) (AddCommMonoid.toAddMonoid.{u4} (β₁ i) (_inst_7 i))))) N (Dfinsupp.addCommMonoid.{u1, u4} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u4, u2} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u1, max u4 u3} ι (fun (i : ι) => LinearMap.{u2, u2, u4, u3} R R _inst_1 _inst_1 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(Semiring.toNonAssocSemiring.{u2} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u4, u3} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.module.{u2, u2, 0, u4, u3} R R Nat (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u3} N _inst_4) (AddMonoid.nat_smulCommClass'.{u2, u3} R N (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} N _inst_4) (Module.toDistribMulAction.{u2, u3} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.module.{u2, u2, 0, max u1 u4, u3} R R Nat (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} (β₁ i) (AddMonoid.toAddZeroClass.{u4} (β₁ i) (AddCommMonoid.toAddMonoid.{u4} (β₁ i) (_inst_7 i))))) N _inst_1 _inst_1 (Dfinsupp.addCommMonoid.{u1, u4} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u4, u2} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u3} N _inst_4) (AddMonoid.nat_smulCommClass'.{u2, u3} R N (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} N _inst_4) (Module.toDistribMulAction.{u2, u3} R N _inst_1 _inst_4 _inst_5))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)) (Dfinsupp.lsum.{u1, u2, 0, u4, u3} ι R Nat (fun (i : ι) => β₁ i) N (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i) _inst_4 _inst_5 Nat.semiring (AddCommMonoid.natModule.{u3} N _inst_4) (AddMonoid.nat_smulCommClass'.{u2, u3} R N (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} N _inst_4) (Module.toDistribMulAction.{u2, u3} R N _inst_1 _inst_4 _inst_5))) (fun (i : ι) => LinearMap.comp.{u2, u2, u2, u4, u5, u3} R R R (β₁ i) (β₂ i) N _inst_1 _inst_1 _inst_1 (_inst_7 i) (_inst_8 i) _inst_4 (_inst_10 i) (_inst_11 i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomCompTriple.right_ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (h i) (f i))) l)
 but is expected to have type
-  forall {ι : Type.{u1}} {R : Type.{u3}} {N : Type.{u2}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u3} R] [_inst_4 : AddCommMonoid.{u2} N] [_inst_5 : Module.{u3, u2} R N _inst_1 _inst_4] {β₁ : ι -> Type.{u5}} {β₂ : ι -> Type.{u4}} [_inst_7 : forall (i : ι), AddCommMonoid.{u5} (β₁ i)] [_inst_8 : forall (i : ι), AddCommMonoid.{u4} (β₂ i)] [_inst_10 : forall (i : ι), Module.{u3, u5} R (β₁ i) _inst_1 (_inst_7 i)] [_inst_11 : forall (i : ι), Module.{u3, u4} R (β₂ i) _inst_1 (_inst_8 i)] [_inst_12 : forall (i : ι) (x : β₁ i), Decidable (Ne.{succ u5} (β₁ i) x (OfNat.ofNat.{u5} (β₁ i) 0 (Zero.toOfNat0.{u5} (β₁ i) (AddMonoid.toZero.{u5} (β₁ i) (AddCommMonoid.toAddMonoid.{u5} (β₁ i) (_inst_7 i))))))] [_inst_13 : forall (i : ι) (x : β₂ i), Decidable (Ne.{succ u4} (β₂ i) x (OfNat.ofNat.{u4} (β₂ i) 0 (Zero.toOfNat0.{u4} (β₂ i) (AddMonoid.toZero.{u4} (β₂ i) (AddCommMonoid.toAddMonoid.{u4} (β₂ i) (_inst_8 i))))))] {f : forall (i : ι), LinearMap.{u3, u3, u5, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) (β₂ i) (_inst_7 i) (_inst_8 i) (_inst_10 i) (_inst_11 i)} {h : forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5} {l : Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))}, Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) => N) (FunLike.coe.{max (max (succ u1) (succ u5)) (succ u4), max (succ u1) (succ u5), max (succ u1) (succ u4)} (LinearMap.{u3, u3, max u5 u1, max u4 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, 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ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u1 u4) u2} (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Module.toDistribMulAction.{0, max (max u1 u4) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat.semiring (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Pi.module.{u1, max u4 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u4, u2} R R Nat (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))))))) (SMulZeroClass.toSMul.{0, max (max u1 u4) u2} Nat (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) (AddMonoid.toZero.{max (max u1 u4) u2} (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u1 u4) u2} (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun 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β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u1 u4) u2} (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) (LinearMap.addCommMonoid.{u3, u3, max u1 u4, u2} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun 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(LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) (LinearMap.addCommMonoid.{u3, u3, max u1 u4, u2} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u1 u4) u2} Nat (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u3, u3, max u1 u4, u2} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u4, u2} R R Nat (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u4) u2, 0, max (max u1 u4) u2, max (max u1 u4) u2} (LinearEquiv.{0, 0, max (max u1 u4) u2, max u2 u4 u1} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} 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(AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u4, u2} R R Nat (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R 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(Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) (LinearMap.addCommMonoid.{u3, u3, max u1 u4, u2} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u1 u4) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R 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_inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))))) (Module.toDistribMulAction.{0, max (max u1 u4) u2} Nat (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => 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(_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u4 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u4, u2} R R Nat (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u4, u2} R R Nat (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) Nat.semiring (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, max u1 u4, u2} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u4 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u4, u2} R R Nat (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u4, u2} R R Nat (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))) (SemilinearEquivClass.instSemilinearMapClass.{0, 0, max (max u1 u4) u2, max (max u1 u4) u2, max (max u1 u4) u2} Nat Nat (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) (LinearEquiv.{0, 0, max (max u1 u4) u2, max u2 u4 u1} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, max u1 u4, u2} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u4 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u4, u2} R R Nat (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u4, u2} R R Nat (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, max u1 u4, u2} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u4 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u4, u2} R R Nat (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u4, u2} R R Nat (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{0, 0, max (max u1 u4) u2, max (max u1 u4) u2} Nat Nat (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, max u1 u4, u2} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u4 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) 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(fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (SMulZeroClass.toSMul.{0, max (max u1 u5) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (AddMonoid.toZero.{max (max u1 u5) u2} (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (AddCommMonoid.toAddMonoid.{max (max 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(Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u1 u5) u2} (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (DistribMulAction.toDistribSMul.{0, max (max u1 u5) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u1 u5) u2} (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Module.toDistribMulAction.{0, max (max u1 u5) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) Nat.semiring (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Pi.module.{u1, max u5 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u5, u2} R R Nat (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))))))) (SMulZeroClass.toSMul.{0, max (max u1 u5) u2} Nat (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (AddMonoid.toZero.{max (max u1 u5) u2} (LinearMap.{u3, u3, max 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ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (DistribMulAction.toDistribSMul.{0, max (max u1 u5) u2} Nat (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u1 u5) u2} (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ 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=> β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u5, u2} R R Nat (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u5) u2, 0, max (max u1 u5) u2, max (max u1 u5) u2} (LinearEquiv.{0, 0, max (max u1 u5) u2, max u2 u5 u1} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι 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R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u5 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u5, u2} R R Nat (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u5, u2} R R Nat (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) Nat (forall 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(AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))))) (Module.toDistribMulAction.{0, max (max u1 u5) u2} Nat (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u3, u3, max u1 u5, u2} R R (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) 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(fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))) (SemilinearEquivClass.instSemilinearMapClass.{0, 0, max (max u1 u5) u2, max (max u1 u5) u2, max (max u1 u5) u2} Nat Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R 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_inst_1 (_inst_7 i) (_inst_8 i) _inst_4 (_inst_10 i) (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomCompTriple.ids.{u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (h i) (f i))) l)
+  forall {ι : Type.{u1}} {R : Type.{u3}} {N : Type.{u2}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u3} R] [_inst_4 : AddCommMonoid.{u2} N] [_inst_5 : Module.{u3, u2} R N _inst_1 _inst_4] {β₁ : ι -> Type.{u5}} {β₂ : ι -> Type.{u4}} [_inst_7 : forall (i : ι), AddCommMonoid.{u5} (β₁ i)] [_inst_8 : forall (i : ι), AddCommMonoid.{u4} (β₂ i)] [_inst_10 : forall (i : ι), Module.{u3, u5} R (β₁ i) _inst_1 (_inst_7 i)] [_inst_11 : forall (i : ι), Module.{u3, u4} R (β₂ i) _inst_1 (_inst_8 i)] [_inst_12 : forall (i : ι) (x : β₁ i), Decidable (Ne.{succ u5} (β₁ i) x (OfNat.ofNat.{u5} (β₁ i) 0 (Zero.toOfNat0.{u5} (β₁ i) (AddMonoid.toZero.{u5} (β₁ i) (AddCommMonoid.toAddMonoid.{u5} (β₁ i) (_inst_7 i))))))] [_inst_13 : forall (i : ι) (x : β₂ i), Decidable (Ne.{succ u4} (β₂ i) x (OfNat.ofNat.{u4} (β₂ i) 0 (Zero.toOfNat0.{u4} (β₂ i) (AddMonoid.toZero.{u4} (β₂ i) (AddCommMonoid.toAddMonoid.{u4} (β₂ i) (_inst_8 i))))))] {f : forall (i : ι), LinearMap.{u3, u3, u5, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) (β₂ i) (_inst_7 i) (_inst_8 i) (_inst_10 i) (_inst_11 i)} {h : forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5} {l : Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))}, Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) => N) (FunLike.coe.{max (max (succ u1) (succ u5)) (succ u4), max (succ u1) (succ u5), max (succ u1) (succ u4)} (LinearMap.{u3, u3, max u5 u1, max u4 u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, 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_inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (AddMonoid.toAddZeroClass.{max (max u1 u4) u2} (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u1 u4) u2} (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (DistribMulAction.toDistribSMul.{0, max (max u1 u4) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u1 u4) u2} (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Module.toDistribMulAction.{0, max (max u1 u4) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat.semiring (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Pi.module.{u1, max u4 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u4, u2} R R Nat (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))))))) (SMulZeroClass.toSMul.{0, max (max u1 u4) u2} Nat (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) (AddMonoid.toZero.{max (max u1 u4) u2} (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u1 u4) u2} (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun 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(LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) (LinearMap.addCommMonoid.{u3, u3, max u1 u4, u2} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u1 u4) u2} Nat (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u3, u3, max u1 u4, u2} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u4, u2} R R Nat (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u4) u2, 0, max (max u1 u4) u2, max (max u1 u4) u2} (LinearEquiv.{0, 0, max (max u1 u4) u2, max u2 u4 u1} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} 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(AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u4, u2} R R Nat (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R 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(Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) (LinearMap.addCommMonoid.{u3, u3, max u1 u4, u2} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u1 u4) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat.semiring (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Pi.module.{u1, max u4 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u4, u2} R R Nat (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))))) (Module.toDistribMulAction.{0, max (max u1 u4) u2} Nat (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u3, u3, max u1 u4, u2} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u4, u2} R R Nat (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (SemilinearMapClass.distribMulActionHomClass.{0, max (max u1 u4) u2, max (max u1 u4) u2, max (max u1 u4) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) 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(_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u4 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u4, u2} R R Nat (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u4, u2} R R Nat (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) Nat.semiring (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, max u1 u4, u2} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u4 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u4, u2} R R Nat (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u4, u2} R R Nat (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))) (SemilinearEquivClass.instSemilinearMapClass.{0, 0, max (max u1 u4) u2, max (max u1 u4) u2, max (max u1 u4) u2} Nat Nat (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) (LinearEquiv.{0, 0, max (max u1 u4) u2, max u2 u4 u1} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, max u1 u4, u2} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u4 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u4, u2} R R Nat (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u4, u2} R R Nat (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, max u1 u4, u2} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u4 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u4, u2} R R Nat (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u4, u2} R R Nat (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => 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_inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) => LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) _x) (SMulHomClass.toFunLike.{max (max u1 u5) u2, 0, max (max u1 u5) u2, max (max u1 u5) u2} (LinearEquiv.{0, 0, max (max u1 u5) u2, max u2 u5 u1} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, max u1 u5, u2} R R (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u5 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u5, u2} R R Nat (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u5, u2} R R Nat (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (SMulZeroClass.toSMul.{0, max (max u1 u5) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (AddMonoid.toZero.{max (max u1 u5) u2} (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u1 u5) u2} (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{0, max (max u1 u5) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (AddMonoid.toAddZeroClass.{max (max u1 u5) u2} (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u1 u5) u2} (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (DistribMulAction.toDistribSMul.{0, max (max u1 u5) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u1 u5) u2} (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Module.toDistribMulAction.{0, max (max u1 u5) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) Nat.semiring (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Pi.module.{u1, max u5 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u5, u2} R R Nat (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))))))) (SMulZeroClass.toSMul.{0, max (max u1 u5) u2} Nat (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (AddMonoid.toZero.{max (max u1 u5) u2} (LinearMap.{u3, u3, max 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(Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (LinearMap.addCommMonoid.{u3, u3, max u1 u5, u2} R R (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (DistribSMul.toSMulZeroClass.{0, max (max u1 u5) u2} Nat (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) 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=> β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u5, u2} R R Nat (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u5) u2, 0, max (max u1 u5) u2, max (max u1 u5) u2} (LinearEquiv.{0, 0, max (max u1 u5) u2, max u2 u5 u1} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι 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R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u5 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u5, u2} R R Nat (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u5, u2} R R Nat (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) Nat (forall 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(AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))))) (Module.toDistribMulAction.{0, max (max u1 u5) u2} Nat (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u3, u3, max u1 u5, u2} R R (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) 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(fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))) (SemilinearEquivClass.instSemilinearMapClass.{0, 0, max (max u1 u5) u2, max (max u1 u5) u2, max (max u1 u5) u2} Nat Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (LinearEquiv.{0, 0, max (max u1 u5) u2, max u2 u5 u1} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, max u1 u5, u2} R R (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u5 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u5, u2} R R Nat (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u5, u2} R R Nat (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, max u1 u5, u2} R R (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u5 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u5, u2} R R Nat (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u5, u2} R R Nat (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{0, 0, max (max u1 u5) u2, max (max u1 u5) u2} Nat Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, max u1 u5, u2} R R (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u5 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u5, u2} R R Nat (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u5, u2} R R Nat (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u1, u3, 0, u5, u2} ι R Nat β₁ N (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i) _inst_4 _inst_5 Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))) (fun (i : ι) => LinearMap.comp.{u3, u3, u3, u5, u4, u2} R R R (β₁ i) (β₂ i) N _inst_1 _inst_1 _inst_1 (_inst_7 i) (_inst_8 i) _inst_4 (_inst_10 i) (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomCompTriple.ids.{u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (h i) (f i))) l)
 Case conversion may be inaccurate. Consider using '#align dfinsupp.sum_map_range_index.linear_map Dfinsupp.sum_mapRange_index.linearMapₓ'. -/
 theorem sum_mapRange_index.linearMap [∀ (i : ι) (x : β₁ i), Decidable (x ≠ 0)]
     [∀ (i : ι) (x : β₂ i), Decidable (x ≠ 0)] {f : ∀ i, β₁ i →ₗ[R] β₂ i} {h : ∀ i, β₂ i →ₗ[R] N}
@@ -414,7 +414,7 @@ noncomputable def coprodMap (f : ∀ i : ι, M i →ₗ[R] N) : (Π₀ i, M i) 
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : ι -> Type.{u3}} {N : Type.{u4}} [_inst_1 : Semiring.{u2} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (M i)] [_inst_3 : forall (i : ι), Module.{u2, u3} R (M i) _inst_1 (_inst_2 i)] [_inst_4 : AddCommMonoid.{u4} N] [_inst_5 : Module.{u2, u4} R N _inst_1 _inst_4] [_inst_6 : DecidableEq.{succ u1} ι] [_inst_7 : forall (x : N), Decidable (Ne.{succ u4} N x (OfNat.ofNat.{u4} N 0 (OfNat.mk.{u4} N 0 (Zero.zero.{u4} N (AddZeroClass.toHasZero.{u4} N (AddMonoid.toAddZeroClass.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_4)))))))] (f : forall (i : ι), LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (x : Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} ((fun (i : ι) => M i) i) (AddMonoid.toAddZeroClass.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i))))), Eq.{succ u4} N (coeFn.{max (succ (max u1 u3)) (succ u4), max (succ (max u1 u3)) (succ u4)} (LinearMap.{u2, u2, max u1 u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => M i) i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} ((fun (i : ι) => M i) i) (AddMonoid.toAddZeroClass.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) ((fun (i : ι) => _inst_2 i) i))))) N (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => M i) i) (fun (i : ι) => (fun (i : ι) => _inst_2 i) i)) _inst_4 (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => (fun (i : ι) => M i) i) _inst_1 (fun (i : ι) => (fun (i : ι) => _inst_2 i) i) (fun (i : ι) => (fun (i : ι) => _inst_3 i) i)) _inst_5) (fun (_x : LinearMap.{u2, u2, max u1 u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => M i) i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} ((fun (i : ι) => M i) i) (AddMonoid.toAddZeroClass.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) ((fun (i : ι) => _inst_2 i) i))))) N (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => M i) i) (fun (i : ι) => (fun (i : ι) => _inst_2 i) i)) _inst_4 (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => (fun (i : ι) => M i) i) _inst_1 (fun (i : ι) => (fun (i : ι) => _inst_2 i) i) (fun (i : ι) => (fun (i : ι) => _inst_3 i) i)) _inst_5) => (Dfinsupp.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => M i) i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} ((fun (i : ι) => M i) i) (AddMonoid.toAddZeroClass.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) ((fun (i : ι) => _inst_2 i) i))))) -> N) (LinearMap.hasCoeToFun.{u2, u2, max u1 u3, u4} R R (Dfinsupp.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => M i) i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} ((fun (i : ι) => M i) i) (AddMonoid.toAddZeroClass.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) ((fun (i : ι) => _inst_2 i) i))))) N _inst_1 _inst_1 (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => M i) i) (fun (i : ι) => (fun (i : ι) => _inst_2 i) i)) _inst_4 (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => (fun (i : ι) => M i) i) _inst_1 (fun (i : ι) => (fun (i : ι) => _inst_2 i) i) (fun (i : ι) => (fun (i : ι) => _inst_3 i) i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Dfinsupp.coprodMap.{u1, u2, u3, u4} ι R (fun (i : ι) => M i) N _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) _inst_4 _inst_5 (fun (a : ι) (b : ι) => _inst_6 a b) (fun (x : N) => _inst_7 x) f) x) (Finsupp.sum.{u1, u4, u4} ι N N (AddZeroClass.toHasZero.{u4} N (AddMonoid.toAddZeroClass.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_4))) _inst_4 (Dfinsupp.toFinsupp.{u1, u4} ι N (fun (a : ι) (b : ι) => _inst_6 a b) (AddZeroClass.toHasZero.{u4} N (AddMonoid.toAddZeroClass.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_4))) (fun (x : N) => _inst_7 x) (Dfinsupp.mapRange.{u1, u3, u4} ι (fun (i : ι) => M i) (fun (i : ι) => N) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i)))) (fun (i : ι) => AddZeroClass.toHasZero.{u4} N (AddMonoid.toAddZeroClass.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_4))) (fun (i : ι) => coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (fun (_x : LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) => (M i) -> N) (LinearMap.hasCoeToFun.{u2, u2, u3, u4} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (f i)) (fun (i : ι) => LinearMap.map_zero.{u2, u2, u3, u4} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (f i)) x)) (fun (i : ι) => id.{succ u4} N))
 but is expected to have type
-  forall {ι : Type.{u1}} {R : Type.{u4}} {M : ι -> Type.{u3}} {N : Type.{u2}} [_inst_1 : Semiring.{u4} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (M i)] [_inst_3 : forall (i : ι), Module.{u4, u3} R (M i) _inst_1 (_inst_2 i)] [_inst_4 : AddCommMonoid.{u2} N] [_inst_5 : Module.{u4, u2} R N _inst_1 _inst_4] [_inst_6 : DecidableEq.{succ u1} ι] [_inst_7 : forall (x : N), Decidable (Ne.{succ u2} N x (OfNat.ofNat.{u2} N 0 (Zero.toOfNat0.{u2} N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_4)))))] (f : forall (i : ι), LinearMap.{u4, u4, u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (x : Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) => N) x) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u3), succ u2} (LinearMap.{u4, u4, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u3, u4} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5) (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) (fun (_x : Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) => N) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u1 u3, u2} R R (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u3, u4} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Dfinsupp.coprodMap.{u1, u4, u3, u2} ι R (fun (i : ι) => M i) N _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) _inst_4 _inst_5 (fun (a : ι) (b : ι) => _inst_6 a b) (fun (x : N) => _inst_7 x) f) x) (Finsupp.sum.{u1, u2, u2} ι N N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_4)) _inst_4 (Dfinsupp.toFinsupp.{u1, u2} ι N (fun (a : ι) (b : ι) => _inst_6 a b) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_4)) (fun (x : N) => _inst_7 x) (Dfinsupp.mapRange.{u1, u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => N) (fun (i : ι) => AddMonoid.toZero.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))) (fun (i : ι) => AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_4)) (fun (i : ι) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (LinearMap.{u4, u4, u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (M i) (fun (_x : M i) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M i) => N) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, u2} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (f i)) (fun (i : ι) => LinearMap.map_zero.{u4, u4, u3, u2} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (f i)) x)) (fun (i : ι) => id.{succ u2} N))
+  forall {ι : Type.{u1}} {R : Type.{u4}} {M : ι -> Type.{u3}} {N : Type.{u2}} [_inst_1 : Semiring.{u4} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (M i)] [_inst_3 : forall (i : ι), Module.{u4, u3} R (M i) _inst_1 (_inst_2 i)] [_inst_4 : AddCommMonoid.{u2} N] [_inst_5 : Module.{u4, u2} R N _inst_1 _inst_4] [_inst_6 : DecidableEq.{succ u1} ι] [_inst_7 : forall (x : N), Decidable (Ne.{succ u2} N x (OfNat.ofNat.{u2} N 0 (Zero.toOfNat0.{u2} N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_4)))))] (f : forall (i : ι), LinearMap.{u4, u4, u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (x : Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) => N) x) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u3), succ u2} (LinearMap.{u4, u4, max u3 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u3, u4} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5) (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) (fun (_x : Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) => N) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u1 u3, u2} R R (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u3, u4} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (Dfinsupp.coprodMap.{u1, u4, u3, u2} ι R (fun (i : ι) => M i) N _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) _inst_4 _inst_5 (fun (a : ι) (b : ι) => _inst_6 a b) (fun (x : N) => _inst_7 x) f) x) (Finsupp.sum.{u1, u2, u2} ι N N (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_4)) _inst_4 (Dfinsupp.toFinsupp.{u1, u2} ι N (fun (a : ι) (b : ι) => _inst_6 a b) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_4)) (fun (x : N) => _inst_7 x) (Dfinsupp.mapRange.{u1, u3, u2} ι (fun (i : ι) => M i) (fun (i : ι) => N) (fun (i : ι) => AddMonoid.toZero.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))) (fun (i : ι) => AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_4)) (fun (i : ι) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (LinearMap.{u4, u4, u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (M i) (fun (_x : M i) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M i) => N) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, u2} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (f i)) (fun (i : ι) => LinearMap.map_zero.{u4, u4, u3, u2} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (f i)) x)) (fun (i : ι) => id.{succ u2} N))
 Case conversion may be inaccurate. Consider using '#align dfinsupp.coprod_map_apply Dfinsupp.coprodMap_applyₓ'. -/
 theorem coprodMap_apply (f : ∀ i : ι, M i →ₗ[R] N) (x : Π₀ i, M i) :
     coprodMap f x =
@@ -470,7 +470,7 @@ theorem dfinsupp_sum_mem {β : ι → Type _} [∀ i, Zero (β i)] [∀ (i) (x :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} N] [_inst_3 : Module.{u2, u3} R N _inst_1 _inst_2] {β : ι -> Type.{u4}} [_inst_4 : forall (i : ι), AddZeroClass.{u4} (β i)] (S : Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (f : Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) (g : forall (i : ι), AddMonoidHom.{u4, u3} (β i) N (_inst_4 i) (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_2))), (forall (c : ι), (Ne.{succ u4} (β c) (coeFn.{succ (max u1 u4), max (succ u1) (succ u4)} (Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) (fun (_x : Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) => forall (i : ι), β i) (Dfinsupp.hasCoeToFun.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) f c) (OfNat.ofNat.{u4} (β c) 0 (OfNat.mk.{u4} (β c) 0 (Zero.zero.{u4} (β c) (AddZeroClass.toHasZero.{u4} (β c) (_inst_4 c)))))) -> (Membership.Mem.{u3, u3} N (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (coeFn.{max (succ u3) (succ u4), max (succ u4) (succ u3)} (AddMonoidHom.{u4, u3} (β c) N (_inst_4 c) (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_2))) (fun (_x : AddMonoidHom.{u4, u3} (β c) N (_inst_4 c) (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_2))) => (β c) -> N) (AddMonoidHom.hasCoeToFun.{u4, u3} (β c) N (_inst_4 c) (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_2))) (g c) (coeFn.{succ (max u1 u4), max (succ u1) (succ u4)} (Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) (fun (_x : Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) => forall (i : ι), β i) (Dfinsupp.hasCoeToFun.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) f c)) S)) -> (Membership.Mem.{u3, u3} N (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (coeFn.{max (succ u3) (succ (max u1 u4)), max (succ (max u1 u4)) (succ u3)} (AddMonoidHom.{max u1 u4, u3} (Dfinsupp.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} ((fun (i : ι) => β i) i) ((fun (i : ι) => _inst_4 i) i))) N (Dfinsupp.addZeroClass.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => (fun (i : ι) => _inst_4 i) i)) (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_2))) (fun (_x : AddMonoidHom.{max u1 u4, u3} (Dfinsupp.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} ((fun (i : ι) => β i) i) ((fun (i : ι) => _inst_4 i) i))) N (Dfinsupp.addZeroClass.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => (fun (i : ι) => _inst_4 i) i)) (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_2))) => (Dfinsupp.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} ((fun (i : ι) => β i) i) ((fun (i : ι) => _inst_4 i) i))) -> N) (AddMonoidHom.hasCoeToFun.{max u1 u4, u3} (Dfinsupp.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} ((fun (i : ι) => β i) i) ((fun (i : ι) => _inst_4 i) i))) N (Dfinsupp.addZeroClass.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => (fun (i : ι) => _inst_4 i) i)) (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N _inst_2))) (Dfinsupp.sumAddHom.{u1, u4, u3} ι N (fun (i : ι) => β i) (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => _inst_4 i) _inst_2 g) f) S)
 but is expected to have type
-  forall {ι : Type.{u1}} {R : Type.{u3}} {N : Type.{u2}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} N] [_inst_3 : Module.{u3, u2} R N _inst_1 _inst_2] {β : ι -> Type.{u4}} [_inst_4 : forall (i : ι), AddZeroClass.{u4} (β i)] (S : Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (f : Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) (g : forall (i : ι), AddMonoidHom.{u4, u2} (β i) N (_inst_4 i) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))), (forall (c : ι), (Ne.{succ u4} ((fun (i : ι) => (fun (i : ι) => β i) i) c) (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (Dfinsupp.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i)) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => β i) i) _x) (Dfinsupp.funLike.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i)) i)) f c) (OfNat.ofNat.{u4} ((fun (i : ι) => (fun (i : ι) => β i) i) c) 0 (Zero.toOfNat0.{u4} ((fun (i : ι) => (fun (i : ι) => β i) i) c) (AddZeroClass.toZero.{u4} ((fun (i : ι) => (fun (i : ι) => β i) i) c) (_inst_4 c))))) -> (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : β c) => N) (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (Dfinsupp.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i)) i)) ι (fun (a : ι) => (fun (i : ι) => (fun (i : ι) => β i) i) a) (Dfinsupp.funLike.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i)) i)) f c)) (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) (FunLike.coe.{max (succ u2) (succ u4), succ u4, succ u2} (AddMonoidHom.{u4, u2} (β c) N (_inst_4 c) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) (β c) (fun (_x : β c) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : β c) => N) _x) (AddHomClass.toFunLike.{max u2 u4, u4, u2} (AddMonoidHom.{u4, u2} (β c) N (_inst_4 c) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) (β c) N (AddZeroClass.toAdd.{u4} (β c) (_inst_4 c)) (AddZeroClass.toAdd.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) (AddMonoidHomClass.toAddHomClass.{max u2 u4, u4, u2} (AddMonoidHom.{u4, u2} (β c) N (_inst_4 c) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) (β c) N (_inst_4 c) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2)) (AddMonoidHom.addMonoidHomClass.{u4, u2} (β c) N (_inst_4 c) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))))) (g c) (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (Dfinsupp.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i)) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => β i) i) _x) (Dfinsupp.funLike.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i)) i)) f c)) S)) -> (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) => N) f) (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u4), max (succ u1) (succ u4), succ u2} (AddMonoidHom.{max u4 u1, u2} (Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) N (Dfinsupp.addZeroClass.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => _inst_4 i)) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) (fun (_x : Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) => N) _x) (AddHomClass.toFunLike.{max (max u1 u2) u4, max u1 u4, u2} (AddMonoidHom.{max u4 u1, u2} (Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) N (Dfinsupp.addZeroClass.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => _inst_4 i)) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) N (AddZeroClass.toAdd.{max u1 u4} (Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) (Dfinsupp.addZeroClass.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => _inst_4 i))) (AddZeroClass.toAdd.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) (AddMonoidHomClass.toAddHomClass.{max (max u1 u2) u4, max u1 u4, u2} (AddMonoidHom.{max u4 u1, u2} (Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) N (Dfinsupp.addZeroClass.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => _inst_4 i)) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) N (Dfinsupp.addZeroClass.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => _inst_4 i)) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2)) (AddMonoidHom.addMonoidHomClass.{max u1 u4, u2} (Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) N (Dfinsupp.addZeroClass.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => _inst_4 i)) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))))) (Dfinsupp.sumAddHom.{u1, u4, u2} ι N (fun (i : ι) => β i) (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => _inst_4 i) _inst_2 g) f) S)
+  forall {ι : Type.{u1}} {R : Type.{u3}} {N : Type.{u2}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} N] [_inst_3 : Module.{u3, u2} R N _inst_1 _inst_2] {β : ι -> Type.{u4}} [_inst_4 : forall (i : ι), AddZeroClass.{u4} (β i)] (S : Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (f : Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) (g : forall (i : ι), AddMonoidHom.{u4, u2} (β i) N (_inst_4 i) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))), (forall (c : ι), (Ne.{succ u4} ((fun (i : ι) => (fun (i : ι) => β i) i) c) (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (Dfinsupp.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i)) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => β i) i) _x) (Dfinsupp.funLike.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i)) i)) f c) (OfNat.ofNat.{u4} ((fun (i : ι) => (fun (i : ι) => β i) i) c) 0 (Zero.toOfNat0.{u4} ((fun (i : ι) => (fun (i : ι) => β i) i) c) (AddZeroClass.toZero.{u4} ((fun (i : ι) => (fun (i : ι) => β i) i) c) (_inst_4 c))))) -> (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : β c) => N) (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (Dfinsupp.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i)) i)) ι (fun (a : ι) => (fun (i : ι) => (fun (i : ι) => β i) i) a) (Dfinsupp.funLike.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i)) i)) f c)) (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) (FunLike.coe.{max (succ u2) (succ u4), succ u4, succ u2} (AddMonoidHom.{u4, u2} (β c) N (_inst_4 c) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) (β c) (fun (_x : β c) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : β c) => N) _x) (AddHomClass.toFunLike.{max u2 u4, u4, u2} (AddMonoidHom.{u4, u2} (β c) N (_inst_4 c) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) (β c) N (AddZeroClass.toAdd.{u4} (β c) (_inst_4 c)) (AddZeroClass.toAdd.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) (AddMonoidHomClass.toAddHomClass.{max u2 u4, u4, u2} (AddMonoidHom.{u4, u2} (β c) N (_inst_4 c) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) (β c) N (_inst_4 c) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2)) (AddMonoidHom.addMonoidHomClass.{u4, u2} (β c) N (_inst_4 c) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))))) (g c) (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (Dfinsupp.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i)) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => β i) i) _x) (Dfinsupp.funLike.{u1, u4} ι (fun (i : ι) => (fun (i : ι) => β i) i) (fun (i : ι) => (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i)) i)) f c)) S)) -> (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) => N) f) (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u4), max (succ u1) (succ u4), succ u2} (AddMonoidHom.{max u4 u1, u2} (Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) N (Dfinsupp.addZeroClass.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => _inst_4 i)) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) (fun (_x : Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) => N) _x) (AddHomClass.toFunLike.{max (max u1 u2) u4, max u1 u4, u2} (AddMonoidHom.{max u4 u1, u2} (Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) N (Dfinsupp.addZeroClass.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => _inst_4 i)) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) N (AddZeroClass.toAdd.{max u1 u4} (Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) (Dfinsupp.addZeroClass.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => _inst_4 i))) (AddZeroClass.toAdd.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) (AddMonoidHomClass.toAddHomClass.{max (max u1 u2) u4, max u1 u4, u2} (AddMonoidHom.{max u4 u1, u2} (Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) N (Dfinsupp.addZeroClass.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => _inst_4 i)) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) N (Dfinsupp.addZeroClass.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => _inst_4 i)) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2)) (AddMonoidHom.addMonoidHomClass.{max u1 u4, u2} (Dfinsupp.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toZero.{u4} ((fun (i : ι) => β i) i) (_inst_4 i))) N (Dfinsupp.addZeroClass.{u1, u4} ι (fun (i : ι) => β i) (fun (i : ι) => _inst_4 i)) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))))) (Dfinsupp.sumAddHom.{u1, u4, u2} ι N (fun (i : ι) => β i) (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => _inst_4 i) _inst_2 g) f) S)
 Case conversion may be inaccurate. Consider using '#align submodule.dfinsupp_sum_add_hom_mem Submodule.dfinsupp_sumAddHom_memₓ'. -/
 theorem dfinsupp_sumAddHom_mem {β : ι → Type _} [∀ i, AddZeroClass (β i)] (S : Submodule R N)
     (f : Π₀ i, β i) (g : ∀ i, β i →+ N) (h : ∀ c, f c ≠ 0 → g c (f c) ∈ S) :
@@ -528,7 +528,7 @@ theorem bsupᵢ_eq_range_dfinsupp_lsum (p : ι → Prop) [DecidablePred p] (S :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} N] [_inst_3 : Module.{u2, u3} R N _inst_1 _inst_2] (p : ι -> (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (x : N), Iff (Membership.Mem.{u3, u3} N (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) x (supᵢ.{u3, succ u1} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u3} R N _inst_1 _inst_2 _inst_3))) ι p)) (Exists.{succ (max u1 u3)} (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} 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(Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (i : ι) => Submodule.addCommMonoid.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_2 (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3) (fun (_x : LinearMap.{u2, u2, max u1 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (AddMonoid.toAddZeroClass.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (AddCommMonoid.toAddMonoid.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N 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_inst_3 (p i))) _inst_3) => (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (AddMonoid.toAddZeroClass.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (AddCommMonoid.toAddMonoid.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} 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 but is expected to have type
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Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 _inst_3 Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3))) (fun (i : ι) => Submodule.subtype.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) f) x))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_iff_exists_dfinsupp Submodule.mem_supᵢ_iff_exists_dfinsuppₓ'. -/
 theorem mem_supᵢ_iff_exists_dfinsupp (p : ι → Submodule R N) (x : N) :
     x ∈ supᵢ p ↔ ∃ f : Π₀ i, p i, Dfinsupp.lsum ℕ (fun i => (p i).Subtype) f = x :=
@@ -554,7 +554,7 @@ theorem mem_supᵢ_iff_exists_dfinsupp' (p : ι → Submodule R N) [∀ (i) (x :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} N] [_inst_3 : Module.{u2, u3} R N _inst_1 _inst_2] (p : ι -> Prop) [_inst_4 : DecidablePred.{succ u1} ι p] (S : ι -> (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (x : N), Iff (Membership.Mem.{u3, u3} N (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) x (supᵢ.{u3, succ u1} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u3} R N _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => supᵢ.{u3, 0} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u3} R N _inst_1 _inst_2 _inst_3))) (p i) (fun (h : p i) => S i)))) (Exists.{succ (max u1 u3)} (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (S i)) (fun (i : ι) => Submodule.hasZero.{u2, u3} R N _inst_1 _inst_2 _inst_3 (S i))) (fun (f : Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (S i)) (fun (i : ι) => Submodule.hasZero.{u2, u3} R N _inst_1 _inst_2 _inst_3 (S i))) => Eq.{succ u3} N (coeFn.{max (succ (max u1 u3)) (succ u3), max (succ (max u1 u3)) (succ u3)} (LinearMap.{u2, u2, max u1 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (S i)) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (S i)) (AddMonoid.toAddZeroClass.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N 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_inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (S i)) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u2, u3} R N _inst_1 _inst_2 _inst_3 (S i)) (fun (i : ι) => Submodule.module.{u2, u3} R N _inst_1 _inst_2 _inst_3 (S i))) _inst_3) (fun (_x : LinearMap.{u2, u2, max u1 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (S i)) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (S i)) (AddMonoid.toAddZeroClass.{u3} 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u2} ι R (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (S i)) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u2, u3} R N _inst_1 _inst_2 _inst_3 (S i)) (fun (i : ι) => Submodule.module.{u2, u3} R N _inst_1 _inst_2 _inst_3 (S i))) _inst_3) => (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (S i)) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) 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 but is expected to have type
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(Submodule.instSetLikeSubmodule.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (AddCommMonoid.toAddMonoid.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u1} ι (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) (fun (i : ι) => Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))) _inst_2 (Dfinsupp.module.{u3, u1, u2} ι R (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) _inst_1 (fun (i : ι) => Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) (fun (i : ι) => Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} N _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R N (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_2) (Module.toDistribMulAction.{u2, u1} R N _inst_1 _inst_2 _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u3, u2, 0, u1, u1} ι R Nat (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) N (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) (fun (i : ι) => Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)) _inst_2 _inst_3 Nat.semiring (AddCommMonoid.natModule.{u1} N _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R N (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} N _inst_2) (Module.toDistribMulAction.{u2, u1} R N _inst_1 _inst_2 _inst_3))) (fun (i : ι) => Submodule.subtype.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i))) (Dfinsupp.filter.{u3, u1} ι (fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) (fun (i : ι) => AddMonoid.toZero.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (AddCommMonoid.toAddMonoid.{u1} ((fun (i : ι) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u2, u1} R N _inst_1 _inst_2 _inst_3)) x (S i))) i) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R N _inst_1 _inst_2 _inst_3 (S i)))) p (fun (a : ι) => _inst_4 a) f)) x))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_bsupr_iff_exists_dfinsupp Submodule.mem_bsupr_iff_exists_dfinsuppₓ'. -/
 theorem mem_bsupr_iff_exists_dfinsupp (p : ι → Prop) [DecidablePred p] (S : ι → Submodule R N)
     (x : N) :
@@ -571,7 +571,7 @@ omit dec_ι
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} N] [_inst_3 : Module.{u2, u3} R N _inst_1 _inst_2] {s : Finset.{u1} ι} (p : ι -> (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (a : N), Iff (Membership.Mem.{u3, u3} N (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) a (supᵢ.{u3, succ u1} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u3} R N _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => supᵢ.{u3, 0} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u3} R N _inst_1 _inst_2 _inst_3))) (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i s) (fun (H : Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i s) => p i)))) (Exists.{max (succ u1) (succ u3)} (forall (i : ι), coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (μ : forall (i : ι), coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) => Eq.{succ u3} N (Finset.sum.{u3, u1} N ι _inst_2 s (fun (i : ι) => (fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) N (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) N (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) N (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) N (coeSubtype.{succ u3} N (fun (x : N) => Membership.Mem.{u3, u3} N (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) x (p i)))))) (μ i))) a))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {N : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} N] [s : Module.{u2, u1} R N _inst_2 _inst_3] {p : Finset.{u3} ι} (a : ι -> (Submodule.{u2, u1} R N _inst_2 _inst_3 s)) (a_1 : N), Iff (Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.instSetLikeSubmodule.{u2, u1} R N _inst_2 _inst_3 s)) a_1 (supᵢ.{u1, succ u3} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (Submodule.completeLattice.{u2, u1} R N _inst_2 _inst_3 s))) ι (fun (i : ι) => supᵢ.{u1, 0} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (Submodule.completeLattice.{u2, u1} R N _inst_2 _inst_3 s))) (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i p) (fun (h._@.Mathlib.LinearAlgebra.Dfinsupp._hyg.5092 : Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i p) => a i)))) (Exists.{max (succ u3) (succ u1)} (forall (i : ι), Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.instSetLikeSubmodule.{u2, u1} R N _inst_2 _inst_3 s)) x (a i))) (fun (μ : forall (i : ι), Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.instSetLikeSubmodule.{u2, u1} R N _inst_2 _inst_3 s)) x (a i))) => Eq.{succ u1} N (Finset.sum.{u1, u3} N ι _inst_3 p (fun (i : ι) => Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.instSetLikeSubmodule.{u2, u1} R N _inst_2 _inst_3 s) (a i))) (μ i))) a_1))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {N : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} N] [s : Module.{u2, u1} R N _inst_2 _inst_3] {p : Finset.{u3} ι} (a : ι -> (Submodule.{u2, u1} R N _inst_2 _inst_3 s)) (a_1 : N), Iff (Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.instSetLikeSubmodule.{u2, u1} R N _inst_2 _inst_3 s)) a_1 (supᵢ.{u1, succ u3} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (Submodule.completeLattice.{u2, u1} R N _inst_2 _inst_3 s))) ι (fun (i : ι) => supᵢ.{u1, 0} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (Submodule.completeLattice.{u2, u1} R N _inst_2 _inst_3 s))) (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i p) (fun (h._@.Mathlib.LinearAlgebra.Dfinsupp._hyg.5132 : Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i p) => a i)))) (Exists.{max (succ u3) (succ u1)} (forall (i : ι), Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.instSetLikeSubmodule.{u2, u1} R N _inst_2 _inst_3 s)) x (a i))) (fun (μ : forall (i : ι), Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submodule.{u2, u1} R N _inst_2 _inst_3 s) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.instSetLikeSubmodule.{u2, u1} R N _inst_2 _inst_3 s)) x (a i))) => Eq.{succ u1} N (Finset.sum.{u1, u3} N ι _inst_3 p (fun (i : ι) => Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R N _inst_2 _inst_3 s) N (Submodule.instSetLikeSubmodule.{u2, u1} R N _inst_2 _inst_3 s) (a i))) (μ i))) a_1))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_finset_iff_exists_sum Submodule.mem_supᵢ_finset_iff_exists_sumₓ'. -/
 theorem mem_supᵢ_finset_iff_exists_sum {s : Finset ι} (p : ι → Submodule R N) (a : N) :
     (a ∈ ⨆ i ∈ s, p i) ↔ ∃ μ : ∀ i, p i, (∑ i in s, (μ i : N)) = a := by
@@ -624,7 +624,7 @@ variable [Semiring R] [AddCommMonoid N] [Module R N]
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} N] [_inst_3 : Module.{u2, u3} R N _inst_1 _inst_2] (p : ι -> (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3)), Iff (CompleteLattice.Independent.{succ u1, u3} ι (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u3} R N _inst_1 _inst_2 _inst_3) p) (forall (i : ι) (x : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (v : Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (i : ι) => 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 but is expected to have type
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(x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)))) i v)) (Subtype.val.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Set.{u2} N) (Set.instMembershipSet.{u2} N) x (SetLike.coe.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (p i))) x)) -> (Eq.{succ u2} (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) x (OfNat.ofNat.{u2} (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) 0 (Zero.toOfNat0.{u2} (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (Submodule.instZeroSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))))
 Case conversion may be inaccurate. Consider using '#align complete_lattice.independent_iff_forall_dfinsupp CompleteLattice.independent_iff_forall_dfinsuppₓ'. -/
 /-- Independence of a family of submodules can be expressed as a quantifier over `dfinsupp`s.
 
@@ -648,7 +648,7 @@ theorem independent_iff_forall_dfinsupp (p : ι → Submodule R N) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} N] [_inst_3 : Module.{u2, u3} R N _inst_1 _inst_2] (p : ι -> (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3)), (Function.Injective.{succ (max u1 u3), succ u3} (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (AddMonoid.toAddZeroClass.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (AddCommMonoid.toAddMonoid.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (Submodule.addCommMonoid.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i)))))) N (coeFn.{max (succ (max u1 u3)) (succ u3), max (succ (max u1 u3)) (succ u3)} (LinearMap.{u2, u2, max u1 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (i : ι) => 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_inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (i : ι) => Submodule.addCommMonoid.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_2 (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3) (fun (_x : LinearMap.{u2, u2, max u1 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) 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(Submodule.addCommMonoid.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i)))))) N (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (i : ι) => Submodule.addCommMonoid.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_2 (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) _inst_1 (fun (i : ι) => Submodule.addCommMonoid.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.module.{u2, u3} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3) => (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ 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u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) _inst_1 (fun (i : ι) => Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} 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(Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, max u1 u2, u2} R R (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_2 (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) _inst_1 (fun (i : ι) => Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N _inst_1 _inst_1 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u2, u2} R R Nat (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N _inst_1 _inst_1 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u2, u2} R R Nat (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_2 (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) _inst_1 (fun (i : ι) => Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u1, u3, 0, u2, u2} ι R Nat (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 _inst_3 Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3))) (fun (i : ι) => Submodule.subtype.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))) -> (CompleteLattice.Independent.{succ u1, u2} ι (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u3, u2} R N _inst_1 _inst_2 _inst_3) p)
 Case conversion may be inaccurate. Consider using '#align complete_lattice.independent_of_dfinsupp_lsum_injective CompleteLattice.independent_of_dfinsupp_lsum_injectiveₓ'. -/
 /- If `dfinsupp.lsum` applied with `submodule.subtype` is injective then the submodules are
 independent. -/
@@ -668,7 +668,7 @@ theorem independent_of_dfinsupp_lsum_injective (p : ι → Submodule R N)
 lean 3 declaration is
   forall {ι : Type.{u1}} {N : Type.{u2}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_2 : AddCommMonoid.{u2} N] (p : ι -> (AddSubmonoid.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2)))), (Function.Injective.{succ (max u1 u2), succ u2} (Dfinsupp.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => coeSort.{succ u2, succ (succ u2)} (AddSubmonoid.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (AddSubmonoid.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) N (AddSubmonoid.setLike.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2)))) (p i)) i) (fun (i : ι) => AddZeroClass.toHasZero.{u2} ((fun (i : ι) => coeSort.{succ u2, succ (succ u2)} (AddSubmonoid.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (AddSubmonoid.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) N (AddSubmonoid.setLike.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2)))) (p i)) i) ((fun (i : ι) => AddSubmonoid.toAddZeroClass.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2)) (p i)) i))) N (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ (max u1 u2)) (succ u2)} (AddMonoidHom.{max u1 u2, u2} (Dfinsupp.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => coeSort.{succ u2, succ (succ u2)} (AddSubmonoid.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (AddSubmonoid.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) N (AddSubmonoid.setLike.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2)))) (p i)) i) (fun (i : ι) => AddZeroClass.toHasZero.{u2} ((fun (i : ι) => coeSort.{succ u2, succ (succ u2)} (AddSubmonoid.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (AddSubmonoid.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) N (AddSubmonoid.setLike.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2)))) (p i)) i) ((fun (i : ι) => AddSubmonoid.toAddZeroClass.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2)) (p i)) i))) N (Dfinsupp.addZeroClass.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => coeSort.{succ u2, succ (succ u2)} (AddSubmonoid.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (AddSubmonoid.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) N (AddSubmonoid.setLike.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2)))) (p i)) i) (fun (i : ι) => (fun (i : ι) => 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_inst_2))) (SetLike.instMembership.{u2, u2} (AddSubmonoid.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) N (AddSubmonoid.instSetLikeAddSubmonoid.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2)))) x (p i))) (fun (i : ι) => AddSubmonoid.toAddZeroClass.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2)) (p i))) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (AddSubmonoid.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) (SetLike.instMembership.{u2, u2} (AddSubmonoid.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) N (AddSubmonoid.instSetLikeAddSubmonoid.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2)))) x (p i))) (fun (i : ι) => AddZeroClass.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (AddSubmonoid.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) (SetLike.instMembership.{u2, u2} (AddSubmonoid.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) N (AddSubmonoid.instSetLikeAddSubmonoid.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2)))) x (p i))) i) (AddSubmonoid.toAddZeroClass.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2)) (p i)))) N (AddZeroClass.toAdd.{max u1 u2} (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (AddSubmonoid.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) (SetLike.instMembership.{u2, u2} (AddSubmonoid.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) N (AddSubmonoid.instSetLikeAddSubmonoid.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2)))) x (p i))) (fun (i : ι) => AddZeroClass.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (AddSubmonoid.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) (SetLike.instMembership.{u2, u2} (AddSubmonoid.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) N (AddSubmonoid.instSetLikeAddSubmonoid.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2)))) x (p i))) i) (AddSubmonoid.toAddZeroClass.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2)) (p i)))) (Dfinsupp.addZeroClass.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (AddSubmonoid.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) (SetLike.instMembership.{u2, u2} (AddSubmonoid.{u2} N (AddMonoid.toAddZeroClass.{u2} N 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: ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (AddSubmonoid.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) (SetLike.instMembership.{u2, u2} (AddSubmonoid.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) N (AddSubmonoid.instSetLikeAddSubmonoid.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2)))) x (p i))) (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => AddSubmonoid.toAddZeroClass.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2)) (p i)) _inst_2 (fun (i : ι) => AddSubmonoid.subtype.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2)) (p i))))) -> (CompleteLattice.Independent.{succ u1, u2} ι (AddSubmonoid.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_2))) p)
 Case conversion may be inaccurate. Consider using '#align complete_lattice.independent_of_dfinsupp_sum_add_hom_injective CompleteLattice.independent_of_dfinsupp_sumAddHom_injectiveₓ'. -/
 /- If `dfinsupp.sum_add_hom` applied with `add_submonoid.subtype` is injective then the additive
 submonoids are independent. -/
@@ -708,7 +708,7 @@ variable [Ring R] [AddCommGroup N] [Module R N]
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align complete_lattice.independent_of_dfinsupp_sum_add_hom_injective' CompleteLattice.independent_of_dfinsupp_sumAddHom_injective'ₓ'. -/
 /- If `dfinsupp.sum_add_hom` applied with `add_submonoid.subtype` is injective then the additive
 subgroups are independent. -/
@@ -723,7 +723,7 @@ theorem independent_of_dfinsupp_sumAddHom_injective' (p : ι → AddSubgroup N)
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} N] [_inst_3 : Module.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2)] {p : ι -> (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3)}, (CompleteLattice.Independent.{succ u1, u3} ι (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) (Submodule.completeLattice.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) p) -> (Function.Injective.{succ (max u1 u3), succ u3} (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) N (Submodule.setLike.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3)) (p i)) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) N (Submodule.setLike.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3)) (p i)) (AddMonoid.toAddZeroClass.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) N 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 but is expected to have type
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Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u1, u3, 0, u2, u2} ι R Nat (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (fun (a : ι) (b : ι) => dec_ι a b) (Ring.toSemiring.{u3} R _inst_1) (fun (i : ι) => Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (fun (i : ι) => 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_inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) 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(Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (Ring.toSemiring.{u3} R _inst_1) (fun (i : ι) => Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (fun (i : ι) => 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(AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u2, u2} R R Nat (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u2} N (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u2, u2} R R Nat (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (Ring.toSemiring.{u3} R _inst_1) (fun (i : ι) => Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (fun (i : ι) => Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u2} N (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u1, u3, 0, u2, u2} ι R Nat (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (fun (a : ι) (b : ι) => dec_ι a b) (Ring.toSemiring.{u3} R _inst_1) (fun (i : ι) => Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (fun (i : ι) => Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 Nat.semiring (AddCommMonoid.natModule.{u2} N (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3))) (fun (i : ι) => Submodule.subtype.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)))))
 Case conversion may be inaccurate. Consider using '#align complete_lattice.independent.dfinsupp_lsum_injective CompleteLattice.Independent.dfinsupp_lsum_injectiveₓ'. -/
 /-- The canonical map out of a direct sum of a family of submodules is injective when the submodules
 are `complete_lattice.independent`.
@@ -757,7 +757,7 @@ theorem Independent.dfinsupp_lsum_injective {p : ι → Submodule R N} (h : Inde
 lean 3 declaration is
   forall {ι : Type.{u1}} {N : Type.{u2}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_2 : AddCommGroup.{u2} N] {p : ι -> (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))}, (CompleteLattice.Independent.{succ u1, u2} ι (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) (AddSubgroup.completeLattice.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) p) -> (Function.Injective.{succ (max u1 u2), succ u2} (Dfinsupp.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => coeSort.{succ u2, succ (succ u2)} (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) N (AddSubgroup.setLike.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (p i)) i) (fun (i : ι) => AddZeroClass.toHasZero.{u2} ((fun (i : ι) => coeSort.{succ u2, succ (succ u2)} (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (AddSubgroup.{u2} N 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 but is expected to have type
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(AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) (SetLike.instMembership.{u2, u2} (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) N (AddSubgroup.instSetLikeAddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) x (p i))) (fun (i : ι) => AddSubmonoid.toAddZeroClass.{u2} N (AddMonoid.toAddZeroClass.{u2} N (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)))) (AddSubgroup.toAddSubmonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2) (p i)))) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)))))) (Dfinsupp.sumAddHom.{u1, u2, u2} ι N (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) (SetLike.instMembership.{u2, u2} (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) N (AddSubgroup.instSetLikeAddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) x (p i))) (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => AddSubmonoid.toAddZeroClass.{u2} N (AddMonoid.toAddZeroClass.{u2} N (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)))) (AddSubgroup.toAddSubmonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2) (p i))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (fun (i : ι) => AddSubgroup.subtype.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2) (p i)))))
 Case conversion may be inaccurate. Consider using '#align complete_lattice.independent.dfinsupp_sum_add_hom_injective CompleteLattice.Independent.dfinsupp_sumAddHom_injectiveₓ'. -/
 /-- The canonical map out of a direct sum of a family of additive subgroups is injective when the
 additive subgroups are `complete_lattice.independent`. -/
@@ -772,7 +772,7 @@ theorem Independent.dfinsupp_sumAddHom_injective {p : ι → AddSubgroup N} (h :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} N] [_inst_3 : Module.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2)] (p : ι -> (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3)), Iff (CompleteLattice.Independent.{succ u1, u3} ι (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) (Submodule.completeLattice.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) p) (Function.Injective.{succ (max u1 u3), succ u3} (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R 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(AddGroup.toSubNegMonoid.{u3} N (AddCommGroup.toAddGroup.{u3} N _inst_2))) (Module.toDistribMulAction.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3))) (fun (i : ι) => Submodule.subtype.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3 (p i)))))
 but is expected to have type
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Nat.semiring (AddCommMonoid.natModule.{u2} N (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u2, u2} R R Nat (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) 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Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (Ring.toSemiring.{u3} R _inst_1) (fun (i : ι) => Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (fun (i : ι) => Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u2} N (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u1, u3, 0, u2, u2} ι R Nat (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (fun (a : ι) (b : ι) => dec_ι a b) (Ring.toSemiring.{u3} R _inst_1) (fun (i : ι) => Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (fun (i : ι) => Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 Nat.semiring (AddCommMonoid.natModule.{u2} N (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3))) (fun (i : ι) => Submodule.subtype.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)))))
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Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (Ring.toSemiring.{u3} R _inst_1) (fun (i : ι) => Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (fun (i : ι) => Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u2} N (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u1, u3, 0, u2, u2} ι R Nat (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (fun (a : ι) (b : ι) => dec_ι a b) (Ring.toSemiring.{u3} R _inst_1) (fun (i : ι) => Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (fun (i : ι) => Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 Nat.semiring (AddCommMonoid.natModule.{u2} N (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (Module.toDistribMulAction.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3))) (fun (i : ι) => Submodule.subtype.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)))))
 Case conversion may be inaccurate. Consider using '#align complete_lattice.independent_iff_dfinsupp_lsum_injective CompleteLattice.independent_iff_dfinsupp_lsum_injectiveₓ'. -/
 /-- A family of submodules over an additive group are independent if and only iff `dfinsupp.lsum`
 applied with `submodule.subtype` is injective.
@@ -788,7 +788,7 @@ theorem independent_iff_dfinsupp_lsum_injective (p : ι → Submodule R N) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {N : Type.{u2}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_2 : AddCommGroup.{u2} N] (p : ι -> (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))), Iff (CompleteLattice.Independent.{succ u1, u2} ι (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) (AddSubgroup.completeLattice.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) p) (Function.Injective.{succ (max u1 u2), succ u2} (Dfinsupp.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => coeSort.{succ u2, succ (succ u2)} (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) N (AddSubgroup.setLike.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) (p i)) i) (fun (i : ι) => AddZeroClass.toHasZero.{u2} ((fun (i : ι) => coeSort.{succ u2, succ (succ u2)} (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (AddSubgroup.{u2} N 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 but is expected to have type
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(AddCommGroup.toAddGroup.{u2} N _inst_2))) x (p i))) i) (AddSubmonoid.toAddZeroClass.{u2} N (AddMonoid.toAddZeroClass.{u2} N (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)))) (AddSubgroup.toAddSubmonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2) (p i))))) N (AddZeroClass.toAdd.{max u1 u2} (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) (SetLike.instMembership.{u2, u2} (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) N (AddSubgroup.instSetLikeAddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) x (p i))) (fun (i : ι) => AddZeroClass.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) (SetLike.instMembership.{u2, u2} (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) N (AddSubgroup.instSetLikeAddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) x (p i))) i) (AddSubmonoid.toAddZeroClass.{u2} N (AddMonoid.toAddZeroClass.{u2} N (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)))) (AddSubgroup.toAddSubmonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2) (p i))))) (Dfinsupp.addZeroClass.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) (SetLike.instMembership.{u2, u2} (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) N (AddSubgroup.instSetLikeAddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) x (p i))) (fun (i : ι) => AddSubmonoid.toAddZeroClass.{u2} N (AddMonoid.toAddZeroClass.{u2} N (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)))) (AddSubgroup.toAddSubmonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2) (p i))))) (AddZeroClass.toAdd.{u2} N (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)))) (AddMonoidHomClass.toAddHomClass.{max u1 u2, max u1 u2, u2} (AddMonoidHom.{max u2 u1, u2} (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) (SetLike.instMembership.{u2, u2} (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) N (AddSubgroup.instSetLikeAddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) x (p i))) (fun (i : ι) => AddZeroClass.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) (SetLike.instMembership.{u2, u2} (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) N (AddSubgroup.instSetLikeAddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) x (p i))) i) (AddSubmonoid.toAddZeroClass.{u2} N (AddMonoid.toAddZeroClass.{u2} N (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)))) (AddSubgroup.toAddSubmonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2) (p i))))) N (Dfinsupp.addZeroClass.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) (SetLike.instMembership.{u2, u2} (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) N (AddSubgroup.instSetLikeAddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) x (p i))) (fun (i : ι) => AddSubmonoid.toAddZeroClass.{u2} N (AddMonoid.toAddZeroClass.{u2} N (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)))) (AddSubgroup.toAddSubmonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2) (p i)))) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)))) (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) (SetLike.instMembership.{u2, u2} (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) N (AddSubgroup.instSetLikeAddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) x (p i))) (fun (i : ι) => AddZeroClass.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) (SetLike.instMembership.{u2, u2} (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) N (AddSubgroup.instSetLikeAddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) x (p i))) i) (AddSubmonoid.toAddZeroClass.{u2} N (AddMonoid.toAddZeroClass.{u2} N (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)))) (AddSubgroup.toAddSubmonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2) (p i))))) N (Dfinsupp.addZeroClass.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) (SetLike.instMembership.{u2, u2} (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) N (AddSubgroup.instSetLikeAddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) x (p i))) (fun (i : ι) => AddSubmonoid.toAddZeroClass.{u2} N (AddMonoid.toAddZeroClass.{u2} N (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)))) (AddSubgroup.toAddSubmonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2) (p i)))) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N (AddCommGroup.toAddCommMonoid.{u2} N _inst_2))) (AddMonoidHom.addMonoidHomClass.{max u1 u2, u2} (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) (SetLike.instMembership.{u2, u2} (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) N (AddSubgroup.instSetLikeAddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) x (p i))) (fun (i : ι) => AddZeroClass.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) (SetLike.instMembership.{u2, u2} (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) N (AddSubgroup.instSetLikeAddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) x (p i))) i) (AddSubmonoid.toAddZeroClass.{u2} N (AddMonoid.toAddZeroClass.{u2} N (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)))) (AddSubgroup.toAddSubmonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2) (p i))))) N (Dfinsupp.addZeroClass.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) (SetLike.instMembership.{u2, u2} (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) N (AddSubgroup.instSetLikeAddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) x (p i))) (fun (i : ι) => AddSubmonoid.toAddZeroClass.{u2} N (AddMonoid.toAddZeroClass.{u2} N (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)))) (AddSubgroup.toAddSubmonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2) (p i)))) (AddMonoid.toAddZeroClass.{u2} N (AddCommMonoid.toAddMonoid.{u2} N (AddCommGroup.toAddCommMonoid.{u2} N _inst_2)))))) (Dfinsupp.sumAddHom.{u1, u2, u2} ι N (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) (SetLike.instMembership.{u2, u2} (AddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)) N (AddSubgroup.instSetLikeAddSubgroup.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2))) x (p i))) (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => AddSubmonoid.toAddZeroClass.{u2} N (AddMonoid.toAddZeroClass.{u2} N (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2)))) (AddSubgroup.toAddSubmonoid.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2) (p i))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (fun (i : ι) => AddSubgroup.subtype.{u2} N (AddCommGroup.toAddGroup.{u2} N _inst_2) (p i)))))
 Case conversion may be inaccurate. Consider using '#align complete_lattice.independent_iff_dfinsupp_sum_add_hom_injective CompleteLattice.independent_iff_dfinsupp_sumAddHom_injectiveₓ'. -/
 /-- A family of additive subgroups over an additive group are independent if and only if
 `dfinsupp.sum_add_hom` applied with `add_subgroup.subtype` is injective. -/

f4758115

bump to nightly-2023-03-09-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/21e3562c5e12d846c7def5eff8cdbc520d7d4936

061741a1

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Kenny Lau
 
 ! This file was ported from Lean 3 source module linear_algebra.dfinsupp
-! leanprover-community/mathlib commit a148d797a1094ab554ad4183a4ad6f130358ef64
+! leanprover-community/mathlib commit f47581155c818e6361af4e4fda60d27d020c226b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.LinearAlgebra.Basis
 /-!
 # Properties of the module `Π₀ i, M i`
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Given an indexed collection of `R`-modules `M i`, the `R`-module structure on `Π₀ i, M i`
 is defined in `data.dfinsupp`.

a148d797

bump to nightly-2023-03-04-12

mathlib commit https://github.com/leanprover-community/mathlib/commit/62e8311c791f02c47451bf14aa2501048e7c2f33

726b2da6

Diff

@@ -680,7 +680,7 @@ theorem independent_of_dfinsupp_sumAddHom_injective (p : ι → AddSubmonoid N)
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} N] [_inst_3 : Module.{u2, u3} R N _inst_1 _inst_2] [_inst_4 : forall (m : R), Decidable (Ne.{succ u2} R m (OfNat.ofNat.{u2} R 0 (OfNat.mk.{u2} R 0 (Zero.zero.{u2} R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))))] (p : ι -> (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3)) {v : ι -> N} (hv : forall (i : ι), Membership.Mem.{u3, u3} N (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (v i) (p i)), Eq.{max (succ (max u1 u2)) (succ u3)} (LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) N (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) _inst_3) (LinearMap.comp.{u2, u2, u2, max u1 u2, max u1 u3, u3} R R R (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) (Dfinsupp.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (AddMonoid.toAddZeroClass.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) N (Submodule.setLike.{u2, u3} R N _inst_1 _inst_2 _inst_3)) (p i)) (AddCommMonoid.toAddMonoid.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R N _inst_1 _inst_2 _inst_3) 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 but is expected to have type
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=> Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u1, u3, 0, u2, u2} ι R Nat (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 _inst_3 Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3))) (fun (i : ι) => Submodule.subtype.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) (LinearMap.comp.{u3, u3, u3, max u1 u3, max u1 u3, max u1 u2} R R R (Finsupp.{u1, u3} ι R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (Dfinsupp.{u1, u3} ι (fun (i : ι) => R) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => R) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => R) i) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))) _inst_1 _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u3} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u3, u3} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (Dfinsupp.module.{u1, u3, u3} ι R (fun (i : ι) => R) _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => Semiring.toModule.{u3} R _inst_1)) (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) _inst_1 (fun (i : ι) => Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomCompTriple.ids.{u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Dfinsupp.mapRange.linearMap.{u1, u3, u3, u2} ι R _inst_1 (fun (i : ι) => R) (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Semiring.toModule.{u3} R _inst_1) (fun (i : ι) => Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => LinearMap.toSpanSingleton.{u3, u2} R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) _inst_1 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (Subtype.mk.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i)) (v i) (hv i)))) (LinearEquiv.toLinearMap.{u3, u3, max u1 u3, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.{u1, u3} ι R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (Dfinsupp.{u1, u3} ι (fun (i : ι) => R) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (_i : ι) => R) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (_i : ι) => R) i) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (Finsupp.addCommMonoid.{u1, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u3} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u3, u3} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (Dfinsupp.module.{u1, u3, u3} ι R (fun (i : ι) => R) _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => Semiring.toModule.{u3} R _inst_1)) (finsuppLequivDfinsupp.{u1, u3, u3} ι R R (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (m : R) => _inst_4 m) (Semiring.toModule.{u3} R _inst_1))))) (Finsupp.total.{u1, u2, u3} ι N R _inst_1 _inst_2 _inst_3 v)
+  forall {ι : Type.{u1}} {R : Type.{u3}} {N : Type.{u2}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} N] [_inst_3 : Module.{u3, u2} R N _inst_1 _inst_2] [_inst_4 : forall (m : R), Decidable (Ne.{succ u3} R m (OfNat.ofNat.{u3} R 0 (Zero.toOfNat0.{u3} R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)))))] (p : ι -> (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) {v : ι -> N} (hv : forall (i : ι), Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) (v i) (p i)), Eq.{max (max (succ u1) (succ u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Finsupp.{u1, u3} ι R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R 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_inst_2 _inst_3 (p i))) (LinearMap.comp.{u3, u3, u3, max u1 u3, max u1 u3, max u1 u2} R R R (Finsupp.{u1, u3} ι R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (Dfinsupp.{u1, u3} ι (fun (i : ι) => R) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => R) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => R) i) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))) _inst_1 _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u3} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) (Finsupp.module.{u1, u3, u3} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (Dfinsupp.module.{u1, u3, u3} ι R (fun (i : ι) => R) _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => Semiring.toModule.{u3} R _inst_1)) (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) _inst_1 (fun (i : ι) => Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomCompTriple.ids.{u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Dfinsupp.mapRange.linearMap.{u1, u3, u3, u2} ι R _inst_1 (fun (i : ι) => R) (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Semiring.toModule.{u3} R _inst_1) (fun (i : ι) => Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => LinearMap.toSpanSingleton.{u3, u2} R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) _inst_1 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (Subtype.mk.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i)) (v i) (hv i)))) (LinearEquiv.toLinearMap.{u3, u3, max u1 u3, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.{u1, u3} ι R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (Dfinsupp.{u1, u3} ι (fun (i : ι) => R) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (_i : ι) => R) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (_i : ι) => R) i) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (Finsupp.addCommMonoid.{u1, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u3} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u1, u3, u3} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (Dfinsupp.module.{u1, u3, u3} ι R (fun (i : ι) => R) _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => Semiring.toModule.{u3} R _inst_1)) (finsuppLequivDfinsupp.{u1, u3, u3} ι R R (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (m : R) => _inst_4 m) (Semiring.toModule.{u3} R _inst_1))))) (Finsupp.total.{u1, u2, u3} ι N R _inst_1 _inst_2 _inst_3 v)
 Case conversion may be inaccurate. Consider using '#align complete_lattice.lsum_comp_map_range_to_span_singleton CompleteLattice.lsum_comp_mapRange_toSpanSingletonₓ'. -/
 /-- Combining `dfinsupp.lsum` with `linear_map.to_span_singleton` is the same as `finsupp.total` -/
 theorem lsum_comp_mapRange_toSpanSingleton [∀ m : R, Decidable (m ≠ 0)] (p : ι → Submodule R N)

a148d797

bump to nightly-2023-03-02-23

mathlib commit https://github.com/leanprover-community/mathlib/commit/195fcd60ff2bfe392543bceb0ec2adcdb472db4c

ec1a9cbb

Diff

@@ -50,6 +50,12 @@ variable [AddCommMonoid N] [Module R N]
 
 include dec_ι
 
+/- warning: dfinsupp.lmk -> Dfinsupp.lmk is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {M : ι -> Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (M i)] [_inst_3 : forall (i : ι), Module.{u2, u3} R (M i) _inst_1 (_inst_2 i)] (s : Finset.{u1} ι), LinearMap.{u2, u2, max u1 u3, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (forall (i : coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} ι) (Set.{u1} ι) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (Finset.Set.hasCoeT.{u1} ι))) s)), M ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : 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+Case conversion may be inaccurate. Consider using '#align dfinsupp.lmk Dfinsupp.lmkₓ'. -/
 /-- `dfinsupp.mk` as a `linear_map`. -/
 def lmk (s : Finset ι) : (∀ i : (↑s : Set ι), M i) →ₗ[R] Π₀ i, M i
     where
@@ -58,6 +64,12 @@ def lmk (s : Finset ι) : (∀ i : (↑s : Set ι), M i) →ₗ[R] Π₀ i, M i
   map_smul' c x := mk_smul c x
 #align dfinsupp.lmk Dfinsupp.lmk
 
+/- warning: dfinsupp.lsingle -> Dfinsupp.lsingle is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align dfinsupp.lsingle Dfinsupp.lsingleₓ'. -/
 /-- `dfinsupp.single` as a `linear_map` -/
 def lsingle (i) : M i →ₗ[R] Π₀ i, M i :=
   { Dfinsupp.singleAddHom _ _ with
@@ -65,11 +77,23 @@ def lsingle (i) : M i →ₗ[R] Π₀ i, M i :=
     map_smul' := single_smul }
 #align dfinsupp.lsingle Dfinsupp.lsingle
 
+/- warning: dfinsupp.lhom_ext -> Dfinsupp.lhom_ext is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align dfinsupp.lhom_ext Dfinsupp.lhom_extₓ'. -/
 /-- Two `R`-linear maps from `Π₀ i, M i` which agree on each `single i x` agree everywhere. -/
 theorem lhom_ext ⦃φ ψ : (Π₀ i, M i) →ₗ[R] N⦄ (h : ∀ i x, φ (single i x) = ψ (single i x)) : φ = ψ :=
   LinearMap.toAddMonoidHom_injective <| addHom_ext h
 #align dfinsupp.lhom_ext Dfinsupp.lhom_ext
 
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+Case conversion may be inaccurate. Consider using '#align dfinsupp.lhom_ext' Dfinsupp.lhom_ext'ₓ'. -/
 /-- Two `R`-linear maps from `Π₀ i, M i` which agree on each `single i x` agree everywhere.
 
 See note [partially-applied ext lemmas].
@@ -82,6 +106,12 @@ theorem lhom_ext' ⦃φ ψ : (Π₀ i, M i) →ₗ[R] N⦄ (h : ∀ i, φ.comp (
 
 omit dec_ι
 
+/- warning: dfinsupp.lapply -> Dfinsupp.lapply is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align dfinsupp.lapply Dfinsupp.lapplyₓ'. -/
 /-- Interpret `λ (f : Π₀ i, M i), f i` as a linear map. -/
 def lapply (i : ι) : (Π₀ i, M i) →ₗ[R] M i
     where
@@ -92,11 +122,23 @@ def lapply (i : ι) : (Π₀ i, M i) →ₗ[R] M i
 
 include dec_ι
 
+/- warning: dfinsupp.lmk_apply -> Dfinsupp.lmk_apply is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align dfinsupp.lmk_apply Dfinsupp.lmk_applyₓ'. -/
 @[simp]
 theorem lmk_apply (s : Finset ι) (x) : (lmk s : _ →ₗ[R] Π₀ i, M i) x = mk s x :=
   rfl
 #align dfinsupp.lmk_apply Dfinsupp.lmk_apply
 
+/- warning: dfinsupp.lsingle_apply -> Dfinsupp.lsingle_apply is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align dfinsupp.lsingle_apply Dfinsupp.lsingle_applyₓ'. -/
 @[simp]
 theorem lsingle_apply (i : ι) (x : M i) : (lsingle i : _ →ₗ[R] _) x = single i x :=
   rfl
@@ -104,6 +146,12 @@ theorem lsingle_apply (i : ι) (x : M i) : (lsingle i : _ →ₗ[R] _) x = singl
 
 omit dec_ι
 
+/- warning: dfinsupp.lapply_apply -> Dfinsupp.lapply_apply is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align dfinsupp.lapply_apply Dfinsupp.lapply_applyₓ'. -/
 @[simp]
 theorem lapply_apply (i : ι) (f : Π₀ i, M i) : (lapply i : _ →ₗ[R] _) f = f i :=
   rfl
@@ -111,6 +159,12 @@ theorem lapply_apply (i : ι) (f : Π₀ i, M i) : (lapply i : _ →ₗ[R] _) f
 
 section Lsum
 
+/- warning: dfinsupp.add_comm_monoid_of_linear_map -> Dfinsupp.addCommMonoidOfLinearMap is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {M : ι -> Type.{u3}} {N : Type.{u4}} [_inst_1 : Semiring.{u2} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (M i)] [_inst_3 : forall (i : ι), Module.{u2, u3} R (M i) _inst_1 (_inst_2 i)] [_inst_4 : AddCommMonoid.{u4} N] [_inst_5 : Module.{u2, u4} R N _inst_1 _inst_4], AddCommMonoid.{max u1 u3 u4} (Dfinsupp.{u1, max u3 u4} ι (fun (i : ι) => LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (fun (i : ι) => LinearMap.hasZero.{u2, u2, u3, u4} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))
+but is expected to have type
+  forall {ι : Type.{u1}} {R : Type.{u2}} {M : ι -> Type.{u3}} {N : Type.{u4}} [_inst_1 : Semiring.{u2} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (M i)] [_inst_3 : forall (i : ι), Module.{u2, u3} R (M i) _inst_1 (_inst_2 i)] [_inst_4 : AddCommMonoid.{u4} N] [_inst_5 : Module.{u2, u4} R N _inst_1 _inst_4], AddCommMonoid.{max (max u4 u3) u1} (Dfinsupp.{u1, max u4 u3} ι (fun (i : ι) => LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (fun (i : ι) => LinearMap.instZeroLinearMap.{u2, u2, u3, u4} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))
+Case conversion may be inaccurate. Consider using '#align dfinsupp.add_comm_monoid_of_linear_map Dfinsupp.addCommMonoidOfLinearMapₓ'. -/
 /-- Typeclass inference can't find `dfinsupp.add_comm_monoid` without help for this case.
 This instance allows it to be found where it is needed on the LHS of the colon in
 `dfinsupp.module_of_linear_map`. -/
@@ -118,6 +172,12 @@ instance addCommMonoidOfLinearMap : AddCommMonoid (Π₀ i : ι, M i →ₗ[R] N
   @Dfinsupp.addCommMonoid _ (fun i => M i →ₗ[R] N) _
 #align dfinsupp.add_comm_monoid_of_linear_map Dfinsupp.addCommMonoidOfLinearMap
 
+/- warning: dfinsupp.module_of_linear_map -> Dfinsupp.moduleOfLinearMap is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {S : Type.{u3}} {M : ι -> Type.{u4}} {N : Type.{u5}} [_inst_1 : Semiring.{u2} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u4} (M i)] [_inst_3 : forall (i : ι), Module.{u2, u4} R (M i) _inst_1 (_inst_2 i)] [_inst_4 : AddCommMonoid.{u5} N] [_inst_5 : Module.{u2, u5} R N _inst_1 _inst_4] [_inst_6 : Semiring.{u3} S] [_inst_7 : Module.{u3, u5} S N _inst_6 _inst_4] [_inst_8 : SMulCommClass.{u2, u3, u5} R S N (SMulZeroClass.toHasSmul.{u2, u5} R N (AddZeroClass.toHasZero.{u5} N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4))) (SMulWithZero.toSmulZeroClass.{u2, u5} R N (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))) (AddZeroClass.toHasZero.{u5} N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4))) (MulActionWithZero.toSMulWithZero.{u2, u5} R N (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddZeroClass.toHasZero.{u5} N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4))) (Module.toMulActionWithZero.{u2, u5} R N _inst_1 _inst_4 _inst_5)))) (SMulZeroClass.toHasSmul.{u3, u5} S N (AddZeroClass.toHasZero.{u5} N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4))) (SMulWithZero.toSmulZeroClass.{u3, u5} S N (MulZeroClass.toHasZero.{u3} S (MulZeroOneClass.toMulZeroClass.{u3} S (MonoidWithZero.toMulZeroOneClass.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_6)))) (AddZeroClass.toHasZero.{u5} N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4))) (MulActionWithZero.toSMulWithZero.{u3, u5} S N (Semiring.toMonoidWithZero.{u3} S _inst_6) (AddZeroClass.toHasZero.{u5} N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4))) (Module.toMulActionWithZero.{u3, u5} S N _inst_6 _inst_4 _inst_7))))], Module.{u3, max u1 u4 u5} S (Dfinsupp.{u1, max u4 u5} ι (fun (i : ι) => LinearMap.{u2, u2, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (fun (i : ι) => LinearMap.hasZero.{u2, u2, u4, u5} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_6 (Dfinsupp.addCommMonoidOfLinearMap.{u1, u2, u4, u5} ι R (fun (i : ι) => M i) N _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) _inst_4 _inst_5)
+but is expected to have type
+  forall {ι : Type.{u1}} {R : Type.{u2}} {S : Type.{u3}} {M : ι -> Type.{u4}} {N : Type.{u5}} [_inst_1 : Semiring.{u2} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u4} (M i)] [_inst_3 : forall (i : ι), Module.{u2, u4} R (M i) _inst_1 (_inst_2 i)] [_inst_4 : AddCommMonoid.{u5} N] [_inst_5 : Module.{u2, u5} R N _inst_1 _inst_4] [_inst_6 : Semiring.{u3} S] [_inst_7 : Module.{u3, u5} S N _inst_6 _inst_4] [_inst_8 : SMulCommClass.{u2, u3, u5} R S N (SMulZeroClass.toSMul.{u2, u5} R N (AddMonoid.toZero.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u5} R N (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u5} R N (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4)) (Module.toMulActionWithZero.{u2, u5} R N _inst_1 _inst_4 _inst_5)))) (SMulZeroClass.toSMul.{u3, u5} S N (AddMonoid.toZero.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4)) (SMulWithZero.toSMulZeroClass.{u3, u5} S N (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_6)) (AddMonoid.toZero.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4)) (MulActionWithZero.toSMulWithZero.{u3, u5} S N (Semiring.toMonoidWithZero.{u3} S _inst_6) (AddMonoid.toZero.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4)) (Module.toMulActionWithZero.{u3, u5} S N _inst_6 _inst_4 _inst_7))))], Module.{u3, max (max u5 u4) u1} S (Dfinsupp.{u1, max u5 u4} ι (fun (i : ι) => LinearMap.{u2, u2, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (fun (i : ι) => LinearMap.instZeroLinearMap.{u2, u2, u4, u5} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_6 (Dfinsupp.addCommMonoidOfLinearMap.{u1, u2, u4, u5} ι R (fun (i : ι) => M i) N _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) _inst_4 _inst_5)
+Case conversion may be inaccurate. Consider using '#align dfinsupp.module_of_linear_map Dfinsupp.moduleOfLinearMapₓ'. -/
 /-- Typeclass inference can't find `dfinsupp.module` without help for this case.
 This is needed to define `dfinsupp.lsum` below.
 
@@ -133,6 +193,12 @@ variable (S)
 
 include dec_ι
 
+/- warning: dfinsupp.lsum -> Dfinsupp.lsum is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} (S : Type.{u3}) {M : ι -> Type.{u4}} {N : Type.{u5}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u4} (M i)] [_inst_3 : forall (i : ι), Module.{u2, u4} R (M i) _inst_1 (_inst_2 i)] [_inst_4 : AddCommMonoid.{u5} N] [_inst_5 : Module.{u2, u5} R N _inst_1 _inst_4] [_inst_6 : Semiring.{u3} S] [_inst_7 : Module.{u3, u5} S N _inst_6 _inst_4] [_inst_8 : SMulCommClass.{u2, u3, u5} R S N (SMulZeroClass.toHasSmul.{u2, u5} R N (AddZeroClass.toHasZero.{u5} N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4))) (SMulWithZero.toSmulZeroClass.{u2, u5} R N (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))) (AddZeroClass.toHasZero.{u5} N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4))) (MulActionWithZero.toSMulWithZero.{u2, u5} R N (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddZeroClass.toHasZero.{u5} N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4))) (Module.toMulActionWithZero.{u2, u5} R N _inst_1 _inst_4 _inst_5)))) (SMulZeroClass.toHasSmul.{u3, u5} S N (AddZeroClass.toHasZero.{u5} N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4))) (SMulWithZero.toSmulZeroClass.{u3, u5} S N (MulZeroClass.toHasZero.{u3} S (MulZeroOneClass.toMulZeroClass.{u3} S (MonoidWithZero.toMulZeroOneClass.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_6)))) (AddZeroClass.toHasZero.{u5} N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4))) (MulActionWithZero.toSMulWithZero.{u3, u5} S N (Semiring.toMonoidWithZero.{u3} S _inst_6) (AddZeroClass.toHasZero.{u5} N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4))) (Module.toMulActionWithZero.{u3, u5} S N _inst_6 _inst_4 _inst_7))))], LinearEquiv.{u3, u3, max u1 u4 u5, max (max u1 u4) u5} S S _inst_6 _inst_6 (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_6)) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_6)) (RingHomInvPair.ids.{u3} S _inst_6) (RingHomInvPair.ids.{u3} S _inst_6) (forall (i : ι), LinearMap.{u2, u2, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (LinearMap.{u2, u2, max u1 u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} (M i) (AddMonoid.toAddZeroClass.{u4} (M i) (AddCommMonoid.toAddMonoid.{u4} (M i) (_inst_2 i))))) N (Dfinsupp.addCommMonoid.{u1, u4} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u4, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5) (Pi.addCommMonoid.{u1, max u4 u5} ι (fun (i : ι) => LinearMap.{u2, u2, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u4, u5} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u1 u4, u5} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} (M i) (AddMonoid.toAddZeroClass.{u4} (M i) (AddCommMonoid.toAddMonoid.{u4} (M i) (_inst_2 i))))) N _inst_1 _inst_1 (Dfinsupp.addCommMonoid.{u1, u4} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u4, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u1, max u4 u5, u3} ι (fun (i : ι) => LinearMap.{u2, u2, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) S _inst_6 (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u4, u5} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.module.{u2, u2, u3, u4, u5} R R S (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) _inst_6 _inst_7 _inst_8)) (LinearMap.module.{u2, u2, u3, max u1 u4, u5} R R S (Dfinsupp.{u1, u4} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} (M i) (AddMonoid.toAddZeroClass.{u4} (M i) (AddCommMonoid.toAddMonoid.{u4} (M i) (_inst_2 i))))) N _inst_1 _inst_1 (Dfinsupp.addCommMonoid.{u1, u4} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u4, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) _inst_6 _inst_7 _inst_8)
+but is expected to have type
+  forall {ι : Type.{u1}} {R : Type.{u2}} (S : Type.{u3}) {M : ι -> Type.{u4}} {N : Type.{u5}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u4} (M i)] [_inst_3 : forall (i : ι), Module.{u2, u4} R (M i) _inst_1 (_inst_2 i)] [_inst_4 : AddCommMonoid.{u5} N] [_inst_5 : Module.{u2, u5} R N _inst_1 _inst_4] [_inst_6 : Semiring.{u3} S] [_inst_7 : Module.{u3, u5} S N _inst_6 _inst_4] [_inst_8 : SMulCommClass.{u2, u3, u5} R S N (SMulZeroClass.toSMul.{u2, u5} R N (AddMonoid.toZero.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u5} R N (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u5} R N (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4)) (Module.toMulActionWithZero.{u2, u5} R N _inst_1 _inst_4 _inst_5)))) (SMulZeroClass.toSMul.{u3, u5} S N (AddMonoid.toZero.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4)) (SMulWithZero.toSMulZeroClass.{u3, u5} S N (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_6)) (AddMonoid.toZero.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4)) (MulActionWithZero.toSMulWithZero.{u3, u5} S N (Semiring.toMonoidWithZero.{u3} S _inst_6) (AddMonoid.toZero.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4)) (Module.toMulActionWithZero.{u3, u5} S N _inst_6 _inst_4 _inst_7))))], LinearEquiv.{u3, u3, max (max u1 u4) u5, max u5 u4 u1} S S _inst_6 _inst_6 (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_6)) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_6)) (RingHomInvPair.ids.{u3} S _inst_6) (RingHomInvPair.ids.{u3} S _inst_6) (forall (i : ι), LinearMap.{u2, u2, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (LinearMap.{u2, u2, max u4 u1, u5} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => M i) i) (_inst_2 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u4, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5) (Pi.addCommMonoid.{u1, max u4 u5} ι (fun (i : ι) => LinearMap.{u2, u2, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u4, u5} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u1 u4, u5} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => M i) i) (_inst_2 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u4, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u1, max u4 u5, u3} ι (fun (i : ι) => LinearMap.{u2, u2, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) S _inst_6 (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u4, u5} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u3, u4, u5} R R S (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) _inst_6 _inst_7 _inst_8)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u3, max u1 u4, u5} R R S (Dfinsupp.{u1, u4} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => M i) i) (_inst_2 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u4, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) _inst_6 _inst_7 _inst_8)
+Case conversion may be inaccurate. Consider using '#align dfinsupp.lsum Dfinsupp.lsumₓ'. -/
 /-- The `dfinsupp` version of `finsupp.lsum`.
 
 See note [bundled maps over different rings] for why separate `R` and `S` semirings are used. -/
@@ -166,6 +232,12 @@ def lsum [Semiring S] [Module S N] [SMulCommClass R S N] :
     simp
 #align dfinsupp.lsum Dfinsupp.lsum
 
+/- warning: dfinsupp.lsum_single -> Dfinsupp.lsum_single is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} (S : Type.{u3}) {M : ι -> Type.{u4}} {N : Type.{u5}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u4} (M i)] [_inst_3 : forall (i : ι), Module.{u2, u4} R (M i) _inst_1 (_inst_2 i)] [_inst_4 : AddCommMonoid.{u5} N] [_inst_5 : Module.{u2, u5} R N _inst_1 _inst_4] [_inst_6 : Semiring.{u3} S] [_inst_7 : Module.{u3, u5} S N _inst_6 _inst_4] [_inst_8 : SMulCommClass.{u2, u3, u5} R S N (SMulZeroClass.toHasSmul.{u2, u5} R N (AddZeroClass.toHasZero.{u5} N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4))) (SMulWithZero.toSmulZeroClass.{u2, u5} R N (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))) (AddZeroClass.toHasZero.{u5} N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4))) (MulActionWithZero.toSMulWithZero.{u2, u5} R N (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddZeroClass.toHasZero.{u5} N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4))) (Module.toMulActionWithZero.{u2, u5} R N _inst_1 _inst_4 _inst_5)))) (SMulZeroClass.toHasSmul.{u3, u5} S N (AddZeroClass.toHasZero.{u5} N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4))) (SMulWithZero.toSmulZeroClass.{u3, u5} S N (MulZeroClass.toHasZero.{u3} S (MulZeroOneClass.toMulZeroClass.{u3} S (MonoidWithZero.toMulZeroOneClass.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_6)))) (AddZeroClass.toHasZero.{u5} N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4))) (MulActionWithZero.toSMulWithZero.{u3, u5} S N (Semiring.toMonoidWithZero.{u3} S _inst_6) (AddZeroClass.toHasZero.{u5} N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_4))) (Module.toMulActionWithZero.{u3, u5} S N _inst_6 _inst_4 _inst_7))))] (F : forall (i : ι), LinearMap.{u2, u2, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (i : ι) (x : M i), Eq.{succ u5} N (coeFn.{max (succ (max u1 u4)) (succ u5), max (succ (max u1 u4)) (succ u5)} (LinearMap.{u2, u2, max u1 u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} (M i) (AddMonoid.toAddZeroClass.{u4} (M i) (AddCommMonoid.toAddMonoid.{u4} (M i) (_inst_2 i))))) N (Dfinsupp.addCommMonoid.{u1, u4} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u4, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5) (fun (_x : LinearMap.{u2, u2, max u1 u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} (M i) 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(RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) => (M i) -> N) (LinearMap.hasCoeToFun.{u2, u2, u4, u5} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (F i) x)
+but is expected to have type
+  forall {ι : Type.{u1}} {R : Type.{u3}} (S : Type.{u5}) {M : ι -> Type.{u2}} {N : Type.{u4}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u3} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (M i)] [_inst_3 : forall (i : ι), Module.{u3, u2} R (M i) _inst_1 (_inst_2 i)] [_inst_4 : AddCommMonoid.{u4} N] [_inst_5 : Module.{u3, u4} R N _inst_1 _inst_4] [_inst_6 : Semiring.{u5} S] [_inst_7 : Module.{u5, u4} S N _inst_6 _inst_4] [_inst_8 : SMulCommClass.{u3, u5, u4} R S N (SMulZeroClass.toSMul.{u3, u4} R N (AddMonoid.toZero.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_4)) (SMulWithZero.toSMulZeroClass.{u3, u4} R N (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddMonoid.toZero.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_4)) (MulActionWithZero.toSMulWithZero.{u3, u4} R N (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddMonoid.toZero.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_4)) (Module.toMulActionWithZero.{u3, u4} R N _inst_1 _inst_4 _inst_5)))) (SMulZeroClass.toSMul.{u5, u4} S N (AddMonoid.toZero.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_4)) (SMulWithZero.toSMulZeroClass.{u5, u4} S N (MonoidWithZero.toZero.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_6)) (AddMonoid.toZero.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_4)) (MulActionWithZero.toSMulWithZero.{u5, u4} S N (Semiring.toMonoidWithZero.{u5} S _inst_6) (AddMonoid.toZero.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_4)) (Module.toMulActionWithZero.{u5, u4} S N _inst_6 _inst_4 _inst_7))))] (F : forall (i : ι), LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (i : ι) (x : M i), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Dfinsupp.{u1, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) => N) (Dfinsupp.single.{u1, u2} ι 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ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u4), max (max (succ u1) (succ u2)) (succ u4), max (max (succ u1) (succ u2)) (succ u4)} (LinearEquiv.{u5, u5, max (max u1 u2) u4, max u4 u2 u1} S S _inst_6 _inst_6 (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_6)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_6)) (RingHomInvPair.ids.{u5} S _inst_6) (RingHomInvPair.ids.{u5} S _inst_6) (forall (i : ι), LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (LinearMap.{u3, u3, max u2 u1, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u2} ι (fun (i : ι) => 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_inst_3 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) _inst_6 _inst_7 _inst_8)) S (forall (i : ι), LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (LinearMap.{u3, u3, max u2 u1, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5) (SMulZeroClass.toSMul.{u5, max (max u1 u2) u4} S (forall (i : ι), LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (AddMonoid.toZero.{max (max u1 u2) u4} (forall (i : ι), LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u4} (forall (i : ι), LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (Pi.addCommMonoid.{u1, max u2 u4} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u4} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u5, max (max u1 u2) u4} S (forall (i : ι), LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (AddMonoid.toAddZeroClass.{max (max u1 u2) u4} (forall (i : ι), LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u4} (forall (i : ι), LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (Pi.addCommMonoid.{u1, max u2 u4} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u4} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u5, max (max u1 u2) u4} S (forall (i : ι), LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (MonoidWithZero.toMonoid.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_6)) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u4} (forall (i : ι), LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (Pi.addCommMonoid.{u1, max u2 u4} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u4} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) 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(RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u5, u2, u4} R R S (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) _inst_6 _inst_7 _inst_8)))))) (SMulZeroClass.toSMul.{u5, max (max u1 u2) u4} S (LinearMap.{u3, u3, max u2 u1, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5) (AddMonoid.toZero.{max (max u1 u2) u4} (LinearMap.{u3, u3, max u2 u1, u4} R R _inst_1 _inst_1 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(RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u5, max u1 u2, u4} R R S (Dfinsupp.{u1, u2} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u2, u3} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) _inst_6 _inst_7 _inst_8))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u4, u5, max (max u1 u2) u4, max (max u1 u2) u4} (LinearEquiv.{u5, u5, max (max u1 u2) u4, max u4 u2 u1} S S _inst_6 _inst_6 (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_6)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S _inst_6)) 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dec_ι a b) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) _inst_4 _inst_5 _inst_6 _inst_7 _inst_8) F) (Dfinsupp.single.{u1, u2} ι (fun (i : ι) => M i) (fun (a : ι) (b : ι) => dec_ι a b) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => M i) i) (_inst_2 i))) i x)) (FunLike.coe.{max (succ u2) (succ u4), succ u2, succ u4} (LinearMap.{u3, u3, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) (M i) (fun (_x : M i) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M i) => N) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u4} R R (M i) N _inst_1 _inst_1 (_inst_2 i) _inst_4 (_inst_3 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (F i) x)
+Case conversion may be inaccurate. Consider using '#align dfinsupp.lsum_single Dfinsupp.lsum_singleₓ'. -/
 /-- While `simp` can prove this, it is often convenient to avoid unfolding `lsum` into `sum_add_hom`
 with `dfinsupp.lsum_apply_apply`. -/
 theorem lsum_single [Semiring S] [Module S N] [SMulCommClass R S N] (F : ∀ i, M i →ₗ[R] N) (i)
@@ -189,6 +261,12 @@ variable [∀ i, AddCommMonoid (β i)] [∀ i, AddCommMonoid (β₁ i)] [∀ i,
 
 variable [∀ i, Module R (β i)] [∀ i, Module R (β₁ i)] [∀ i, Module R (β₂ i)]
 
+/- warning: dfinsupp.map_range_smul -> Dfinsupp.mapRange_smul is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {β₁ : ι -> Type.{u3}} {β₂ : ι -> Type.{u4}} [_inst_7 : forall (i : ι), AddCommMonoid.{u3} (β₁ i)] [_inst_8 : forall (i : ι), AddCommMonoid.{u4} (β₂ i)] [_inst_10 : forall (i : ι), Module.{u2, u3} R (β₁ i) _inst_1 (_inst_7 i)] [_inst_11 : forall (i : ι), Module.{u2, u4} R (β₂ i) _inst_1 (_inst_8 i)] (f : forall (i : ι), (β₁ i) -> (β₂ i)) (hf : forall (i : ι), Eq.{succ u4} (β₂ i) (f i (OfNat.ofNat.{u3} (β₁ i) 0 (OfNat.mk.{u3} (β₁ i) 0 (Zero.zero.{u3} (β₁ i) (AddZeroClass.toHasZero.{u3} (β₁ i) (AddMonoid.toAddZeroClass.{u3} (β₁ i) (AddCommMonoid.toAddMonoid.{u3} (β₁ i) (_inst_7 i)))))))) (OfNat.ofNat.{u4} (β₂ i) 0 (OfNat.mk.{u4} (β₂ i) 0 (Zero.zero.{u4} (β₂ i) (AddZeroClass.toHasZero.{u4} (β₂ i) (AddMonoid.toAddZeroClass.{u4} (β₂ i) (AddCommMonoid.toAddMonoid.{u4} (β₂ i) (_inst_8 i)))))))) (r : R), (forall (i : ι) (x : β₁ i), Eq.{succ u4} (β₂ i) (f i (SMul.smul.{u2, u3} R (β₁ i) (SMulZeroClass.toHasSmul.{u2, u3} R (β₁ i) (AddZeroClass.toHasZero.{u3} (β₁ i) (AddMonoid.toAddZeroClass.{u3} (β₁ i) (AddCommMonoid.toAddMonoid.{u3} (β₁ i) (_inst_7 i)))) (SMulWithZero.toSmulZeroClass.{u2, u3} R (β₁ i) (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))) (AddZeroClass.toHasZero.{u3} (β₁ i) (AddMonoid.toAddZeroClass.{u3} (β₁ i) (AddCommMonoid.toAddMonoid.{u3} (β₁ i) (_inst_7 i)))) (MulActionWithZero.toSMulWithZero.{u2, u3} R (β₁ i) (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddZeroClass.toHasZero.{u3} (β₁ i) (AddMonoid.toAddZeroClass.{u3} (β₁ i) (AddCommMonoid.toAddMonoid.{u3} (β₁ i) (_inst_7 i)))) (Module.toMulActionWithZero.{u2, u3} R (β₁ i) _inst_1 (_inst_7 i) (_inst_10 i))))) r x)) (SMul.smul.{u2, u4} R (β₂ i) (SMulZeroClass.toHasSmul.{u2, u4} R (β₂ i) (AddZeroClass.toHasZero.{u4} (β₂ i) (AddMonoid.toAddZeroClass.{u4} (β₂ i) (AddCommMonoid.toAddMonoid.{u4} (β₂ i) (_inst_8 i)))) (SMulWithZero.toSmulZeroClass.{u2, u4} R (β₂ i) (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))) (AddZeroClass.toHasZero.{u4} (β₂ i) (AddMonoid.toAddZeroClass.{u4} (β₂ i) (AddCommMonoid.toAddMonoid.{u4} (β₂ i) (_inst_8 i)))) (MulActionWithZero.toSMulWithZero.{u2, u4} R (β₂ i) (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddZeroClass.toHasZero.{u4} (β₂ i) (AddMonoid.toAddZeroClass.{u4} (β₂ i) (AddCommMonoid.toAddMonoid.{u4} (β₂ i) (_inst_8 i)))) (Module.toMulActionWithZero.{u2, u4} R (β₂ i) _inst_1 (_inst_8 i) (_inst_11 i))))) r (f i x))) -> (forall (g : Dfinsupp.{u1, u3} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} ((fun (i : ι) => β₁ i) i) (AddMonoid.toAddZeroClass.{u3} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => β₁ i) i) (_inst_7 i))))), Eq.{succ (max u1 u4)} (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} (β₂ i) (AddMonoid.toAddZeroClass.{u4} (β₂ i) (AddCommMonoid.toAddMonoid.{u4} (β₂ i) (_inst_8 i))))) (Dfinsupp.mapRange.{u1, u3, u4} ι (fun (i : ι) => β₁ i) (fun (i : ι) => β₂ i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (β₁ i) (AddMonoid.toAddZeroClass.{u3} (β₁ i) (AddCommMonoid.toAddMonoid.{u3} (β₁ i) (_inst_7 i)))) (fun (i : ι) => AddZeroClass.toHasZero.{u4} (β₂ i) (AddMonoid.toAddZeroClass.{u4} (β₂ i) (AddCommMonoid.toAddMonoid.{u4} (β₂ i) (_inst_8 i)))) f hf (SMul.smul.{u2, max u1 u3} R (Dfinsupp.{u1, u3} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (β₁ i) (AddMonoid.toAddZeroClass.{u3} (β₁ i) (AddCommMonoid.toAddMonoid.{u3} (β₁ i) (_inst_7 i))))) (SMulZeroClass.toHasSmul.{u2, max u1 u3} R (Dfinsupp.{u1, u3} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (β₁ i) (AddMonoid.toAddZeroClass.{u3} (β₁ i) (AddCommMonoid.toAddMonoid.{u3} (β₁ i) (_inst_7 i))))) (AddZeroClass.toHasZero.{max u1 u3} (Dfinsupp.{u1, u3} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (β₁ i) (AddMonoid.toAddZeroClass.{u3} (β₁ i) (AddCommMonoid.toAddMonoid.{u3} (β₁ i) (_inst_7 i))))) (AddMonoid.toAddZeroClass.{max u1 u3} (Dfinsupp.{u1, u3} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (β₁ i) (AddMonoid.toAddZeroClass.{u3} (β₁ i) (AddCommMonoid.toAddMonoid.{u3} (β₁ i) (_inst_7 i))))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Dfinsupp.{u1, u3} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (β₁ i) (AddMonoid.toAddZeroClass.{u3} (β₁ i) (AddCommMonoid.toAddMonoid.{u3} (β₁ i) (_inst_7 i))))) (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i))))) (SMulWithZero.toSmulZeroClass.{u2, max u1 u3} R (Dfinsupp.{u1, u3} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (β₁ i) (AddMonoid.toAddZeroClass.{u3} (β₁ i) (AddCommMonoid.toAddMonoid.{u3} (β₁ i) (_inst_7 i))))) (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))) (AddZeroClass.toHasZero.{max u1 u3} (Dfinsupp.{u1, u3} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (β₁ i) (AddMonoid.toAddZeroClass.{u3} (β₁ i) (AddCommMonoid.toAddMonoid.{u3} (β₁ i) (_inst_7 i))))) (AddMonoid.toAddZeroClass.{max u1 u3} (Dfinsupp.{u1, u3} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (β₁ i) (AddMonoid.toAddZeroClass.{u3} (β₁ i) (AddCommMonoid.toAddMonoid.{u3} (β₁ i) (_inst_7 i))))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Dfinsupp.{u1, u3} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (β₁ i) (AddMonoid.toAddZeroClass.{u3} (β₁ i) (AddCommMonoid.toAddMonoid.{u3} (β₁ i) (_inst_7 i))))) (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i))))) (MulActionWithZero.toSMulWithZero.{u2, max u1 u3} R (Dfinsupp.{u1, u3} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (β₁ i) (AddMonoid.toAddZeroClass.{u3} (β₁ i) (AddCommMonoid.toAddMonoid.{u3} (β₁ i) (_inst_7 i))))) (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddZeroClass.toHasZero.{max u1 u3} (Dfinsupp.{u1, u3} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (β₁ i) (AddMonoid.toAddZeroClass.{u3} (β₁ i) (AddCommMonoid.toAddMonoid.{u3} (β₁ i) (_inst_7 i))))) (AddMonoid.toAddZeroClass.{max u1 u3} (Dfinsupp.{u1, u3} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (β₁ i) (AddMonoid.toAddZeroClass.{u3} (β₁ i) (AddCommMonoid.toAddMonoid.{u3} (β₁ i) (_inst_7 i))))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Dfinsupp.{u1, u3} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (β₁ i) (AddMonoid.toAddZeroClass.{u3} (β₁ i) (AddCommMonoid.toAddMonoid.{u3} (β₁ i) (_inst_7 i))))) (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i))))) (Module.toMulActionWithZero.{u2, max u1 u3} R (Dfinsupp.{u1, u3} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (β₁ i) (AddMonoid.toAddZeroClass.{u3} (β₁ i) (AddCommMonoid.toAddMonoid.{u3} (β₁ i) (_inst_7 i))))) _inst_1 (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)))))) r g)) (SMul.smul.{u2, max u1 u4} R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} (β₂ i) (AddMonoid.toAddZeroClass.{u4} (β₂ i) (AddCommMonoid.toAddMonoid.{u4} (β₂ i) (_inst_8 i))))) (SMulZeroClass.toHasSmul.{u2, max u1 u4} R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} (β₂ i) (AddMonoid.toAddZeroClass.{u4} (β₂ i) (AddCommMonoid.toAddMonoid.{u4} (β₂ i) (_inst_8 i))))) (AddZeroClass.toHasZero.{max u1 u4} (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} (β₂ i) (AddMonoid.toAddZeroClass.{u4} (β₂ i) (AddCommMonoid.toAddMonoid.{u4} (β₂ i) (_inst_8 i))))) (AddMonoid.toAddZeroClass.{max u1 u4} (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} (β₂ i) (AddMonoid.toAddZeroClass.{u4} (β₂ i) (AddCommMonoid.toAddMonoid.{u4} (β₂ i) (_inst_8 i))))) (AddCommMonoid.toAddMonoid.{max u1 u4} (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} (β₂ i) (AddMonoid.toAddZeroClass.{u4} (β₂ i) (AddCommMonoid.toAddMonoid.{u4} (β₂ i) (_inst_8 i))))) (Dfinsupp.addCommMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i))))) (SMulWithZero.toSmulZeroClass.{u2, max u1 u4} R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} (β₂ i) (AddMonoid.toAddZeroClass.{u4} (β₂ i) (AddCommMonoid.toAddMonoid.{u4} (β₂ i) (_inst_8 i))))) (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))) (AddZeroClass.toHasZero.{max u1 u4} (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} (β₂ i) (AddMonoid.toAddZeroClass.{u4} (β₂ i) (AddCommMonoid.toAddMonoid.{u4} (β₂ i) (_inst_8 i))))) (AddMonoid.toAddZeroClass.{max u1 u4} (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} (β₂ i) (AddMonoid.toAddZeroClass.{u4} (β₂ i) (AddCommMonoid.toAddMonoid.{u4} (β₂ i) (_inst_8 i))))) (AddCommMonoid.toAddMonoid.{max u1 u4} (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} (β₂ i) (AddMonoid.toAddZeroClass.{u4} (β₂ i) (AddCommMonoid.toAddMonoid.{u4} (β₂ i) (_inst_8 i))))) (Dfinsupp.addCommMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i))))) (MulActionWithZero.toSMulWithZero.{u2, max u1 u4} R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} (β₂ i) (AddMonoid.toAddZeroClass.{u4} (β₂ i) (AddCommMonoid.toAddMonoid.{u4} (β₂ i) (_inst_8 i))))) (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddZeroClass.toHasZero.{max u1 u4} (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} (β₂ i) (AddMonoid.toAddZeroClass.{u4} (β₂ i) (AddCommMonoid.toAddMonoid.{u4} (β₂ i) (_inst_8 i))))) (AddMonoid.toAddZeroClass.{max u1 u4} (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} (β₂ i) (AddMonoid.toAddZeroClass.{u4} (β₂ i) (AddCommMonoid.toAddMonoid.{u4} (β₂ i) (_inst_8 i))))) (AddCommMonoid.toAddMonoid.{max u1 u4} (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} (β₂ i) (AddMonoid.toAddZeroClass.{u4} (β₂ i) (AddCommMonoid.toAddMonoid.{u4} (β₂ i) (_inst_8 i))))) (Dfinsupp.addCommMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i))))) (Module.toMulActionWithZero.{u2, max u1 u4} R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} (β₂ i) (AddMonoid.toAddZeroClass.{u4} (β₂ i) (AddCommMonoid.toAddMonoid.{u4} (β₂ i) (_inst_8 i))))) _inst_1 (Dfinsupp.addCommMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) (Dfinsupp.module.{u1, u4, u2} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)))))) r (Dfinsupp.mapRange.{u1, u3, u4} ι (fun (i : ι) => β₁ i) (fun (i : ι) => β₂ i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (β₁ i) (AddMonoid.toAddZeroClass.{u3} (β₁ i) (AddCommMonoid.toAddMonoid.{u3} (β₁ i) (_inst_7 i)))) (fun (i : ι) => AddZeroClass.toHasZero.{u4} (β₂ i) (AddMonoid.toAddZeroClass.{u4} (β₂ i) (AddCommMonoid.toAddMonoid.{u4} (β₂ i) (_inst_8 i)))) f hf g)))
+but is expected to have type
+  forall {ι : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {β₁ : ι -> Type.{u3}} {β₂ : ι -> Type.{u4}} [_inst_7 : forall (i : ι), AddCommMonoid.{u3} (β₁ i)] [_inst_8 : forall (i : ι), AddCommMonoid.{u4} (β₂ i)] [_inst_10 : forall (i : ι), Module.{u2, u3} R (β₁ i) _inst_1 (_inst_7 i)] [_inst_11 : forall (i : ι), Module.{u2, u4} R (β₂ i) _inst_1 (_inst_8 i)] (f : forall (i : ι), (β₁ i) -> (β₂ i)) (hf : forall (i : ι), Eq.{succ u4} (β₂ i) (f i (OfNat.ofNat.{u3} (β₁ i) 0 (Zero.toOfNat0.{u3} (β₁ i) (AddMonoid.toZero.{u3} (β₁ i) (AddCommMonoid.toAddMonoid.{u3} (β₁ i) (_inst_7 i)))))) (OfNat.ofNat.{u4} (β₂ i) 0 (Zero.toOfNat0.{u4} (β₂ i) (AddMonoid.toZero.{u4} (β₂ i) (AddCommMonoid.toAddMonoid.{u4} (β₂ i) (_inst_8 i)))))) (r : R), (forall (i : ι) (x : β₁ i), Eq.{succ u4} (β₂ i) (f i (HSMul.hSMul.{u2, u3, u3} R (β₁ i) (β₁ i) (instHSMul.{u2, u3} R (β₁ i) (SMulZeroClass.toSMul.{u2, u3} R (β₁ i) (AddMonoid.toZero.{u3} (β₁ i) (AddCommMonoid.toAddMonoid.{u3} (β₁ i) (_inst_7 i))) (SMulWithZero.toSMulZeroClass.{u2, u3} R (β₁ i) (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u3} (β₁ i) (AddCommMonoid.toAddMonoid.{u3} (β₁ i) (_inst_7 i))) (MulActionWithZero.toSMulWithZero.{u2, u3} R (β₁ i) (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u3} (β₁ i) (AddCommMonoid.toAddMonoid.{u3} (β₁ i) (_inst_7 i))) (Module.toMulActionWithZero.{u2, u3} R (β₁ i) _inst_1 (_inst_7 i) (_inst_10 i)))))) r x)) (HSMul.hSMul.{u2, u4, u4} R (β₂ i) (β₂ i) (instHSMul.{u2, u4} R (β₂ i) (SMulZeroClass.toSMul.{u2, u4} R (β₂ i) (AddMonoid.toZero.{u4} (β₂ i) (AddCommMonoid.toAddMonoid.{u4} (β₂ i) (_inst_8 i))) (SMulWithZero.toSMulZeroClass.{u2, u4} R (β₂ i) (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u4} (β₂ i) (AddCommMonoid.toAddMonoid.{u4} (β₂ i) (_inst_8 i))) (MulActionWithZero.toSMulWithZero.{u2, u4} R (β₂ i) (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u4} (β₂ i) (AddCommMonoid.toAddMonoid.{u4} (β₂ i) (_inst_8 i))) (Module.toMulActionWithZero.{u2, u4} R (β₂ i) _inst_1 (_inst_8 i) (_inst_11 i)))))) r (f i x))) -> (forall (g : Dfinsupp.{u1, u3} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))), Eq.{max (succ u1) (succ u4)} (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} (β₂ i) (AddCommMonoid.toAddMonoid.{u4} (β₂ i) (_inst_8 i)))) (Dfinsupp.mapRange.{u1, u3, u4} ι (fun (i : ι) => β₁ i) (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u3} (β₁ i) (AddCommMonoid.toAddMonoid.{u3} (β₁ i) (_inst_7 i))) (fun (i : ι) => AddMonoid.toZero.{u4} (β₂ i) (AddCommMonoid.toAddMonoid.{u4} (β₂ i) (_inst_8 i))) f hf (HSMul.hSMul.{u2, max u1 u3, max u1 u3} R (Dfinsupp.{u1, u3} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) (Dfinsupp.{u1, u3} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) (instHSMul.{u2, max u1 u3} R (Dfinsupp.{u1, u3} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) (Dfinsupp.instSMulDfinsuppToZero.{u1, u3, u2} ι R (fun (i : ι) => β₁ i) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (fun (i : ι) => AddCommMonoid.toAddMonoid.{u3} (β₁ i) (_inst_7 i)) (fun (i : ι) => Module.toDistribMulAction.{u2, u3} R (β₁ i) _inst_1 (_inst_7 i) (_inst_10 i)))) r g)) (HSMul.hSMul.{u2, max u4 u1, max u1 u4} R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} (β₂ i) (AddCommMonoid.toAddMonoid.{u4} (β₂ i) (_inst_8 i)))) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} (β₂ i) (AddCommMonoid.toAddMonoid.{u4} (β₂ i) (_inst_8 i)))) (instHSMul.{u2, max u1 u4} R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} (β₂ i) (AddCommMonoid.toAddMonoid.{u4} (β₂ i) (_inst_8 i)))) (Dfinsupp.instSMulDfinsuppToZero.{u1, u4, u2} ι R (fun (i : ι) => β₂ i) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (fun (i : ι) => AddCommMonoid.toAddMonoid.{u4} (β₂ i) (_inst_8 i)) (fun (i : ι) => Module.toDistribMulAction.{u2, u4} R (β₂ i) _inst_1 (_inst_8 i) (_inst_11 i)))) r (Dfinsupp.mapRange.{u1, u3, u4} ι (fun (i : ι) => β₁ i) (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u3} (β₁ i) (AddCommMonoid.toAddMonoid.{u3} (β₁ i) (_inst_7 i))) (fun (i : ι) => AddMonoid.toZero.{u4} (β₂ i) (AddCommMonoid.toAddMonoid.{u4} (β₂ i) (_inst_8 i))) f hf g)))
+Case conversion may be inaccurate. Consider using '#align dfinsupp.map_range_smul Dfinsupp.mapRange_smulₓ'. -/
 theorem mapRange_smul (f : ∀ i, β₁ i → β₂ i) (hf : ∀ i, f i 0 = 0) (r : R)
     (hf' : ∀ i x, f i (r • x) = r • f i x) (g : Π₀ i, β₁ i) :
     mapRange f hf (r • g) = r • mapRange f hf g :=
@@ -197,6 +275,12 @@ theorem mapRange_smul (f : ∀ i, β₁ i → β₂ i) (hf : ∀ i, f i 0 = 0) (
   simp only [map_range_apply f, coe_smul, Pi.smul_apply, hf']
 #align dfinsupp.map_range_smul Dfinsupp.mapRange_smul
 
+/- warning: dfinsupp.map_range.linear_map -> Dfinsupp.mapRange.linearMap is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {β₁ : ι -> Type.{u3}} {β₂ : ι -> Type.{u4}} [_inst_7 : forall (i : ι), AddCommMonoid.{u3} (β₁ i)] [_inst_8 : forall (i : ι), AddCommMonoid.{u4} (β₂ i)] [_inst_10 : forall (i : ι), Module.{u2, u3} R (β₁ i) _inst_1 (_inst_7 i)] [_inst_11 : forall (i : ι), Module.{u2, u4} R (β₂ i) _inst_1 (_inst_8 i)], (forall (i : ι), LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (β₁ i) (β₂ i) (_inst_7 i) (_inst_8 i) (_inst_10 i) (_inst_11 i)) -> (LinearMap.{u2, u2, max u1 u3, max u1 u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (β₁ i) (AddMonoid.toAddZeroClass.{u3} (β₁ i) (AddCommMonoid.toAddMonoid.{u3} (β₁ i) (_inst_7 i))))) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} (β₂ i) (AddMonoid.toAddZeroClass.{u4} (β₂ i) (AddCommMonoid.toAddMonoid.{u4} (β₂ i) (_inst_8 i))))) (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) (Dfinsupp.addCommMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) (Dfinsupp.module.{u1, u4, u2} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)))
+but is expected to have type
+  forall {ι : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {β₁ : ι -> Type.{u3}} {β₂ : ι -> Type.{u4}} [_inst_7 : forall (i : ι), AddCommMonoid.{u3} (β₁ i)] [_inst_8 : forall (i : ι), AddCommMonoid.{u4} (β₂ i)] [_inst_10 : forall (i : ι), Module.{u2, u3} R (β₁ i) _inst_1 (_inst_7 i)] [_inst_11 : forall (i : ι), Module.{u2, u4} R (β₂ i) _inst_1 (_inst_8 i)], (forall (i : ι), LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (β₁ i) (β₂ i) (_inst_7 i) (_inst_8 i) (_inst_10 i) (_inst_11 i)) -> (LinearMap.{u2, u2, max u3 u1, max u4 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u3} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) (Dfinsupp.module.{u1, u4, u2} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)))
+Case conversion may be inaccurate. Consider using '#align dfinsupp.map_range.linear_map Dfinsupp.mapRange.linearMapₓ'. -/
 /-- `dfinsupp.map_range` as an `linear_map`. -/
 @[simps apply]
 def mapRange.linearMap (f : ∀ i, β₁ i →ₗ[R] β₂ i) : (Π₀ i, β₁ i) →ₗ[R] Π₀ i, β₂ i :=
@@ -207,12 +291,24 @@ def mapRange.linearMap (f : ∀ i, β₁ i →ₗ[R] β₂ i) : (Π₀ i, β₁
     map_smul' := fun r => mapRange_smul _ _ _ fun i => (f i).map_smul r }
 #align dfinsupp.map_range.linear_map Dfinsupp.mapRange.linearMap
 
+/- warning: dfinsupp.map_range.linear_map_id -> Dfinsupp.mapRange.linearMap_id is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {ι : Type.{u3}} {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {β₂ : ι -> Type.{u2}} [_inst_8 : forall (i : ι), AddCommMonoid.{u2} (β₂ i)] [_inst_11 : forall (i : ι), Module.{u1, u2} R (β₂ i) _inst_1 (_inst_8 i)], Eq.{max (succ u3) (succ u2)} (LinearMap.{u1, u1, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Dfinsupp.{u3, u2} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) (Dfinsupp.{u3, u2} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u2} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u2} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i))) (Dfinsupp.mapRange.linearMap.{u3, u1, u2, u2} ι R _inst_1 (fun (i : ι) => β₂ i) (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i) (fun (i : ι) => _inst_11 i) (fun (i : ι) => LinearMap.id.{u1, u2} R (β₂ i) _inst_1 (_inst_8 i) (_inst_11 i))) (LinearMap.id.{u1, max u3 u2} R (Dfinsupp.{u3, u2} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u3, u2} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) (Dfinsupp.module.{u3, u2, u1} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)))
+Case conversion may be inaccurate. Consider using '#align dfinsupp.map_range.linear_map_id Dfinsupp.mapRange.linearMap_idₓ'. -/
 @[simp]
 theorem mapRange.linearMap_id :
     (mapRange.linearMap fun i => (LinearMap.id : β₂ i →ₗ[R] _)) = LinearMap.id :=
   LinearMap.ext mapRange_id
 #align dfinsupp.map_range.linear_map_id Dfinsupp.mapRange.linearMap_id
 
+/- warning: dfinsupp.map_range.linear_map_comp -> Dfinsupp.mapRange.linearMap_comp is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {β : ι -> Type.{u3}} {β₁ : ι -> Type.{u4}} {β₂ : ι -> Type.{u5}} [_inst_6 : forall (i : ι), AddCommMonoid.{u3} (β i)] [_inst_7 : forall (i : ι), AddCommMonoid.{u4} (β₁ i)] [_inst_8 : forall (i : ι), AddCommMonoid.{u5} (β₂ i)] [_inst_9 : forall (i : ι), Module.{u2, u3} R (β i) _inst_1 (_inst_6 i)] [_inst_10 : forall (i : ι), Module.{u2, u4} R (β₁ i) _inst_1 (_inst_7 i)] [_inst_11 : forall (i : ι), Module.{u2, u5} R (β₂ i) _inst_1 (_inst_8 i)] (f : forall (i : ι), LinearMap.{u2, u2, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (β₁ i) (β₂ i) (_inst_7 i) (_inst_8 i) (_inst_10 i) (_inst_11 i)) (f₂ : forall (i : ι), LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (β i) (β₁ i) (_inst_6 i) (_inst_7 i) (_inst_9 i) (_inst_10 i)), Eq.{max (succ (max u1 u3)) (succ (max u1 u5))} (LinearMap.{u2, u2, max u1 u3, max u1 u5} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (β i) (AddMonoid.toAddZeroClass.{u3} (β i) (AddCommMonoid.toAddMonoid.{u3} (β i) (_inst_6 i))))) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddZeroClass.toHasZero.{u5} (β₂ i) (AddMonoid.toAddZeroClass.{u5} (β₂ i) (AddCommMonoid.toAddMonoid.{u5} (β₂ i) (_inst_8 i))))) (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => β i) (fun (i : ι) => _inst_6 i)) (Dfinsupp.addCommMonoid.{u1, u5} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => β i) _inst_1 (fun (i : ι) => _inst_6 i) (fun (i : ι) => _inst_9 i)) (Dfinsupp.module.{u1, u5, u2} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i))) (Dfinsupp.mapRange.linearMap.{u1, u2, u3, u5} ι R _inst_1 (fun (i : ι) => β i) (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_6 i) (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_11 i) (fun (i : ι) => LinearMap.comp.{u2, u2, u2, u3, u4, u5} R R R (β i) (β₁ i) (β₂ i) _inst_1 _inst_1 _inst_1 (_inst_6 i) (_inst_7 i) (_inst_8 i) (_inst_9 i) (_inst_10 i) (_inst_11 i) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomCompTriple.right_ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (f i) (f₂ i))) (LinearMap.comp.{u2, u2, u2, max u1 u3, max u1 u4, max u1 u5} R R R (Dfinsupp.{u1, u3} ι (fun (i : ι) => β i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (β i) (AddMonoid.toAddZeroClass.{u3} (β i) (AddCommMonoid.toAddMonoid.{u3} (β i) (_inst_6 i))))) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} (β₁ i) (AddMonoid.toAddZeroClass.{u4} (β₁ i) (AddCommMonoid.toAddMonoid.{u4} (β₁ i) (_inst_7 i))))) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddZeroClass.toHasZero.{u5} (β₂ i) (AddMonoid.toAddZeroClass.{u5} (β₂ i) (AddCommMonoid.toAddMonoid.{u5} (β₂ i) (_inst_8 i))))) _inst_1 _inst_1 _inst_1 (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => β i) (fun (i : ι) => _inst_6 i)) (Dfinsupp.addCommMonoid.{u1, u4} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) (Dfinsupp.addCommMonoid.{u1, u5} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => β i) _inst_1 (fun (i : ι) => _inst_6 i) (fun (i : ι) => _inst_9 i)) (Dfinsupp.module.{u1, u4, u2} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) (Dfinsupp.module.{u1, u5, u2} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomCompTriple.right_ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Dfinsupp.mapRange.linearMap.{u1, u2, u4, u5} ι R _inst_1 (fun (i : ι) => β₁ i) (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_10 i) (fun (i : ι) => _inst_11 i) f) (Dfinsupp.mapRange.linearMap.{u1, u2, u3, u4} ι R _inst_1 (fun (i : ι) => β i) (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_6 i) (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i) f₂))
+but is expected to have type
+  forall {ι : Type.{u1}} {R : Type.{u5}} [_inst_1 : Semiring.{u5} R] {β : ι -> Type.{u2}} {β₁ : ι -> Type.{u4}} {β₂ : ι -> Type.{u3}} [_inst_6 : forall (i : ι), AddCommMonoid.{u2} (β i)] [_inst_7 : forall (i : ι), AddCommMonoid.{u4} (β₁ i)] [_inst_8 : forall (i : ι), AddCommMonoid.{u3} (β₂ i)] [_inst_9 : forall (i : ι), Module.{u5, u2} R (β i) _inst_1 (_inst_6 i)] [_inst_10 : forall (i : ι), Module.{u5, u4} R (β₁ i) _inst_1 (_inst_7 i)] [_inst_11 : forall (i : ι), Module.{u5, u3} R (β₂ i) _inst_1 (_inst_8 i)] (f : forall (i : ι), LinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (β₁ i) (β₂ i) (_inst_7 i) (_inst_8 i) (_inst_10 i) (_inst_11 i)) (f₂ : forall (i : ι), LinearMap.{u5, u5, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (β i) (β₁ i) (_inst_6 i) (_inst_7 i) (_inst_9 i) (_inst_10 i)), Eq.{max (max (succ u1) (succ u2)) (succ u3)} (LinearMap.{u5, u5, max u2 u1, max u3 u1} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (Dfinsupp.{u1, u2} ι (fun (i : ι) => β i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => β i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => β i) i) (_inst_6 i)))) (Dfinsupp.{u1, u3} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => β i) (fun (i : ι) => _inst_6 i)) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u3} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) (Dfinsupp.module.{u1, u2, u5} ι R (fun (i : ι) => β i) _inst_1 (fun (i : ι) => _inst_6 i) (fun (i : ι) => _inst_9 i)) (Dfinsupp.module.{u1, u3, u5} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i))) (Dfinsupp.mapRange.linearMap.{u1, u5, u2, u3} ι R _inst_1 (fun (i : ι) => β i) (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_6 i) (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_11 i) (fun (i : ι) => LinearMap.comp.{u5, u5, u5, u2, u4, u3} R R R (β i) (β₁ i) (β₂ i) _inst_1 _inst_1 _inst_1 (_inst_6 i) (_inst_7 i) (_inst_8 i) (_inst_9 i) (_inst_10 i) (_inst_11 i) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHomCompTriple.ids.{u5, u5} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (f i) (f₂ i))) (LinearMap.comp.{u5, u5, u5, max u2 u1, max u1 u4, max u1 u3} R R R (Dfinsupp.{u1, u2} ι (fun (i : ι) => β i) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => β i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => β i) i) (_inst_6 i)))) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) (Dfinsupp.{u1, u3} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) _inst_1 _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u2} ι (fun (i : ι) => β i) (fun (i : ι) => _inst_6 i)) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u3} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) (Dfinsupp.module.{u1, u2, u5} ι R (fun (i : ι) => β i) _inst_1 (fun (i : ι) => _inst_6 i) (fun (i : ι) => _inst_9 i)) (Dfinsupp.module.{u1, u4, u5} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) (Dfinsupp.module.{u1, u3, u5} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHomCompTriple.ids.{u5, u5} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1))) (Dfinsupp.mapRange.linearMap.{u1, u5, u4, u3} ι R _inst_1 (fun (i : ι) => β₁ i) (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_10 i) (fun (i : ι) => _inst_11 i) f) (Dfinsupp.mapRange.linearMap.{u1, u5, u2, u4} ι R _inst_1 (fun (i : ι) => β i) (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_6 i) (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i) f₂))
+Case conversion may be inaccurate. Consider using '#align dfinsupp.map_range.linear_map_comp Dfinsupp.mapRange.linearMap_compₓ'. -/
 theorem mapRange.linearMap_comp (f : ∀ i, β₁ i →ₗ[R] β₂ i) (f₂ : ∀ i, β i →ₗ[R] β₁ i) :
     (mapRange.linearMap fun i => (f i).comp (f₂ i)) =
       (mapRange.linearMap f).comp (mapRange.linearMap f₂) :=
@@ -221,6 +317,12 @@ theorem mapRange.linearMap_comp (f : ∀ i, β₁ i →ₗ[R] β₂ i) (f₂ : 
 
 include dec_ι
 
+/- warning: dfinsupp.sum_map_range_index.linear_map -> Dfinsupp.sum_mapRange_index.linearMap is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [dec_ι : DecidableEq.{succ u1} ι] [_inst_1 : Semiring.{u2} R] [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u2, u3} R N _inst_1 _inst_4] {β₁ : ι -> Type.{u4}} {β₂ : ι -> Type.{u5}} [_inst_7 : forall (i : ι), AddCommMonoid.{u4} (β₁ i)] [_inst_8 : forall (i : ι), AddCommMonoid.{u5} (β₂ i)] [_inst_10 : forall (i : ι), Module.{u2, u4} R (β₁ i) _inst_1 (_inst_7 i)] [_inst_11 : forall (i : ι), Module.{u2, u5} R (β₂ i) _inst_1 (_inst_8 i)] [_inst_12 : forall (i : ι) (x : β₁ i), Decidable (Ne.{succ u4} (β₁ i) x (OfNat.ofNat.{u4} (β₁ i) 0 (OfNat.mk.{u4} (β₁ i) 0 (Zero.zero.{u4} (β₁ i) (AddZeroClass.toHasZero.{u4} (β₁ i) (AddMonoid.toAddZeroClass.{u4} (β₁ i) (AddCommMonoid.toAddMonoid.{u4} (β₁ i) (_inst_7 i))))))))] [_inst_13 : forall (i : ι) (x : β₂ i), Decidable (Ne.{succ u5} (β₂ i) x (OfNat.ofNat.{u5} (β₂ i) 0 (OfNat.mk.{u5} (β₂ i) 0 (Zero.zero.{u5} (β₂ i) (AddZeroClass.toHasZero.{u5} (β₂ i) (AddMonoid.toAddZeroClass.{u5} (β₂ i) 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_inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat.semiring (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Pi.module.{u1, max u4 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => 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ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u1 u4) u2} Nat (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u3, u3, max u1 u4, u2} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u4, u2} R R Nat (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} 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(Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) Nat (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u1 u4) u2} (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u1 u4) u2} (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) (LinearMap.addCommMonoid.{u3, u3, max u1 u4, u2} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u1 u4) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat.semiring (Pi.addCommMonoid.{u1, max u4 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Pi.module.{u1, max u4 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u4, u2} R R Nat (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))))) (Module.toDistribMulAction.{0, max (max u1 u4) u2} Nat (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u3, u3, max u1 u4, u2} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u4, u2} R R Nat (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (SemilinearMapClass.distribMulActionHomClass.{0, max (max u1 u4) u2, max (max u1 u4) u2, max (max u1 u4) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) (LinearMap.{u3, u3, max u4 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) 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(_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u4 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u4, u2} R R Nat (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, max u1 u4, u2} R R Nat (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R 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_inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{0, 0, max (max u1 u4) u2, max (max u1 u4) u2} Nat Nat (forall (i : ι), LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) 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(LinearMap.addCommMonoid.{u3, u3, max u1 u4, u2} R R (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) _inst_4 (Dfinsupp.module.{u1, u4, u3} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u4 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₂ i) N (_inst_8 i) _inst_4 (_inst_11 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u4, u2} R R (β₂ i) N _inst_1 _inst_1 (_inst_8 i) _inst_4 (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) 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(fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))) Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (SMulZeroClass.toSMul.{0, max (max u1 u5) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (AddMonoid.toZero.{max (max u1 u5) u2} (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u1 u5) u2} (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{0, max (max u1 u5) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (AddMonoid.toAddZeroClass.{max (max u1 u5) u2} (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u1 u5) u2} (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (DistribMulAction.toDistribSMul.{0, max (max u1 u5) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u1 u5) u2} (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Module.toDistribMulAction.{0, max (max u1 u5) u2} Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) Nat.semiring (Pi.addCommMonoid.{u1, max u5 u2} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Pi.module.{u1, max u5 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u5, u2} R R Nat (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5)))))))) (SMulZeroClass.toSMul.{0, max (max u1 u5) u2} Nat (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (AddMonoid.toZero.{max (max u1 u5) u2} (LinearMap.{u3, u3, max 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(Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (LinearMap.addCommMonoid.{u3, u3, max u1 u5, u2} R R (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (DistribSMul.toSMulZeroClass.{0, max (max u1 u5) u2} Nat (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (AddMonoid.toAddZeroClass.{max (max u1 u5) u2} (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u1 u5) u2} (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (LinearMap.addCommMonoid.{u3, u3, max u1 u5, u2} R R (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (DistribMulAction.toDistribSMul.{0, max (max u1 u5) u2} Nat (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u1 u5) u2} (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ 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_inst_1 _inst_4 _inst_5))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u5) u2, 0, max (max u1 u5) u2, max (max u1 u5) u2} (LinearEquiv.{0, 0, max (max u1 u5) u2, max u2 u5 u1} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι 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R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u5 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u5, u2} R R Nat (β₁ i) N _inst_1 _inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) 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(AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))))) (Module.toDistribMulAction.{0, max (max u1 u5) u2} Nat (LinearMap.{u3, u3, max u5 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u3, u3, max u1 u5, u2} R R (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) 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(fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))) (SemilinearEquivClass.instSemilinearMapClass.{0, 0, max (max u1 u5) u2, max (max u1 u5) u2, max (max u1 u5) u2} Nat Nat (forall (i : ι), LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R 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_inst_1 (_inst_7 i) _inst_4 (_inst_10 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, max u1 u5, u2} R R (Dfinsupp.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u5} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u5} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) N _inst_1 _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u5} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) _inst_4 (Dfinsupp.module.{u1, u5, u3} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Pi.module.{u1, max u5 u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (β₁ i) N (_inst_7 i) _inst_4 (_inst_10 i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u5, u2} R R (β₁ i) N _inst_1 _inst_1 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(AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u1, u3, 0, u5, u2} ι R Nat β₁ N (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i) _inst_4 _inst_5 Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_4) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_4) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_4 _inst_5))) (fun (i : ι) => LinearMap.comp.{u3, u3, u3, u5, u4, u2} R R R (β₁ i) (β₂ i) N _inst_1 _inst_1 _inst_1 (_inst_7 i) (_inst_8 i) _inst_4 (_inst_10 i) (_inst_11 i) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomCompTriple.ids.{u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (h i) (f i))) l)
+Case conversion may be inaccurate. Consider using '#align dfinsupp.sum_map_range_index.linear_map Dfinsupp.sum_mapRange_index.linearMapₓ'. -/
 theorem sum_mapRange_index.linearMap [∀ (i : ι) (x : β₁ i), Decidable (x ≠ 0)]
     [∀ (i : ι) (x : β₂ i), Decidable (x ≠ 0)] {f : ∀ i, β₁ i →ₗ[R] β₂ i} {h : ∀ i, β₂ i →ₗ[R] N}
     {l : Π₀ i, β₁ i} :
@@ -232,6 +334,12 @@ theorem sum_mapRange_index.linearMap [∀ (i : ι) (x : β₁ i), Decidable (x 
 
 omit dec_ι
 
+/- warning: dfinsupp.map_range.linear_equiv -> Dfinsupp.mapRange.linearEquiv is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {β₁ : ι -> Type.{u3}} {β₂ : ι -> Type.{u4}} [_inst_7 : forall (i : ι), AddCommMonoid.{u3} (β₁ i)] [_inst_8 : forall (i : ι), AddCommMonoid.{u4} (β₂ i)] [_inst_10 : forall (i : ι), Module.{u2, u3} R (β₁ i) _inst_1 (_inst_7 i)] [_inst_11 : forall (i : ι), Module.{u2, u4} R (β₂ i) _inst_1 (_inst_8 i)], (forall (i : ι), LinearEquiv.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (β₁ i) (β₂ i) (_inst_7 i) (_inst_8 i) (_inst_10 i) (_inst_11 i)) -> (LinearEquiv.{u2, u2, max u1 u3, max u1 u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (Dfinsupp.{u1, u3} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (β₁ i) (AddMonoid.toAddZeroClass.{u3} (β₁ i) (AddCommMonoid.toAddMonoid.{u3} (β₁ i) (_inst_7 i))))) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddZeroClass.toHasZero.{u4} (β₂ i) (AddMonoid.toAddZeroClass.{u4} (β₂ i) (AddCommMonoid.toAddMonoid.{u4} (β₂ i) (_inst_8 i))))) (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) (Dfinsupp.addCommMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) (Dfinsupp.module.{u1, u4, u2} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)))
+but is expected to have type
+  forall {ι : Type.{u1}} {R : Type.{u2}} [_inst_1 : Semiring.{u2} R] {β₁ : ι -> Type.{u3}} {β₂ : ι -> Type.{u4}} [_inst_7 : forall (i : ι), AddCommMonoid.{u3} (β₁ i)] [_inst_8 : forall (i : ι), AddCommMonoid.{u4} (β₂ i)] [_inst_10 : forall (i : ι), Module.{u2, u3} R (β₁ i) _inst_1 (_inst_7 i)] [_inst_11 : forall (i : ι), Module.{u2, u4} R (β₂ i) _inst_1 (_inst_8 i)], (forall (i : ι), LinearEquiv.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (β₁ i) (β₂ i) (_inst_7 i) (_inst_8 i) (_inst_10 i) (_inst_11 i)) -> (LinearEquiv.{u2, u2, max u3 u1, max u4 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (Dfinsupp.{u1, u3} ι (fun (i : ι) => β₁ i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => β₁ i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => β₁ i) i) (_inst_7 i)))) (Dfinsupp.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => AddMonoid.toZero.{u4} ((fun (i : ι) => β₂ i) i) (AddCommMonoid.toAddMonoid.{u4} ((fun (i : ι) => β₂ i) i) (_inst_8 i)))) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u3} ι (fun (i : ι) => β₁ i) (fun (i : ι) => _inst_7 i)) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u4} ι (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_8 i)) (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => β₁ i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_10 i)) (Dfinsupp.module.{u1, u4, u2} ι R (fun (i : ι) => β₂ i) _inst_1 (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_11 i)))
+Case conversion may be inaccurate. Consider using '#align dfinsupp.map_range.linear_equiv Dfinsupp.mapRange.linearEquivₓ'. -/
 /-- `dfinsupp.map_range.linear_map` as an `linear_equiv`. -/
 @[simps apply]
 def mapRange.linearEquiv (e : ∀ i, β₁ i ≃ₗ[R] β₂ i) : (Π₀ i, β₁ i) ≃ₗ[R] Π₀ i, β₂ i :=
@@ -242,18 +350,36 @@ def mapRange.linearEquiv (e : ∀ i, β₁ i ≃ₗ[R] β₂ i) : (Π₀ i, β
     invFun := mapRange (fun i x => (e i).symm x) fun i => (e i).symm.map_zero }
 #align dfinsupp.map_range.linear_equiv Dfinsupp.mapRange.linearEquiv
 
+/- warning: dfinsupp.map_range.linear_equiv_refl -> Dfinsupp.mapRange.linearEquiv_refl is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align dfinsupp.map_range.linear_equiv_refl Dfinsupp.mapRange.linearEquiv_reflₓ'. -/
 @[simp]
 theorem mapRange.linearEquiv_refl :
     (mapRange.linearEquiv fun i => LinearEquiv.refl R (β₁ i)) = LinearEquiv.refl _ _ :=
   LinearEquiv.ext mapRange_id
 #align dfinsupp.map_range.linear_equiv_refl Dfinsupp.mapRange.linearEquiv_refl
 
+/- warning: dfinsupp.map_range.linear_equiv_trans -> Dfinsupp.mapRange.linearEquiv_trans is a dubious translation:
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f) (Dfinsupp.mapRange.linearEquiv.{u1, u5, u3, u2} ι R _inst_1 (fun (i : ι) => β₁ i) (fun (i : ι) => β₂ i) (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_10 i) (fun (i : ι) => _inst_11 i) f₂))
+Case conversion may be inaccurate. Consider using '#align dfinsupp.map_range.linear_equiv_trans Dfinsupp.mapRange.linearEquiv_transₓ'. -/
 theorem mapRange.linearEquiv_trans (f : ∀ i, β i ≃ₗ[R] β₁ i) (f₂ : ∀ i, β₁ i ≃ₗ[R] β₂ i) :
     (mapRange.linearEquiv fun i => (f i).trans (f₂ i)) =
       (mapRange.linearEquiv f).trans (mapRange.linearEquiv f₂) :=
   LinearEquiv.ext <| mapRange_comp (fun i x => f₂ i x) (fun i x => f i x) _ _ _
 #align dfinsupp.map_range.linear_equiv_trans Dfinsupp.mapRange.linearEquiv_trans
 
+/- warning: dfinsupp.map_range.linear_equiv_symm -> Dfinsupp.mapRange.linearEquiv_symm is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align dfinsupp.map_range.linear_equiv_symm Dfinsupp.mapRange.linearEquiv_symmₓ'. -/
 @[simp]
 theorem mapRange.linearEquiv_symm (e : ∀ i, β₁ i ≃ₗ[R] β₂ i) :
     (mapRange.linearEquiv e).symm = mapRange.linearEquiv fun i => (e i).symm :=
@@ -266,6 +392,12 @@ section CoprodMap
 
 variable [DecidableEq ι] [∀ x : N, Decidable (x ≠ 0)]
 
+/- warning: dfinsupp.coprod_map -> Dfinsupp.coprodMap is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {M : ι -> Type.{u3}} {N : Type.{u4}} [_inst_1 : Semiring.{u2} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (M i)] [_inst_3 : forall (i : ι), Module.{u2, u3} R (M i) _inst_1 (_inst_2 i)] [_inst_4 : AddCommMonoid.{u4} N] [_inst_5 : Module.{u2, u4} R N _inst_1 _inst_4] [_inst_6 : DecidableEq.{succ u1} ι] [_inst_7 : forall (x : N), Decidable (Ne.{succ u4} N x (OfNat.ofNat.{u4} N 0 (OfNat.mk.{u4} N 0 (Zero.zero.{u4} N (AddZeroClass.toHasZero.{u4} N (AddMonoid.toAddZeroClass.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_4)))))))], (forall (i : ι), LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) -> (LinearMap.{u2, u2, max u1 u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_2 i))))) N (Dfinsupp.addCommMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5)
+but is expected to have type
+  forall {ι : Type.{u1}} {R : Type.{u2}} {M : ι -> Type.{u3}} {N : Type.{u4}} [_inst_1 : Semiring.{u2} R] [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (M i)] [_inst_3 : forall (i : ι), Module.{u2, u3} R (M i) _inst_1 (_inst_2 i)] [_inst_4 : AddCommMonoid.{u4} N] [_inst_5 : Module.{u2, u4} R N _inst_1 _inst_4] [_inst_6 : DecidableEq.{succ u1} ι] [_inst_7 : forall (x : N), Decidable (Ne.{succ u4} N x (OfNat.ofNat.{u4} N 0 (Zero.toOfNat0.{u4} N (AddMonoid.toZero.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_4)))))], (forall (i : ι), LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (M i) N (_inst_2 i) _inst_4 (_inst_3 i) _inst_5) -> (LinearMap.{u2, u2, max u3 u1, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Dfinsupp.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_2 i)))) N (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_2 i)) _inst_4 (Dfinsupp.module.{u1, u3, u2} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) _inst_5)
+Case conversion may be inaccurate. Consider using '#align dfinsupp.coprod_map Dfinsupp.coprodMapₓ'. -/
 /-- Given a family of linear maps `f i : M i  →ₗ[R] N`, we can form a linear map
 `(Π₀ i, M i) →ₗ[R] N` which sends `x : Π₀ i, M i` to the sum over `i` of `f i` applied to `x i`.
 This is the map coming from the universal property of `Π₀ i, M i` as the coproduct of the `M i`.
@@ -275,6 +407,12 @@ noncomputable def coprodMap (f : ∀ i : ι, M i →ₗ[R] N) : (Π₀ i, M i) 
     (@finsuppLequivDfinsupp ι R N _ _ _ _ _).symm.toLinearMap ∘ₗ Dfinsupp.mapRange.linearMap f
 #align dfinsupp.coprod_map Dfinsupp.coprodMap
 
+/- warning: dfinsupp.coprod_map_apply -> Dfinsupp.coprodMap_apply is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align dfinsupp.coprod_map_apply Dfinsupp.coprodMap_applyₓ'. -/
 theorem coprodMap_apply (f : ∀ i : ι, M i →ₗ[R] N) (x : Π₀ i, M i) :
     coprodMap f x =
       Finsupp.sum (mapRange (fun i => f i) (fun i => LinearMap.map_zero _) x).toFinsupp fun i =>
@@ -286,6 +424,12 @@ end CoprodMap
 
 section Basis
 
+/- warning: dfinsupp.basis -> Dfinsupp.basis is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align dfinsupp.basis Dfinsupp.basisₓ'. -/
 /-- The direct sum of free modules is free.
 
 Note that while this is stated for `dfinsupp` not `direct_sum`, the types are defeq. -/
@@ -307,18 +451,36 @@ variable [Semiring R] [AddCommMonoid N] [Module R N]
 
 open Dfinsupp
 
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+Case conversion may be inaccurate. Consider using '#align submodule.dfinsupp_sum_mem Submodule.dfinsupp_sum_memₓ'. -/
 theorem dfinsupp_sum_mem {β : ι → Type _} [∀ i, Zero (β i)] [∀ (i) (x : β i), Decidable (x ≠ 0)]
     (S : Submodule R N) (f : Π₀ i, β i) (g : ∀ i, β i → N) (h : ∀ c, f c ≠ 0 → g c (f c) ∈ S) :
     f.Sum g ∈ S :=
   dfinsupp_sum_mem S f g h
 #align submodule.dfinsupp_sum_mem Submodule.dfinsupp_sum_mem
 
+/- warning: submodule.dfinsupp_sum_add_hom_mem -> Submodule.dfinsupp_sumAddHom_mem is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align submodule.dfinsupp_sum_add_hom_mem Submodule.dfinsupp_sumAddHom_memₓ'. -/
 theorem dfinsupp_sumAddHom_mem {β : ι → Type _} [∀ i, AddZeroClass (β i)] (S : Submodule R N)
     (f : Π₀ i, β i) (g : ∀ i, β i →+ N) (h : ∀ c, f c ≠ 0 → g c (f c) ∈ S) :
     Dfinsupp.sumAddHom g f ∈ S :=
   dfinsupp_sumAddHom_mem S f g h
 #align submodule.dfinsupp_sum_add_hom_mem Submodule.dfinsupp_sumAddHom_mem
 
+/- warning: submodule.supr_eq_range_dfinsupp_lsum -> Submodule.supᵢ_eq_range_dfinsupp_lsum is a dubious translation:
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(Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3) (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N 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_inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{0, max u1 u2} Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3) (AddMonoid.toAddZeroClass.{max u1 u2} (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N 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i)) _inst_2 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N _inst_1 _inst_1 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) 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_inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3) (fun (i : ι) => LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N _inst_1 _inst_1 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 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LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N _inst_1 _inst_1 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Pi.module.{u1, u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 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_inst_2 _inst_3 (p i))))
+Case conversion may be inaccurate. Consider using '#align submodule.supr_eq_range_dfinsupp_lsum Submodule.supᵢ_eq_range_dfinsupp_lsumₓ'. -/
 /-- The supremum of a family of submodules is equal to the range of `dfinsupp.lsum`; that is
 every element in the `supr` can be produced from taking a finite number of non-zero elements
 of `p i`, coercing them to `N`, and summing them. -/
@@ -333,11 +495,17 @@ theorem supᵢ_eq_range_dfinsupp_lsum (p : ι → Submodule R N) :
     exact dfinsupp_sumAddHom_mem _ v _ fun i _ => (le_supᵢ p i : p i ≤ _) (v i).Prop
 #align submodule.supr_eq_range_dfinsupp_lsum Submodule.supᵢ_eq_range_dfinsupp_lsum
 
+/- warning: submodule.bsupr_eq_range_dfinsupp_lsum -> Submodule.bsupᵢ_eq_range_dfinsupp_lsum is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align submodule.bsupr_eq_range_dfinsupp_lsum Submodule.bsupᵢ_eq_range_dfinsupp_lsumₓ'. -/
 /-- The bounded supremum of a family of commutative additive submonoids is equal to the range of
 `dfinsupp.sum_add_hom` composed with `dfinsupp.filter_add_monoid_hom`; that is, every element in the
 bounded `supr` can be produced from taking a finite number of non-zero elements from the `S i` that
 satisfy `p i`, coercing them to `γ`, and summing them. -/
-theorem bsupr_eq_range_dfinsupp_lsum (p : ι → Prop) [DecidablePred p] (S : ι → Submodule R N) :
+theorem bsupᵢ_eq_range_dfinsupp_lsum (p : ι → Prop) [DecidablePred p] (S : ι → Submodule R N) :
     (⨆ (i) (h : p i), S i) =
       ((Dfinsupp.lsum ℕ fun i => (S i).Subtype).comp (Dfinsupp.filterLinearMap R _ p)).range :=
   by
@@ -351,13 +519,25 @@ theorem bsupr_eq_range_dfinsupp_lsum (p : ι → Prop) [DecidablePred p] (S : ι
     by_cases hp : p i
     · simp [hp]
     · simp [hp]
-#align submodule.bsupr_eq_range_dfinsupp_lsum Submodule.bsupr_eq_range_dfinsupp_lsum
-
+#align submodule.bsupr_eq_range_dfinsupp_lsum Submodule.bsupᵢ_eq_range_dfinsupp_lsum
+
+/- warning: submodule.mem_supr_iff_exists_dfinsupp -> Submodule.mem_supᵢ_iff_exists_dfinsupp is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_iff_exists_dfinsupp Submodule.mem_supᵢ_iff_exists_dfinsuppₓ'. -/
 theorem mem_supᵢ_iff_exists_dfinsupp (p : ι → Submodule R N) (x : N) :
     x ∈ supᵢ p ↔ ∃ f : Π₀ i, p i, Dfinsupp.lsum ℕ (fun i => (p i).Subtype) f = x :=
   SetLike.ext_iff.mp (supᵢ_eq_range_dfinsupp_lsum p) x
 #align submodule.mem_supr_iff_exists_dfinsupp Submodule.mem_supᵢ_iff_exists_dfinsupp
 
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+Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_iff_exists_dfinsupp' Submodule.mem_supᵢ_iff_exists_dfinsupp'ₓ'. -/
 /-- A variant of `submodule.mem_supr_iff_exists_dfinsupp` with the RHS fully unfolded. -/
 theorem mem_supᵢ_iff_exists_dfinsupp' (p : ι → Submodule R N) [∀ (i) (x : p i), Decidable (x ≠ 0)]
     (x : N) : x ∈ supᵢ p ↔ ∃ f : Π₀ i, p i, (f.Sum fun i xi => ↑xi) = x :=
@@ -367,17 +547,29 @@ theorem mem_supᵢ_iff_exists_dfinsupp' (p : ι → Submodule R N) [∀ (i) (x :
   congr
 #align submodule.mem_supr_iff_exists_dfinsupp' Submodule.mem_supᵢ_iff_exists_dfinsupp'
 
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+Case conversion may be inaccurate. Consider using '#align submodule.mem_bsupr_iff_exists_dfinsupp Submodule.mem_bsupr_iff_exists_dfinsuppₓ'. -/
 theorem mem_bsupr_iff_exists_dfinsupp (p : ι → Prop) [DecidablePred p] (S : ι → Submodule R N)
     (x : N) :
     (x ∈ ⨆ (i) (h : p i), S i) ↔
       ∃ f : Π₀ i, S i, Dfinsupp.lsum ℕ (fun i => (S i).Subtype) (f.filterₓ p) = x :=
-  SetLike.ext_iff.mp (bsupr_eq_range_dfinsupp_lsum p S) x
+  SetLike.ext_iff.mp (bsupᵢ_eq_range_dfinsupp_lsum p S) x
 #align submodule.mem_bsupr_iff_exists_dfinsupp Submodule.mem_bsupr_iff_exists_dfinsupp
 
 open BigOperators
 
 omit dec_ι
 
+/- warning: submodule.mem_supr_finset_iff_exists_sum -> Submodule.mem_supᵢ_finset_iff_exists_sum is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_finset_iff_exists_sum Submodule.mem_supᵢ_finset_iff_exists_sumₓ'. -/
 theorem mem_supᵢ_finset_iff_exists_sum {s : Finset ι} (p : ι → Submodule R N) (a : N) :
     (a ∈ ⨆ i ∈ s, p i) ↔ ∃ μ : ∀ i, p i, (∑ i in s, (μ i : N)) = a := by
   classical
@@ -425,6 +617,12 @@ section Semiring
 
 variable [Semiring R] [AddCommMonoid N] [Module R N]
 
+/- warning: complete_lattice.independent_iff_forall_dfinsupp -> CompleteLattice.independent_iff_forall_dfinsupp is a dubious translation:
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LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N _inst_1 _inst_1 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (DistribMulAction.toDistribSMul.{0, max u1 u2} Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, 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+Case conversion may be inaccurate. Consider using '#align complete_lattice.independent_iff_forall_dfinsupp CompleteLattice.independent_iff_forall_dfinsuppₓ'. -/
 /-- Independence of a family of submodules can be expressed as a quantifier over `dfinsupp`s.
 
 This is an intermediate result used to prove
@@ -443,6 +641,12 @@ theorem independent_iff_forall_dfinsupp (p : ι → Submodule R N) :
   rfl
 #align complete_lattice.independent_iff_forall_dfinsupp CompleteLattice.independent_iff_forall_dfinsupp
 
+/- warning: complete_lattice.independent_of_dfinsupp_lsum_injective -> CompleteLattice.independent_of_dfinsupp_lsum_injective is a dubious translation:
+lean 3 declaration is
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LinearMap.addCommMonoid.{u3, u3, u2, u2} R R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N _inst_1 _inst_1 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (DistribMulAction.toDistribSMul.{0, max u1 u2} Nat (forall (i : ι), LinearMap.{u3, u3, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, 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+Case conversion may be inaccurate. Consider using '#align complete_lattice.independent_of_dfinsupp_lsum_injective CompleteLattice.independent_of_dfinsupp_lsum_injectiveₓ'. -/
 /- If `dfinsupp.lsum` applied with `submodule.subtype` is injective then the submodules are
 independent. -/
 theorem independent_of_dfinsupp_lsum_injective (p : ι → Submodule R N)
@@ -457,6 +661,12 @@ theorem independent_of_dfinsupp_lsum_injective (p : ι → Submodule R N)
   simpa [eq_comm] using this
 #align complete_lattice.independent_of_dfinsupp_lsum_injective CompleteLattice.independent_of_dfinsupp_lsum_injective
 
+/- warning: complete_lattice.independent_of_dfinsupp_sum_add_hom_injective -> CompleteLattice.independent_of_dfinsupp_sumAddHom_injective is a dubious translation:
+lean 3 declaration is
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(AddCommMonoid.toAddMonoid.{u2} N _inst_2))) p)
+Case conversion may be inaccurate. Consider using '#align complete_lattice.independent_of_dfinsupp_sum_add_hom_injective CompleteLattice.independent_of_dfinsupp_sumAddHom_injectiveₓ'. -/
 /- If `dfinsupp.sum_add_hom` applied with `add_submonoid.subtype` is injective then the additive
 submonoids are independent. -/
 theorem independent_of_dfinsupp_sumAddHom_injective (p : ι → AddSubmonoid N)
@@ -466,8 +676,14 @@ theorem independent_of_dfinsupp_sumAddHom_injective (p : ι → AddSubmonoid N)
   exact independent_of_dfinsupp_lsum_injective _ h
 #align complete_lattice.independent_of_dfinsupp_sum_add_hom_injective CompleteLattice.independent_of_dfinsupp_sumAddHom_injective
 
+/- warning: complete_lattice.lsum_comp_map_range_to_span_singleton -> CompleteLattice.lsum_comp_mapRange_toSpanSingleton is a dubious translation:
+lean 3 declaration is
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=> Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Dfinsupp.lsum.{u1, u3, 0, u2, u2} ι R Nat (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) N (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (fun (i : ι) => Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) _inst_2 _inst_3 Nat.semiring (AddCommMonoid.natModule.{u2} N _inst_2) (AddMonoid.nat_smulCommClass'.{u3, u2} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} N _inst_2) (Module.toDistribMulAction.{u3, u2} R N _inst_1 _inst_2 _inst_3))) (fun (i : ι) => Submodule.subtype.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))) (LinearMap.comp.{u3, u3, u3, max u1 u3, max u1 u3, max u1 u2} R R R (Finsupp.{u1, u3} ι R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (Dfinsupp.{u1, u3} ι (fun (i : ι) => R) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => R) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => R) i) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) i) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i))))) _inst_1 _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) 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(RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomCompTriple.ids.{u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Dfinsupp.mapRange.linearMap.{u1, u3, u3, u2} ι R _inst_1 (fun (i : ι) => R) (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => Semiring.toModule.{u3} R _inst_1) (fun (i : ι) => Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (fun (i : ι) => LinearMap.toSpanSingleton.{u3, u2} R (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i))) _inst_1 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3 (p i)) (Subtype.mk.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N _inst_1 _inst_2 _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N _inst_1 _inst_2 _inst_3)) x (p i)) (v i) (hv i)))) (LinearEquiv.toLinearMap.{u3, u3, max u1 u3, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Finsupp.{u1, u3} ι R (AddMonoid.toZero.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (Dfinsupp.{u1, u3} ι (fun (i : ι) => R) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (_i : ι) => R) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (_i : ι) => R) i) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (Finsupp.addCommMonoid.{u1, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u1, u3} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u3, u3} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (Dfinsupp.module.{u1, u3, u3} ι R (fun (i : ι) => R) _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (i : ι) => Semiring.toModule.{u3} R _inst_1)) (finsuppLequivDfinsupp.{u1, u3, u3} ι R R (fun (a : ι) (b : ι) => dec_ι a b) _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (fun (m : R) => _inst_4 m) (Semiring.toModule.{u3} R _inst_1))))) (Finsupp.total.{u1, u2, u3} ι N R _inst_1 _inst_2 _inst_3 v)
+Case conversion may be inaccurate. Consider using '#align complete_lattice.lsum_comp_map_range_to_span_singleton CompleteLattice.lsum_comp_mapRange_toSpanSingletonₓ'. -/
 /-- Combining `dfinsupp.lsum` with `linear_map.to_span_singleton` is the same as `finsupp.total` -/
-theorem lsum_comp_map_range_toSpanSingleton [∀ m : R, Decidable (m ≠ 0)] (p : ι → Submodule R N)
+theorem lsum_comp_mapRange_toSpanSingleton [∀ m : R, Decidable (m ≠ 0)] (p : ι → Submodule R N)
     {v : ι → N} (hv : ∀ i : ι, v i ∈ p i) :
     ((lsum ℕ) fun i => (p i).Subtype : _ →ₗ[R] _).comp
         ((mapRange.linearMap fun i => LinearMap.toSpanSingleton R (↥(p i)) ⟨v i, hv i⟩ :
@@ -477,7 +693,7 @@ theorem lsum_comp_map_range_toSpanSingleton [∀ m : R, Decidable (m ≠ 0)] (p
   by
   ext
   simp
-#align complete_lattice.lsum_comp_map_range_to_span_singleton CompleteLattice.lsum_comp_map_range_toSpanSingleton
+#align complete_lattice.lsum_comp_map_range_to_span_singleton CompleteLattice.lsum_comp_mapRange_toSpanSingleton
 
 end Semiring
 
@@ -485,6 +701,12 @@ section Ring
 
 variable [Ring R] [AddCommGroup N] [Module R N]
 
+/- warning: complete_lattice.independent_of_dfinsupp_sum_add_hom_injective' -> CompleteLattice.independent_of_dfinsupp_sumAddHom_injective' is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align complete_lattice.independent_of_dfinsupp_sum_add_hom_injective' CompleteLattice.independent_of_dfinsupp_sumAddHom_injective'ₓ'. -/
 /- If `dfinsupp.sum_add_hom` applied with `add_submonoid.subtype` is injective then the additive
 subgroups are independent. -/
 theorem independent_of_dfinsupp_sumAddHom_injective' (p : ι → AddSubgroup N)
@@ -494,6 +716,12 @@ theorem independent_of_dfinsupp_sumAddHom_injective' (p : ι → AddSubgroup N)
   exact independent_of_dfinsupp_lsum_injective _ h
 #align complete_lattice.independent_of_dfinsupp_sum_add_hom_injective' CompleteLattice.independent_of_dfinsupp_sumAddHom_injective'
 
+/- warning: complete_lattice.independent.dfinsupp_lsum_injective -> CompleteLattice.Independent.dfinsupp_lsum_injective is a dubious translation:
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_inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))))) (LinearMap.addCommMonoid.{u3, u3, max u1 u2, u2} R R (Dfinsupp.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) 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u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (fun (i : ι) => Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i))) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) (Pi.module.{u1, u2, 0} ι (fun (i : ι) => LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N 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_inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3) N (Submodule.instSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3)) x (p i))) N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} N _inst_2) _inst_3 (p i)) _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 0, u2, u2} R R Nat (Subtype.{succ u2} N (fun (x : N) => 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+Case conversion may be inaccurate. Consider using '#align complete_lattice.independent.dfinsupp_lsum_injective CompleteLattice.Independent.dfinsupp_lsum_injectiveₓ'. -/
 /-- The canonical map out of a direct sum of a family of submodules is injective when the submodules
 are `complete_lattice.independent`.
 
@@ -522,6 +750,12 @@ theorem Independent.dfinsupp_lsum_injective {p : ι → Submodule R N} (h : Inde
     add_eq_zero_iff_eq_neg, ← Submodule.coe_neg] at hm
 #align complete_lattice.independent.dfinsupp_lsum_injective CompleteLattice.Independent.dfinsupp_lsum_injective
 
+/- warning: complete_lattice.independent.dfinsupp_sum_add_hom_injective -> CompleteLattice.Independent.dfinsupp_sumAddHom_injective is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align complete_lattice.independent.dfinsupp_sum_add_hom_injective CompleteLattice.Independent.dfinsupp_sumAddHom_injectiveₓ'. -/
 /-- The canonical map out of a direct sum of a family of additive subgroups is injective when the
 additive subgroups are `complete_lattice.independent`. -/
 theorem Independent.dfinsupp_sumAddHom_injective {p : ι → AddSubgroup N} (h : Independent p) :
@@ -531,6 +765,12 @@ theorem Independent.dfinsupp_sumAddHom_injective {p : ι → AddSubgroup N} (h :
   exact h.dfinsupp_lsum_injective
 #align complete_lattice.independent.dfinsupp_sum_add_hom_injective CompleteLattice.Independent.dfinsupp_sumAddHom_injective
 
+/- warning: complete_lattice.independent_iff_dfinsupp_lsum_injective -> CompleteLattice.independent_iff_dfinsupp_lsum_injective is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align complete_lattice.independent_iff_dfinsupp_lsum_injective CompleteLattice.independent_iff_dfinsupp_lsum_injectiveₓ'. -/
 /-- A family of submodules over an additive group are independent if and only iff `dfinsupp.lsum`
 applied with `submodule.subtype` is injective.
 
@@ -541,6 +781,12 @@ theorem independent_iff_dfinsupp_lsum_injective (p : ι → Submodule R N) :
   ⟨Independent.dfinsupp_lsum_injective, independent_of_dfinsupp_lsum_injective p⟩
 #align complete_lattice.independent_iff_dfinsupp_lsum_injective CompleteLattice.independent_iff_dfinsupp_lsum_injective
 
+/- warning: complete_lattice.independent_iff_dfinsupp_sum_add_hom_injective -> CompleteLattice.independent_iff_dfinsupp_sumAddHom_injective is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align complete_lattice.independent_iff_dfinsupp_sum_add_hom_injective CompleteLattice.independent_iff_dfinsupp_sumAddHom_injectiveₓ'. -/
 /-- A family of additive subgroups over an additive group are independent if and only if
 `dfinsupp.sum_add_hom` applied with `add_subgroup.subtype` is injective. -/
 theorem independent_iff_dfinsupp_sumAddHom_injective (p : ι → AddSubgroup N) :
@@ -550,6 +796,12 @@ theorem independent_iff_dfinsupp_sumAddHom_injective (p : ι → AddSubgroup N)
 
 omit dec_ι
 
+/- warning: complete_lattice.independent.linear_independent -> CompleteLattice.Independent.linearIndependent is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} N] [_inst_3 : Module.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2)] [_inst_4 : NoZeroSMulDivisors.{u2, u3} R N (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (SubNegMonoid.toAddMonoid.{u3} N (AddGroup.toSubNegMonoid.{u3} N (AddCommGroup.toAddGroup.{u3} N _inst_2))))) (SMulZeroClass.toHasSmul.{u2, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N _inst_2)))) (SMulWithZero.toSmulZeroClass.{u2, u3} R N (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N _inst_2)))) (MulActionWithZero.toSMulWithZero.{u2, u3} R N (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N _inst_2)))) (Module.toMulActionWithZero.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3))))] (p : ι -> (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3)), (CompleteLattice.Independent.{succ u1, u3} ι (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) (Submodule.completeLattice.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) p) -> (forall {v : ι -> N}, (forall (i : ι), Membership.Mem.{u3, u3} N (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) N (Submodule.setLike.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3)) (v i) (p i)) -> (forall (i : ι), Ne.{succ u3} N (v i) (OfNat.ofNat.{u3} N 0 (OfNat.mk.{u3} N 0 (Zero.zero.{u3} N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (SubNegMonoid.toAddMonoid.{u3} N (AddGroup.toSubNegMonoid.{u3} N (AddCommGroup.toAddGroup.{u3} N _inst_2))))))))) -> (LinearIndependent.{u1, u2, u3} ι R N v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3))
+but is expected to have type
+  forall {ι : Type.{u1}} {R : Type.{u3}} {N : Type.{u2}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : Ring.{u3} R] [_inst_3 : AddCommGroup.{u2} N] [_inst_4 : Module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3)] [p : NoZeroSMulDivisors.{u3, u2} R N (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_2))) (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N _inst_3))))) (SMulZeroClass.toSMul.{u3, u2} R N (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N _inst_3))))) (SMulWithZero.toSMulZeroClass.{u3, u2} R N (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_2))) (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N _inst_3))))) (MulActionWithZero.toSMulWithZero.{u3, u2} R N (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_2)) (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N _inst_3))))) (Module.toMulActionWithZero.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4))))] (hp : ι -> (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4)), (CompleteLattice.Independent.{succ u1, u2} ι (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4) (Submodule.completeLattice.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4) hp) -> (forall {hv : ι -> N}, (forall (i : ι), Membership.mem.{u2, u2} N (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4) N (Submodule.instSetLikeSubmodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4)) (hv i) (hp i)) -> (forall (i : ι), Ne.{succ u2} N (hv i) (OfNat.ofNat.{u2} N 0 (Zero.toOfNat0.{u2} N (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N _inst_3)))))))) -> (LinearIndependent.{u1, u3, u2} ι R N hv (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4))
+Case conversion may be inaccurate. Consider using '#align complete_lattice.independent.linear_independent CompleteLattice.Independent.linearIndependentₓ'. -/
 /-- If a family of submodules is `independent`, then a choice of nonzero vector from each submodule
 forms a linearly independent family.
 
@@ -572,6 +824,12 @@ theorem Independent.linearIndependent [NoZeroSMulDivisors R N] (p : ι → Submo
     simp [this, ha]
 #align complete_lattice.independent.linear_independent CompleteLattice.Independent.linearIndependent
 
+/- warning: complete_lattice.independent_iff_linear_independent_of_ne_zero -> CompleteLattice.independent_iff_linearIndependent_of_ne_zero is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {N : Type.{u3}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} N] [_inst_3 : Module.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2)] [_inst_4 : NoZeroSMulDivisors.{u2, u3} R N (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (SubNegMonoid.toAddMonoid.{u3} N (AddGroup.toSubNegMonoid.{u3} N (AddCommGroup.toAddGroup.{u3} N _inst_2))))) (SMulZeroClass.toHasSmul.{u2, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N _inst_2)))) (SMulWithZero.toSmulZeroClass.{u2, u3} R N (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N _inst_2)))) (MulActionWithZero.toSMulWithZero.{u2, u3} R N (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N _inst_2)))) (Module.toMulActionWithZero.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3))))] {v : ι -> N}, (forall (i : ι), Ne.{succ u3} N (v i) (OfNat.ofNat.{u3} N 0 (OfNat.mk.{u3} N 0 (Zero.zero.{u3} N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (SubNegMonoid.toAddMonoid.{u3} N (AddGroup.toSubNegMonoid.{u3} N (AddCommGroup.toAddGroup.{u3} N _inst_2))))))))) -> (Iff (CompleteLattice.Independent.{succ u1, u3} ι (Submodule.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) (Submodule.completeLattice.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3) (fun (i : ι) => Submodule.span.{u2, u3} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3 (Singleton.singleton.{u3, u3} N (Set.{u3} N) (Set.hasSingleton.{u3} N) (v i)))) (LinearIndependent.{u1, u2, u3} ι R N v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_2) _inst_3))
+but is expected to have type
+  forall {ι : Type.{u1}} {R : Type.{u3}} {N : Type.{u2}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : Ring.{u3} R] [_inst_3 : AddCommGroup.{u2} N] [_inst_4 : Module.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3)] [v : NoZeroSMulDivisors.{u3, u2} R N (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_2))) (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N _inst_3))))) (SMulZeroClass.toSMul.{u3, u2} R N (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N _inst_3))))) (SMulWithZero.toSMulZeroClass.{u3, u2} R N (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_2))) (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N _inst_3))))) (MulActionWithZero.toSMulWithZero.{u3, u2} R N (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R _inst_2)) (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N _inst_3))))) (Module.toMulActionWithZero.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4))))] {h_ne_zero : ι -> N}, (forall (i : ι), Ne.{succ u2} N (h_ne_zero i) (OfNat.ofNat.{u2} N 0 (Zero.toOfNat0.{u2} N (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N _inst_3)))))))) -> (Iff (CompleteLattice.Independent.{succ u1, u2} ι (Submodule.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4) (Submodule.completeLattice.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4) (fun (i : ι) => Submodule.span.{u3, u2} R N (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4 (Singleton.singleton.{u2, u2} N (Set.{u2} N) (Set.instSingletonSet.{u2} N) (h_ne_zero i)))) (LinearIndependent.{u1, u3, u2} ι R N h_ne_zero (Ring.toSemiring.{u3} R _inst_2) (AddCommGroup.toAddCommMonoid.{u2} N _inst_3) _inst_4))
+Case conversion may be inaccurate. Consider using '#align complete_lattice.independent_iff_linear_independent_of_ne_zero CompleteLattice.independent_iff_linearIndependent_of_ne_zeroₓ'. -/
 theorem independent_iff_linearIndependent_of_ne_zero [NoZeroSMulDivisors R N] {v : ι → N}
     (h_ne_zero : ∀ i, v i ≠ 0) : (Independent fun i => R ∙ v i) ↔ LinearIndependent R v :=
   ⟨fun hv => hv.LinearIndependent _ (fun i => Submodule.mem_span_singleton_self <| v i) h_ne_zero,

a148d797

bump to nightly-2023-02-21-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

1107b979

Changes in mathlib4

mathlib3

mathlib4

a148d797

chore: adapt to multiple goal linter 3 (#12372)

A PR analogous to #12338 and #12361: reformatting proofs following the multiple goals linter of #12339.

d29b3780

Diff

@@ -407,7 +407,7 @@ theorem mem_iSup_finset_iff_exists_sum {s : Finset ι} (p : ι → Submodule R N
         · exact hi
       simp only [DFinsupp.sum]
       rw [Finset.sum_subset support_mk_subset, ← hμ]
-      exact Finset.sum_congr rfl fun x hx => congr_arg Subtype.val <| mk_of_mem hx
+      · exact Finset.sum_congr rfl fun x hx => congr_arg Subtype.val <| mk_of_mem hx
       · intro x _ hx
         rw [mem_support_iff, not_ne_iff] at hx
         rw [hx]

a148d797

chore(*): remove empty lines between variable statements (#11418)

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

75c86f04

Diff

@@ -40,7 +40,6 @@ variable {ι : Type*} {R : Type*} {S : Type*} {M : ι → Type*} {N : Type*}
 namespace DFinsupp
 
 variable [Semiring R] [∀ i, AddCommMonoid (M i)] [∀ i, Module R (M i)]
-
 variable [AddCommMonoid N] [Module R N]
 
 section DecidableEq
@@ -185,9 +184,7 @@ The names should match the equivalent bundled `Finsupp.mapRange` definitions.
 section mapRange
 
 variable {β β₁ β₂ : ι → Type*}
-
 variable [∀ i, AddCommMonoid (β i)] [∀ i, AddCommMonoid (β₁ i)] [∀ i, AddCommMonoid (β₂ i)]
-
 variable [∀ i, Module R (β i)] [∀ i, Module R (β₁ i)] [∀ i, Module R (β₂ i)]
 
 theorem mapRange_smul (f : ∀ i, β₁ i → β₂ i) (hf : ∀ i, f i 0 = 0) (r : R)
@@ -587,7 +584,6 @@ variable {M : Type*} {M' : Type*} {M₁ : Type*} {M₂ : Type*} {M₃ : Type*} {
 variable {N : Type*} {N₂ : Type*}
 variable {ι : Type*}
 variable {V : Type*} {V₂ : Type*}
-
 variable [Semiring R] [Semiring R₂] [Semiring R₃]
 variable [AddCommMonoid M] [AddCommMonoid M₂] [AddCommMonoid M₃]
 variable {σ₁₂ : R →+* R₂} {σ₂₃ : R₂ →+* R₃} {σ₁₃ : R →+* R₃}
@@ -648,15 +644,10 @@ section DFinsupp
 open DFinsupp
 
 variable [Semiring R] [Semiring R₂]
-
 variable [AddCommMonoid M] [AddCommMonoid M₂]
-
 variable [Module R M] [Module R₂ M₂]
-
 variable {τ₁₂ : R →+* R₂} {τ₂₁ : R₂ →+* R}
-
 variable [RingHomInvPair τ₁₂ τ₂₁] [RingHomInvPair τ₂₁ τ₁₂]
-
 variable {γ : ι → Type*} [DecidableEq ι]

a148d797

chore: remove stream-of-consciousness uses of have, replace and suffices (#10640)

No changes to tactic file, it's just boring fixes throughout the library.

This follows on from #6964.

Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

a13e8040

Diff

@@ -396,8 +396,7 @@ theorem mem_iSup_finset_iff_exists_sum {s : Finset ι} (p : ι → Submodule R N
         rw [mem_support_iff, not_ne_iff]
         ext
         rw [coe_zero, ← mem_bot R]
-        suffices : ⊥ = ⨆ (_ : x ∈ s), p x
-        · exact this.symm ▸ coe_mem (μ x)
+        suffices ⊥ = ⨆ (_ : x ∈ s), p x from this.symm ▸ coe_mem (μ x)
         exact (iSup_neg hx).symm
       · intro x _ hx
         rw [mem_support_iff, not_ne_iff] at hx
@@ -450,10 +449,9 @@ theorem independent_of_dfinsupp_lsum_injective (p : ι → Submodule R N)
     Independent p := by
   rw [independent_iff_forall_dfinsupp]
   intro i x v hv
-  replace hv :
-    lsum ℕ (M := fun i ↦ ↥(p i)) (fun i => (p i).subtype) (erase i v) =
-      lsum ℕ (M := fun i ↦ ↥(p i)) (fun i => (p i).subtype) (single i x)
-  · simpa only [lsum_single] using hv
+  replace hv : lsum ℕ (M := fun i ↦ ↥(p i)) (fun i => (p i).subtype) (erase i v) =
+      lsum ℕ (M := fun i ↦ ↥(p i)) (fun i => (p i).subtype) (single i x) := by
+    simpa only [lsum_single] using hv
   have := DFunLike.ext_iff.mp (h hv) i
   simpa [eq_comm] using this
 #align complete_lattice.independent_of_dfinsupp_lsum_injective CompleteLattice.independent_of_dfinsupp_lsum_injective

a148d797

chore(LinearAlgebra,BigOperators): drop some decidability assumptions (#10237)

Found by a linter from #10235.

3646044d

Diff

@@ -37,14 +37,16 @@ function with finite support, module, linear algebra
 
 variable {ι : Type*} {R : Type*} {S : Type*} {M : ι → Type*} {N : Type*}
 
-variable [dec_ι : DecidableEq ι]
-
 namespace DFinsupp
 
 variable [Semiring R] [∀ i, AddCommMonoid (M i)] [∀ i, Module R (M i)]
 
 variable [AddCommMonoid N] [Module R N]
 
+section DecidableEq
+
+variable [DecidableEq ι]
+
 /-- `DFinsupp.mk` as a `LinearMap`. -/
 def lmk (s : Finset ι) : (∀ i : (↑s : Set ι), M i) →ₗ[R] Π₀ i, M i where
   toFun := mk s
@@ -137,8 +139,7 @@ def lsum [Semiring S] [Module S N] [SMulCommClass R S N] :
     (∀ i, M i →ₗ[R] N) ≃ₗ[S] (Π₀ i, M i) →ₗ[R] N where
   toFun F :=
     { toFun := sumAddHom fun i => (F i).toAddMonoidHom
-      -- Porting note: needed to (β := M) hint below
-      map_add' := (DFinsupp.liftAddHom (β := M) (fun (i : ι) => (F i).toAddMonoidHom)).map_add
+      map_add' := (DFinsupp.liftAddHom fun (i : ι) => (F i).toAddMonoidHom).map_add
       map_smul' := fun c f => by
         dsimp
         apply DFinsupp.induction f
@@ -174,12 +175,13 @@ theorem lsum_single [Semiring S] [Module S N] [SMulCommClass R S N] (F : ∀ i,
 
 end Lsum
 
+end DecidableEq
+
 /-! ### Bundled versions of `DFinsupp.mapRange`
 
 The names should match the equivalent bundled `Finsupp.mapRange` definitions.
 -/
 
-
 section mapRange
 
 variable {β β₁ β₂ : ι → Type*}
@@ -217,13 +219,10 @@ theorem mapRange.linearMap_comp (f : ∀ i, β₁ i →ₗ[R] β₂ i) (f₂ : 
     (fun i => (f i).map_zero) (fun i => (f₂ i).map_zero) (by simp)
 #align dfinsupp.map_range.linear_map_comp DFinsupp.mapRange.linearMap_comp
 
-theorem sum_mapRange_index.linearMap [∀ (i : ι) (x : β₁ i), Decidable (x ≠ 0)]
-    [∀ (i : ι) (x : β₂ i), Decidable (x ≠ 0)] {f : ∀ i, β₁ i →ₗ[R] β₂ i} {h : ∀ i, β₂ i →ₗ[R] N}
-    {l : Π₀ i, β₁ i} :
-    -- Porting note: Needed to add (M := ...) below
-    (DFinsupp.lsum ℕ (M := β₂)) h (mapRange.linearMap f l)
-      = (DFinsupp.lsum ℕ (M := β₁)) (fun i => (h i).comp (f i)) l := by
-  simpa [DFinsupp.sumAddHom_apply] using sum_mapRange_index fun i => by simp
+theorem sum_mapRange_index.linearMap [DecidableEq ι] {f : ∀ i, β₁ i →ₗ[R] β₂ i}
+    {h : ∀ i, β₂ i →ₗ[R] N} {l : Π₀ i, β₁ i} :
+    DFinsupp.lsum ℕ h (mapRange.linearMap f l) = DFinsupp.lsum ℕ (fun i => (h i).comp (f i)) l := by
+  classical simpa [DFinsupp.sumAddHom_apply] using sum_mapRange_index fun i => by simp
 #align dfinsupp.sum_map_range_index.linear_map DFinsupp.sum_mapRange_index.linearMap
 
 /-- `DFinsupp.mapRange.linearMap` as a `LinearEquiv`. -/
@@ -289,6 +288,10 @@ variable [Semiring R] [AddCommMonoid N] [Module R N]
 
 open DFinsupp
 
+section DecidableEq
+
+variable [DecidableEq ι]
+
 theorem dfinsupp_sum_mem {β : ι → Type*} [∀ i, Zero (β i)] [∀ (i) (x : β i), Decidable (x ≠ 0)]
     (S : Submodule R N) (f : Π₀ i, β i) (g : ∀ i, β i → N) (h : ∀ c, f c ≠ 0 → g c (f c) ∈ S) :
     f.sum g ∈ S :=
@@ -356,6 +359,16 @@ theorem mem_iSup_iff_exists_dfinsupp' (p : ι → Submodule R N) [∀ (i) (x : p
     LinearMap.toAddMonoidHom_coe, coeSubtype]
 #align submodule.mem_supr_iff_exists_dfinsupp' Submodule.mem_iSup_iff_exists_dfinsupp'
 
+theorem mem_biSup_iff_exists_dfinsupp (p : ι → Prop) [DecidablePred p] (S : ι → Submodule R N)
+    (x : N) :
+    (x ∈ ⨆ (i) (_ : p i), S i) ↔
+      ∃ f : Π₀ i, S i,
+        DFinsupp.lsum ℕ (M := fun i ↦ ↥(S i)) (fun i => (S i).subtype) (f.filter p) = x :=
+  SetLike.ext_iff.mp (biSup_eq_range_dfinsupp_lsum p S) x
+#align submodule.mem_bsupr_iff_exists_dfinsupp Submodule.mem_biSup_iff_exists_dfinsupp
+
+end DecidableEq
+
 lemma mem_iSup_iff_exists_finsupp (p : ι → Submodule R N) (x : N) :
     x ∈ iSup p ↔ ∃ (f : ι →₀ N), (∀ i, f i ∈ p i) ∧ (f.sum fun _i xi ↦ xi) = x := by
   classical
@@ -366,14 +379,6 @@ lemma mem_iSup_iff_exists_finsupp (p : ι → Submodule R N) (x : N) :
   · ext; simp
   · simp [Finsupp.mem_support_iff.mp hi]
 
-theorem mem_biSup_iff_exists_dfinsupp (p : ι → Prop) [DecidablePred p] (S : ι → Submodule R N)
-    (x : N) :
-    (x ∈ ⨆ (i) (_ : p i), S i) ↔
-      ∃ f : Π₀ i, S i,
-        DFinsupp.lsum ℕ (M := fun i ↦ ↥(S i)) (fun i => (S i).subtype) (f.filter p) = x :=
-  SetLike.ext_iff.mp (biSup_eq_range_dfinsupp_lsum p S) x
-#align submodule.mem_bsupr_iff_exists_dfinsupp Submodule.mem_biSup_iff_exists_dfinsupp
-
 open BigOperators
 
 theorem mem_iSup_finset_iff_exists_sum {s : Finset ι} (p : ι → Submodule R N) (a : N) :
@@ -421,7 +426,7 @@ open DFinsupp
 
 section Semiring
 
-variable [Semiring R] [AddCommMonoid N] [Module R N]
+variable [DecidableEq ι] [Semiring R] [AddCommMonoid N] [Module R N]
 
 /-- Independence of a family of submodules can be expressed as a quantifier over `DFinsupp`s.
 
@@ -477,7 +482,7 @@ end Semiring
 
 section Ring
 
-variable [Ring R] [AddCommGroup N] [Module R N]
+variable [DecidableEq ι] [Ring R] [AddCommGroup N] [Module R N]
 
 /- If `DFinsupp.sumAddHom` applied with `AddSubmonoid.subtype` is injective then the additive
 subgroups are independent. -/

a148d797

chore(*): rename FunLike to DFunLike (#9785)

This prepares for the introduction of a non-dependent synonym of FunLike, which helps a lot with keeping #8386 readable.

This is entirely search-and-replace in 680197f combined with manual fixes in 4145626, e900597 and b8428f8. The commands that generated this change:

sed -i 's/\bFunLike\b/DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoFunLike\b/toDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/import Mathlib.Data.DFunLike/import Mathlib.Data.FunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bHom_FunLike\b/Hom_DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean     
sed -i 's/\binstFunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bfunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoo many metavariables to apply `fun_like.has_coe_to_fun`/too many metavariables to apply `DFunLike.hasCoeToFun`/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean

Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

82656743

Diff

@@ -449,7 +449,7 @@ theorem independent_of_dfinsupp_lsum_injective (p : ι → Submodule R N)
     lsum ℕ (M := fun i ↦ ↥(p i)) (fun i => (p i).subtype) (erase i v) =
       lsum ℕ (M := fun i ↦ ↥(p i)) (fun i => (p i).subtype) (single i x)
   · simpa only [lsum_single] using hv
-  have := FunLike.ext_iff.mp (h hv) i
+  have := DFunLike.ext_iff.mp (h hv) i
   simpa [eq_comm] using this
 #align complete_lattice.independent_of_dfinsupp_lsum_injective CompleteLattice.independent_of_dfinsupp_lsum_injective

a148d797

chore(*): drop $/<| before fun (#9361)

Subset of #9319

3694e27d

Diff

@@ -362,7 +362,7 @@ lemma mem_iSup_iff_exists_finsupp (p : ι → Submodule R N) (x : N) :
   rw [mem_iSup_iff_exists_dfinsupp']
   refine ⟨fun ⟨f, hf⟩ ↦ ⟨⟨f.support, fun i ↦ (f i : N), by simp⟩, by simp, hf⟩, ?_⟩
   rintro ⟨f, hf, rfl⟩
-  refine ⟨DFinsupp.mk f.support <| fun i ↦ ⟨f i, hf i⟩, Finset.sum_congr ?_ fun i hi ↦ ?_⟩
+  refine ⟨DFinsupp.mk f.support fun i ↦ ⟨f i, hf i⟩, Finset.sum_congr ?_ fun i hi ↦ ?_⟩
   · ext; simp
   · simp [Finsupp.mem_support_iff.mp hi]

a148d797

chore: redistribute some of the results in LinearAlgebra.Basic (#7801)

This reduces the file from ~2600 lines to ~1600 lines.

Co-authored-by: Vierkantor <vierkantor@vierkantor.com> Co-authored-by: Floris van Doorn <fpvdoorn@gmail.com>

eb292821

Diff

@@ -572,3 +572,98 @@ theorem independent_iff_linearIndependent_of_ne_zero [NoZeroSMulDivisors R N] {v
 end Ring
 
 end CompleteLattice
+
+namespace LinearMap
+
+section AddCommMonoid
+
+variable {R : Type*} {R₁ : Type*} {R₂ : Type*} {R₃ : Type*} {R₄ : Type*}
+variable {S : Type*}
+variable {K : Type*} {K₂ : Type*}
+variable {M : Type*} {M' : Type*} {M₁ : Type*} {M₂ : Type*} {M₃ : Type*} {M₄ : Type*}
+variable {N : Type*} {N₂ : Type*}
+variable {ι : Type*}
+variable {V : Type*} {V₂ : Type*}
+
+variable [Semiring R] [Semiring R₂] [Semiring R₃]
+variable [AddCommMonoid M] [AddCommMonoid M₂] [AddCommMonoid M₃]
+variable {σ₁₂ : R →+* R₂} {σ₂₃ : R₂ →+* R₃} {σ₁₃ : R →+* R₃}
+variable [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃]
+variable [Module R M] [Module R₂ M₂] [Module R₃ M₃]
+
+open Submodule
+
+section DFinsupp
+
+open DFinsupp
+
+variable {γ : ι → Type*} [DecidableEq ι]
+
+section Sum
+
+variable [∀ i, Zero (γ i)] [∀ (i) (x : γ i), Decidable (x ≠ 0)]
+
+#align linear_map.map_dfinsupp_sum map_dfinsupp_sumₓ
+#align linear_equiv.map_dfinsupp_sum map_dfinsupp_sumₓ
+
+theorem coe_dfinsupp_sum (t : Π₀ i, γ i) (g : ∀ i, γ i → M →ₛₗ[σ₁₂] M₂) :
+    ⇑(t.sum g) = t.sum fun i d => g i d := rfl
+#align linear_map.coe_dfinsupp_sum LinearMap.coe_dfinsupp_sum
+
+@[simp]
+theorem dfinsupp_sum_apply (t : Π₀ i, γ i) (g : ∀ i, γ i → M →ₛₗ[σ₁₂] M₂) (b : M) :
+    (t.sum g) b = t.sum fun i d => g i d b :=
+  sum_apply _ _ _
+#align linear_map.dfinsupp_sum_apply LinearMap.dfinsupp_sum_apply
+
+end Sum
+
+section SumAddHom
+
+variable [∀ i, AddZeroClass (γ i)]
+
+@[simp]
+theorem map_dfinsupp_sumAddHom (f : M →ₛₗ[σ₁₂] M₂) {t : Π₀ i, γ i} {g : ∀ i, γ i →+ M} :
+    f (sumAddHom g t) = sumAddHom (fun i => f.toAddMonoidHom.comp (g i)) t :=
+  f.toAddMonoidHom.map_dfinsupp_sumAddHom _ _
+#align linear_map.map_dfinsupp_sum_add_hom LinearMap.map_dfinsupp_sumAddHom
+
+end SumAddHom
+
+end DFinsupp
+
+end AddCommMonoid
+
+end LinearMap
+
+namespace LinearEquiv
+
+variable {R : Type*} {R₂ : Type*} {M : Type*} {M₂ : Type*} {ι : Type*}
+
+section DFinsupp
+
+open DFinsupp
+
+variable [Semiring R] [Semiring R₂]
+
+variable [AddCommMonoid M] [AddCommMonoid M₂]
+
+variable [Module R M] [Module R₂ M₂]
+
+variable {τ₁₂ : R →+* R₂} {τ₂₁ : R₂ →+* R}
+
+variable [RingHomInvPair τ₁₂ τ₂₁] [RingHomInvPair τ₂₁ τ₁₂]
+
+variable {γ : ι → Type*} [DecidableEq ι]
+
+
+@[simp]
+theorem map_dfinsupp_sumAddHom [∀ i, AddZeroClass (γ i)] (f : M ≃ₛₗ[τ₁₂] M₂) (t : Π₀ i, γ i)
+    (g : ∀ i, γ i →+ M) :
+    f (sumAddHom g t) = sumAddHom (fun i => f.toAddEquiv.toAddMonoidHom.comp (g i)) t :=
+  f.toAddEquiv.map_dfinsupp_sumAddHom _ _
+#align linear_equiv.map_dfinsupp_sum_add_hom LinearEquiv.map_dfinsupp_sumAddHom
+
+end DFinsupp
+
+end LinearEquiv

a148d797

feat: miscellaneous linear algebra lemmas (#8157)

ccd15763

Diff

@@ -337,13 +337,18 @@ theorem biSup_eq_range_dfinsupp_lsum (p : ι → Prop) [DecidablePred p] (S : ι
     · simp [hp]
 #align submodule.bsupr_eq_range_dfinsupp_lsum Submodule.biSup_eq_range_dfinsupp_lsum
 
+/-- A characterisation of the span of a family of submodules.
+
+See also `Submodule.mem_iSup_iff_exists_finsupp`. -/
 theorem mem_iSup_iff_exists_dfinsupp (p : ι → Submodule R N) (x : N) :
     x ∈ iSup p ↔
       ∃ f : Π₀ i, p i, DFinsupp.lsum ℕ (M := fun i ↦ ↥(p i)) (fun i => (p i).subtype) f = x :=
   SetLike.ext_iff.mp (iSup_eq_range_dfinsupp_lsum p) x
 #align submodule.mem_supr_iff_exists_dfinsupp Submodule.mem_iSup_iff_exists_dfinsupp
 
-/-- A variant of `Submodule.mem_iSup_iff_exists_dfinsupp` with the RHS fully unfolded. -/
+/-- A variant of `Submodule.mem_iSup_iff_exists_dfinsupp` with the RHS fully unfolded.
+
+See also `Submodule.mem_iSup_iff_exists_finsupp`. -/
 theorem mem_iSup_iff_exists_dfinsupp' (p : ι → Submodule R N) [∀ (i) (x : p i), Decidable (x ≠ 0)]
     (x : N) : x ∈ iSup p ↔ ∃ f : Π₀ i, p i, (f.sum fun i xi => ↑xi) = x := by
   rw [mem_iSup_iff_exists_dfinsupp]
@@ -351,6 +356,16 @@ theorem mem_iSup_iff_exists_dfinsupp' (p : ι → Submodule R N) [∀ (i) (x : p
     LinearMap.toAddMonoidHom_coe, coeSubtype]
 #align submodule.mem_supr_iff_exists_dfinsupp' Submodule.mem_iSup_iff_exists_dfinsupp'
 
+lemma mem_iSup_iff_exists_finsupp (p : ι → Submodule R N) (x : N) :
+    x ∈ iSup p ↔ ∃ (f : ι →₀ N), (∀ i, f i ∈ p i) ∧ (f.sum fun _i xi ↦ xi) = x := by
+  classical
+  rw [mem_iSup_iff_exists_dfinsupp']
+  refine ⟨fun ⟨f, hf⟩ ↦ ⟨⟨f.support, fun i ↦ (f i : N), by simp⟩, by simp, hf⟩, ?_⟩
+  rintro ⟨f, hf, rfl⟩
+  refine ⟨DFinsupp.mk f.support <| fun i ↦ ⟨f i, hf i⟩, Finset.sum_congr ?_ fun i hi ↦ ?_⟩
+  · ext; simp
+  · simp [Finsupp.mem_support_iff.mp hi]
+
 theorem mem_biSup_iff_exists_dfinsupp (p : ι → Prop) [DecidablePred p] (S : ι → Submodule R N)
     (x : N) :
     (x ∈ ⨆ (i) (_ : p i), S i) ↔

a148d797

Revert "chore: revert #7703 (#7710)"

This reverts commit f3695eb2.

ab56fa28

Diff

@@ -81,7 +81,8 @@ def lapply (i : ι) : (Π₀ i, M i) →ₗ[R] M i where
   map_smul' c f := smul_apply c f i
 #align dfinsupp.lapply DFinsupp.lapply
 
-@[simp]
+-- This lemma has always been bad, but the linter only noticed after lean4#2644.
+@[simp, nolint simpNF]
 theorem lmk_apply (s : Finset ι) (x) : (lmk s : _ →ₗ[R] Π₀ i, M i) x = mk s x :=
   rfl
 #align dfinsupp.lmk_apply DFinsupp.lmk_apply

a148d797

chore: revert #7703 (#7710)

This reverts commit 26eb2b0a.

f3695eb2

Diff

@@ -81,8 +81,7 @@ def lapply (i : ι) : (Π₀ i, M i) →ₗ[R] M i where
   map_smul' c f := smul_apply c f i
 #align dfinsupp.lapply DFinsupp.lapply
 
--- This lemma has always been bad, but the linter only noticed after lean4#2644.
-@[simp, nolint simpNF]
+@[simp]
 theorem lmk_apply (s : Finset ι) (x) : (lmk s : _ →ₗ[R] Π₀ i, M i) x = mk s x :=
   rfl
 #align dfinsupp.lmk_apply DFinsupp.lmk_apply

a148d797

chore: bump toolchain to v4.2.0-rc2 (#7703)

This includes all the changes from #7606.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

26eb2b0a

Diff

@@ -81,7 +81,8 @@ def lapply (i : ι) : (Π₀ i, M i) →ₗ[R] M i where
   map_smul' c f := smul_apply c f i
 #align dfinsupp.lapply DFinsupp.lapply
 
-@[simp]
+-- This lemma has always been bad, but the linter only noticed after lean4#2644.
+@[simp, nolint simpNF]
 theorem lmk_apply (s : Finset ι) (x) : (lmk s : _ →ₗ[R] Π₀ i, M i) x = mk s x :=
   rfl
 #align dfinsupp.lmk_apply DFinsupp.lmk_apply

a148d797

style: fix multiple spaces before colon (#7411)

Purely cosmetic PR

41584956

Diff

@@ -221,7 +221,7 @@ theorem sum_mapRange_index.linearMap [∀ (i : ι) (x : β₁ i), Decidable (x 
     {l : Π₀ i, β₁ i} :
     -- Porting note: Needed to add (M := ...) below
     (DFinsupp.lsum ℕ (M := β₂)) h (mapRange.linearMap f l)
-      = (DFinsupp.lsum ℕ (M := β₁)) (fun i => (h i).comp (f i)) l  := by
+      = (DFinsupp.lsum ℕ (M := β₁)) (fun i => (h i).comp (f i)) l := by
   simpa [DFinsupp.sumAddHom_apply] using sum_mapRange_index fun i => by simp
 #align dfinsupp.sum_map_range_index.linear_map DFinsupp.sum_mapRange_index.linearMap

a148d797

chore(LinearAlgebra/DFinsupp): remove dependency on Basis (#6706)

The motivation here is to explore re-defining Basis with DFinsupp instead of Finsupp, in order to make it computable.

5128540f

Diff

@@ -4,7 +4,8 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Kenny Lau
 -/
 import Mathlib.Data.Finsupp.ToDFinsupp
-import Mathlib.LinearAlgebra.Basis
+import Mathlib.LinearAlgebra.Finsupp
+import Mathlib.LinearAlgebra.LinearIndependent
 
 #align_import linear_algebra.dfinsupp from "leanprover-community/mathlib"@"a148d797a1094ab554ad4183a4ad6f130358ef64"
 
@@ -279,19 +280,6 @@ theorem coprodMap_apply_single (f : ∀ i : ι, M i →ₗ[R] N) (i : ι) (x : M
 
 end CoprodMap
 
-section Basis
-
-/-- The direct sum of free modules is free.
-
-Note that while this is stated for `DFinsupp` not `DirectSum`, the types are defeq. -/
-noncomputable def basis {η : ι → Type*} (b : ∀ i, Basis (η i) R (M i)) :
-    Basis (Σi, η i) R (Π₀ i, M i) :=
-  .ofRepr
-    ((mapRange.linearEquiv fun i => (b i).repr).trans (sigmaFinsuppLequivDFinsupp R).symm)
-#align dfinsupp.basis DFinsupp.basis
-
-end Basis
-
 end DFinsupp
 
 namespace Submodule

a148d797

chore(LinearAlgebra/DFinsupp): make DFinsupp.coprodMap computable (#6704)

There was no need to go via Finsupp here.

f25139b7

Diff

@@ -262,21 +262,20 @@ variable [DecidableEq ι] [∀ x : N, Decidable (x ≠ 0)]
 `(Π₀ i, M i) →ₗ[R] N` which sends `x : Π₀ i, M i` to the sum over `i` of `f i` applied to `x i`.
 This is the map coming from the universal property of `Π₀ i, M i` as the coproduct of the `M i`.
 See also `LinearMap.coprod` for the binary product version. -/
-noncomputable def coprodMap (f : ∀ i : ι, M i →ₗ[R] N) : (Π₀ i, M i) →ₗ[R] N :=
-  (Finsupp.lsum ℕ fun _ : ι => LinearMap.id) ∘ₗ
-    (@finsuppLequivDFinsupp ι R N _ _ _ _ _).symm.toLinearMap ∘ₗ DFinsupp.mapRange.linearMap f
+def coprodMap (f : ∀ i : ι, M i →ₗ[R] N) : (Π₀ i, M i) →ₗ[R] N :=
+  (DFinsupp.lsum ℕ fun _ : ι => LinearMap.id) ∘ₗ DFinsupp.mapRange.linearMap f
 #align dfinsupp.coprod_map DFinsupp.coprodMap
 
 theorem coprodMap_apply (f : ∀ i : ι, M i →ₗ[R] N) (x : Π₀ i, M i) :
     coprodMap f x =
-      Finsupp.sum (mapRange (fun i => f i) (fun _ => LinearMap.map_zero _) x).toFinsupp fun _ =>
+      DFinsupp.sum (mapRange (fun i => f i) (fun _ => LinearMap.map_zero _) x) fun _ =>
         id :=
-  rfl
+  DFinsupp.sumAddHom_apply _ _
 #align dfinsupp.coprod_map_apply DFinsupp.coprodMap_apply
 
 theorem coprodMap_apply_single (f : ∀ i : ι, M i →ₗ[R] N) (i : ι) (x : M i) :
     coprodMap f (single i x) = f i x := by
-  simp [coprodMap_apply]
+  simp [coprodMap]
 
 end CoprodMap

a148d797

chore: fix doc-strings about (c vs C)ounterexamples (#6691)

This PR just touches doc-strings. It fixes capitalization issues involving Counterexamples and adds a missing line-break for better display.

0b511e95

Diff

@@ -490,7 +490,7 @@ are `CompleteLattice.Independent`.
 Note that this is not generally true for `[Semiring R]`, for instance when `A` is the
 `ℕ`-submodules of the positive and negative integers.
 
-See `counterexamples/direct_sum_is_internal.lean` for a proof of this fact. -/
+See `Counterexamples/DirectSumIsInternal.lean` for a proof of this fact. -/
 theorem Independent.dfinsupp_lsum_injective {p : ι → Submodule R N} (h : Independent p) :
     Function.Injective (lsum ℕ (M := fun i ↦ ↥(p i)) fun i => (p i).subtype) := by
   -- simplify everything down to binders over equalities in `N`

a148d797

chore: banish Type _ and Sort _ (#6499)

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

32de3f67

Diff

@@ -34,7 +34,7 @@ much more developed, but many lemmas in that file should be eligible to copy ove
 function with finite support, module, linear algebra
 -/
 
-variable {ι : Type _} {R : Type _} {S : Type _} {M : ι → Type _} {N : Type _}
+variable {ι : Type*} {R : Type*} {S : Type*} {M : ι → Type*} {N : Type*}
 
 variable [dec_ι : DecidableEq ι]
 
@@ -119,8 +119,8 @@ instance moduleOfLinearMap [Semiring S] [Module S N] [SMulCommClass R S N] :
 variable (S)
 
 
-instance {R : Type _} {S : Type _} [Semiring R] [Semiring S] (σ : R →+* S)
-    {σ' : S →+* R} [RingHomInvPair σ σ'] [RingHomInvPair σ' σ] (M : Type _) (M₂ : Type _)
+instance {R : Type*} {S : Type*} [Semiring R] [Semiring S] (σ : R →+* S)
+    {σ' : S →+* R} [RingHomInvPair σ σ'] [RingHomInvPair σ' σ] (M : Type*) (M₂ : Type*)
     [AddCommMonoid M] [AddCommMonoid M₂] [Module R M] [Module S M₂] :
     EquivLike (LinearEquiv σ M M₂) M M₂ :=
   inferInstance
@@ -180,7 +180,7 @@ The names should match the equivalent bundled `Finsupp.mapRange` definitions.
 
 section mapRange
 
-variable {β β₁ β₂ : ι → Type _}
+variable {β β₁ β₂ : ι → Type*}
 
 variable [∀ i, AddCommMonoid (β i)] [∀ i, AddCommMonoid (β₁ i)] [∀ i, AddCommMonoid (β₂ i)]
 
@@ -285,7 +285,7 @@ section Basis
 /-- The direct sum of free modules is free.
 
 Note that while this is stated for `DFinsupp` not `DirectSum`, the types are defeq. -/
-noncomputable def basis {η : ι → Type _} (b : ∀ i, Basis (η i) R (M i)) :
+noncomputable def basis {η : ι → Type*} (b : ∀ i, Basis (η i) R (M i)) :
     Basis (Σi, η i) R (Π₀ i, M i) :=
   .ofRepr
     ((mapRange.linearEquiv fun i => (b i).repr).trans (sigmaFinsuppLequivDFinsupp R).symm)
@@ -301,13 +301,13 @@ variable [Semiring R] [AddCommMonoid N] [Module R N]
 
 open DFinsupp
 
-theorem dfinsupp_sum_mem {β : ι → Type _} [∀ i, Zero (β i)] [∀ (i) (x : β i), Decidable (x ≠ 0)]
+theorem dfinsupp_sum_mem {β : ι → Type*} [∀ i, Zero (β i)] [∀ (i) (x : β i), Decidable (x ≠ 0)]
     (S : Submodule R N) (f : Π₀ i, β i) (g : ∀ i, β i → N) (h : ∀ c, f c ≠ 0 → g c (f c) ∈ S) :
     f.sum g ∈ S :=
   _root_.dfinsupp_sum_mem S f g h
 #align submodule.dfinsupp_sum_mem Submodule.dfinsupp_sum_mem
 
-theorem dfinsupp_sumAddHom_mem {β : ι → Type _} [∀ i, AddZeroClass (β i)] (S : Submodule R N)
+theorem dfinsupp_sumAddHom_mem {β : ι → Type*} [∀ i, AddZeroClass (β i)] (S : Submodule R N)
     (f : Π₀ i, β i) (g : ∀ i, β i →+ N) (h : ∀ c, f c ≠ 0 → g c (f c) ∈ S) :
     DFinsupp.sumAddHom g f ∈ S :=
   _root_.dfinsupp_sumAddHom_mem S f g h

a148d797

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

89aa3a3b

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2018 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Kenny Lau
-
-! This file was ported from Lean 3 source module linear_algebra.dfinsupp
-! leanprover-community/mathlib commit a148d797a1094ab554ad4183a4ad6f130358ef64
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Finsupp.ToDFinsupp
 import Mathlib.LinearAlgebra.Basis
 
+#align_import linear_algebra.dfinsupp from "leanprover-community/mathlib"@"a148d797a1094ab554ad4183a4ad6f130358ef64"
+
 /-!
 # Properties of the module `Π₀ i, M i`

a148d797

chore: cleanup whitespace (#5988)

Grepping for [^ .:{-] [^ :] and reviewing the results. Once I started I couldn't stop. :-)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

12343aa5

Diff

@@ -261,7 +261,7 @@ section CoprodMap
 
 variable [DecidableEq ι] [∀ x : N, Decidable (x ≠ 0)]
 
-/-- Given a family of linear maps `f i : M i  →ₗ[R] N`, we can form a linear map
+/-- Given a family of linear maps `f i : M i →ₗ[R] N`, we can form a linear map
 `(Π₀ i, M i) →ₗ[R] N` which sends `x : Π₀ i, M i` to the sum over `i` of `f i` applied to `x i`.
 This is the map coming from the universal property of `Π₀ i, M i` as the coproduct of the `M i`.
 See also `LinearMap.coprod` for the binary product version. -/

a148d797

chore: rename Dfinsupp to DFinsupp (#5822)

See #4354

268b7d43

Diff

@@ -8,24 +8,24 @@ Authors: Johannes Hölzl, Kenny Lau
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
-import Mathlib.Data.Finsupp.ToDfinsupp
+import Mathlib.Data.Finsupp.ToDFinsupp
 import Mathlib.LinearAlgebra.Basis
 
 /-!
 # Properties of the module `Π₀ i, M i`
 
 Given an indexed collection of `R`-modules `M i`, the `R`-module structure on `Π₀ i, M i`
-is defined in `Data.Dfinsupp`.
+is defined in `Data.DFinsupp`.
 
 In this file we define `LinearMap` versions of various maps:
 
-* `Dfinsupp.lsingle a : M →ₗ[R] Π₀ i, M i`: `Dfinsupp.single a` as a linear map;
+* `DFinsupp.lsingle a : M →ₗ[R] Π₀ i, M i`: `DFinsupp.single a` as a linear map;
 
-* `Dfinsupp.lmk s : (Π i : (↑s : Set ι), M i) →ₗ[R] Π₀ i, M i`: `Dfinsupp.single a` as a linear map;
+* `DFinsupp.lmk s : (Π i : (↑s : Set ι), M i) →ₗ[R] Π₀ i, M i`: `DFinsupp.single a` as a linear map;
 
-* `Dfinsupp.lapply i : (Π₀ i, M i) →ₗ[R] M`: the map `fun f ↦ f i` as a linear map;
+* `DFinsupp.lapply i : (Π₀ i, M i) →ₗ[R] M`: the map `fun f ↦ f i` as a linear map;
 
-* `Dfinsupp.lsum`: `Dfinsupp.sum` or `Dfinsupp.liftAddHom` as a `LinearMap`;
+* `DFinsupp.lsum`: `DFinsupp.sum` or `DFinsupp.liftAddHom` as a `LinearMap`;
 
 ## Implementation notes
 
@@ -41,30 +41,30 @@ variable {ι : Type _} {R : Type _} {S : Type _} {M : ι → Type _} {N : Type _
 
 variable [dec_ι : DecidableEq ι]
 
-namespace Dfinsupp
+namespace DFinsupp
 
 variable [Semiring R] [∀ i, AddCommMonoid (M i)] [∀ i, Module R (M i)]
 
 variable [AddCommMonoid N] [Module R N]
 
-/-- `Dfinsupp.mk` as a `LinearMap`. -/
+/-- `DFinsupp.mk` as a `LinearMap`. -/
 def lmk (s : Finset ι) : (∀ i : (↑s : Set ι), M i) →ₗ[R] Π₀ i, M i where
   toFun := mk s
   map_add' _ _ := mk_add
   map_smul' c x := mk_smul c x
-#align dfinsupp.lmk Dfinsupp.lmk
+#align dfinsupp.lmk DFinsupp.lmk
 
-/-- `Dfinsupp.single` as a `LinearMap` -/
+/-- `DFinsupp.single` as a `LinearMap` -/
 def lsingle (i) : M i →ₗ[R] Π₀ i, M i :=
-  { Dfinsupp.singleAddHom _ _ with
+  { DFinsupp.singleAddHom _ _ with
     toFun := single i
     map_smul' := single_smul }
-#align dfinsupp.lsingle Dfinsupp.lsingle
+#align dfinsupp.lsingle DFinsupp.lsingle
 
 /-- Two `R`-linear maps from `Π₀ i, M i` which agree on each `single i x` agree everywhere. -/
 theorem lhom_ext ⦃φ ψ : (Π₀ i, M i) →ₗ[R] N⦄ (h : ∀ i x, φ (single i x) = ψ (single i x)) : φ = ψ :=
   LinearMap.toAddMonoidHom_injective <| addHom_ext h
-#align dfinsupp.lhom_ext Dfinsupp.lhom_ext
+#align dfinsupp.lhom_ext DFinsupp.lhom_ext
 
 /-- Two `R`-linear maps from `Π₀ i, M i` which agree on each `single i x` agree everywhere.
 
@@ -74,50 +74,50 @@ After apply this lemma, if `M = R` then it suffices to verify `φ (single a 1) =
 theorem lhom_ext' ⦃φ ψ : (Π₀ i, M i) →ₗ[R] N⦄ (h : ∀ i, φ.comp (lsingle i) = ψ.comp (lsingle i)) :
     φ = ψ :=
   lhom_ext fun i => LinearMap.congr_fun (h i)
-#align dfinsupp.lhom_ext' Dfinsupp.lhom_ext'
+#align dfinsupp.lhom_ext' DFinsupp.lhom_ext'
 
 /-- Interpret `fun (f : Π₀ i, M i) ↦ f i` as a linear map. -/
 def lapply (i : ι) : (Π₀ i, M i) →ₗ[R] M i where
   toFun f := f i
   map_add' f g := add_apply f g i
   map_smul' c f := smul_apply c f i
-#align dfinsupp.lapply Dfinsupp.lapply
+#align dfinsupp.lapply DFinsupp.lapply
 
 @[simp]
 theorem lmk_apply (s : Finset ι) (x) : (lmk s : _ →ₗ[R] Π₀ i, M i) x = mk s x :=
   rfl
-#align dfinsupp.lmk_apply Dfinsupp.lmk_apply
+#align dfinsupp.lmk_apply DFinsupp.lmk_apply
 
 @[simp]
 theorem lsingle_apply (i : ι) (x : M i) : (lsingle i : (M i) →ₗ[R] _) x = single i x :=
   rfl
-#align dfinsupp.lsingle_apply Dfinsupp.lsingle_apply
+#align dfinsupp.lsingle_apply DFinsupp.lsingle_apply
 
 @[simp]
 theorem lapply_apply (i : ι) (f : Π₀ i, M i) : (lapply i : (Π₀ i, M i) →ₗ[R] _) f = f i :=
   rfl
-#align dfinsupp.lapply_apply Dfinsupp.lapply_apply
+#align dfinsupp.lapply_apply DFinsupp.lapply_apply
 
 section Lsum
 
 -- Porting note: Unclear how true these docstrings are in lean 4
-/-- Typeclass inference can't find `Dfinsupp.addCommMonoid` without help for this case.
+/-- Typeclass inference can't find `DFinsupp.addCommMonoid` without help for this case.
 This instance allows it to be found where it is needed on the LHS of the colon in
-`Dfinsupp.moduleOfLinearMap`. -/
+`DFinsupp.moduleOfLinearMap`. -/
 instance addCommMonoidOfLinearMap : AddCommMonoid (Π₀ i : ι, M i →ₗ[R] N) :=
   inferInstance
-#align dfinsupp.add_comm_monoid_of_linear_map Dfinsupp.addCommMonoidOfLinearMap
+#align dfinsupp.add_comm_monoid_of_linear_map DFinsupp.addCommMonoidOfLinearMap
 
-/-- Typeclass inference can't find `Dfinsupp.module` without help for this case.
-This is needed to define `Dfinsupp.lsum` below.
+/-- Typeclass inference can't find `DFinsupp.module` without help for this case.
+This is needed to define `DFinsupp.lsum` below.
 
 The cause seems to be an inability to unify the `∀ i, AddCommMonoid (M i →ₗ[R] N)` instance that
 we have with the `∀ i, Zero (M i →ₗ[R] N)` instance which appears as a parameter to the
-`Dfinsupp` type. -/
+`DFinsupp` type. -/
 instance moduleOfLinearMap [Semiring S] [Module S N] [SMulCommClass R S N] :
     Module S (Π₀ i : ι, M i →ₗ[R] N) :=
-  Dfinsupp.module
-#align dfinsupp.module_of_linear_map Dfinsupp.moduleOfLinearMap
+  DFinsupp.module
+#align dfinsupp.module_of_linear_map DFinsupp.moduleOfLinearMap
 
 variable (S)
 
@@ -130,7 +130,7 @@ instance {R : Type _} {S : Type _} [Semiring R] [Semiring S] (σ : R →+* S)
 
 /- Porting note: In every application of lsum that follows, the argument M needs to be explicitly
 supplied, lean does not manage to gather that information itself -/
-/-- The `Dfinsupp` version of `Finsupp.lsum`.
+/-- The `DFinsupp` version of `Finsupp.lsum`.
 
 See note [bundled maps over different rings] for why separate `R` and `S` semirings are used. -/
 @[simps]
@@ -139,10 +139,10 @@ def lsum [Semiring S] [Module S N] [SMulCommClass R S N] :
   toFun F :=
     { toFun := sumAddHom fun i => (F i).toAddMonoidHom
       -- Porting note: needed to (β := M) hint below
-      map_add' := (Dfinsupp.liftAddHom (β := M) (fun (i : ι) => (F i).toAddMonoidHom)).map_add
+      map_add' := (DFinsupp.liftAddHom (β := M) (fun (i : ι) => (F i).toAddMonoidHom)).map_add
       map_smul' := fun c f => by
         dsimp
-        apply Dfinsupp.induction f
+        apply DFinsupp.induction f
         · rw [smul_zero, AddMonoidHom.map_zero, smul_zero]
         · intro a b f _ _ hf
           rw [smul_add, AddMonoidHom.map_add, AddMonoidHom.map_add, smul_add, hf, ← single_smul,
@@ -153,29 +153,29 @@ def lsum [Semiring S] [Module S N] [SMulCommClass R S N] :
     ext
     simp
   right_inv F := by
-    refine Dfinsupp.lhom_ext' (fun i ↦ ?_)
+    refine DFinsupp.lhom_ext' (fun i ↦ ?_)
     ext
     simp
   map_add' F G := by
-    refine Dfinsupp.lhom_ext' (fun i ↦ ?_)
+    refine DFinsupp.lhom_ext' (fun i ↦ ?_)
     ext
     simp
   map_smul' c F := by
-    refine Dfinsupp.lhom_ext' (fun i ↦ ?_)
+    refine DFinsupp.lhom_ext' (fun i ↦ ?_)
     ext
     simp
-#align dfinsupp.lsum Dfinsupp.lsum
+#align dfinsupp.lsum DFinsupp.lsum
 
 /-- While `simp` can prove this, it is often convenient to avoid unfolding `lsum` into `sumAddHom`
-with `Dfinsupp.lsum_apply_apply`. -/
+with `DFinsupp.lsum_apply_apply`. -/
 theorem lsum_single [Semiring S] [Module S N] [SMulCommClass R S N] (F : ∀ i, M i →ₗ[R] N) (i)
     (x : M i) : lsum S (M := M) F (single i x) = F i x := by
   simp
-#align dfinsupp.lsum_single Dfinsupp.lsum_single
+#align dfinsupp.lsum_single DFinsupp.lsum_single
 
 end Lsum
 
-/-! ### Bundled versions of `Dfinsupp.mapRange`
+/-! ### Bundled versions of `DFinsupp.mapRange`
 
 The names should match the equivalent bundled `Finsupp.mapRange` definitions.
 -/
@@ -194,66 +194,66 @@ theorem mapRange_smul (f : ∀ i, β₁ i → β₂ i) (hf : ∀ i, f i 0 = 0) (
     mapRange f hf (r • g) = r • mapRange f hf g := by
   ext
   simp only [mapRange_apply f, coe_smul, Pi.smul_apply, hf']
-#align dfinsupp.map_range_smul Dfinsupp.mapRange_smul
+#align dfinsupp.map_range_smul DFinsupp.mapRange_smul
 
-/-- `Dfinsupp.mapRange` as a `LinearMap`. -/
+/-- `DFinsupp.mapRange` as a `LinearMap`. -/
 @[simps! apply]
 def mapRange.linearMap (f : ∀ i, β₁ i →ₗ[R] β₂ i) : (Π₀ i, β₁ i) →ₗ[R] Π₀ i, β₂ i :=
   { mapRange.addMonoidHom fun i => (f i).toAddMonoidHom with
     toFun := mapRange (fun i x => f i x) fun i => (f i).map_zero
     map_smul' := fun r => mapRange_smul _ (fun i => (f i).map_zero) _ fun i => (f i).map_smul r }
-#align dfinsupp.map_range.linear_map Dfinsupp.mapRange.linearMap
+#align dfinsupp.map_range.linear_map DFinsupp.mapRange.linearMap
 
 @[simp]
 theorem mapRange.linearMap_id :
     (mapRange.linearMap fun i => (LinearMap.id : β₂ i →ₗ[R] _)) = LinearMap.id := by
   ext
   simp [linearMap]
-#align dfinsupp.map_range.linear_map_id Dfinsupp.mapRange.linearMap_id
+#align dfinsupp.map_range.linear_map_id DFinsupp.mapRange.linearMap_id
 
 theorem mapRange.linearMap_comp (f : ∀ i, β₁ i →ₗ[R] β₂ i) (f₂ : ∀ i, β i →ₗ[R] β₁ i) :
     (mapRange.linearMap fun i => (f i).comp (f₂ i)) =
       (mapRange.linearMap f).comp (mapRange.linearMap f₂) :=
   LinearMap.ext <| mapRange_comp (fun i x => f i x) (fun i x => f₂ i x)
     (fun i => (f i).map_zero) (fun i => (f₂ i).map_zero) (by simp)
-#align dfinsupp.map_range.linear_map_comp Dfinsupp.mapRange.linearMap_comp
+#align dfinsupp.map_range.linear_map_comp DFinsupp.mapRange.linearMap_comp
 
 theorem sum_mapRange_index.linearMap [∀ (i : ι) (x : β₁ i), Decidable (x ≠ 0)]
     [∀ (i : ι) (x : β₂ i), Decidable (x ≠ 0)] {f : ∀ i, β₁ i →ₗ[R] β₂ i} {h : ∀ i, β₂ i →ₗ[R] N}
     {l : Π₀ i, β₁ i} :
     -- Porting note: Needed to add (M := ...) below
-    (Dfinsupp.lsum ℕ (M := β₂)) h (mapRange.linearMap f l)
-      = (Dfinsupp.lsum ℕ (M := β₁)) (fun i => (h i).comp (f i)) l  := by
-  simpa [Dfinsupp.sumAddHom_apply] using sum_mapRange_index fun i => by simp
-#align dfinsupp.sum_map_range_index.linear_map Dfinsupp.sum_mapRange_index.linearMap
+    (DFinsupp.lsum ℕ (M := β₂)) h (mapRange.linearMap f l)
+      = (DFinsupp.lsum ℕ (M := β₁)) (fun i => (h i).comp (f i)) l  := by
+  simpa [DFinsupp.sumAddHom_apply] using sum_mapRange_index fun i => by simp
+#align dfinsupp.sum_map_range_index.linear_map DFinsupp.sum_mapRange_index.linearMap
 
-/-- `Dfinsupp.mapRange.linearMap` as a `LinearEquiv`. -/
+/-- `DFinsupp.mapRange.linearMap` as a `LinearEquiv`. -/
 @[simps apply]
 def mapRange.linearEquiv (e : ∀ i, β₁ i ≃ₗ[R] β₂ i) : (Π₀ i, β₁ i) ≃ₗ[R] Π₀ i, β₂ i :=
   { mapRange.addEquiv fun i => (e i).toAddEquiv,
     mapRange.linearMap fun i => (e i).toLinearMap with
     toFun := mapRange (fun i x => e i x) fun i => (e i).map_zero
     invFun := mapRange (fun i x => (e i).symm x) fun i => (e i).symm.map_zero }
-#align dfinsupp.map_range.linear_equiv Dfinsupp.mapRange.linearEquiv
+#align dfinsupp.map_range.linear_equiv DFinsupp.mapRange.linearEquiv
 
 @[simp]
 theorem mapRange.linearEquiv_refl :
     (mapRange.linearEquiv fun i => LinearEquiv.refl R (β₁ i)) = LinearEquiv.refl _ _ :=
   LinearEquiv.ext mapRange_id
-#align dfinsupp.map_range.linear_equiv_refl Dfinsupp.mapRange.linearEquiv_refl
+#align dfinsupp.map_range.linear_equiv_refl DFinsupp.mapRange.linearEquiv_refl
 
 theorem mapRange.linearEquiv_trans (f : ∀ i, β i ≃ₗ[R] β₁ i) (f₂ : ∀ i, β₁ i ≃ₗ[R] β₂ i) :
     (mapRange.linearEquiv fun i => (f i).trans (f₂ i)) =
       (mapRange.linearEquiv f).trans (mapRange.linearEquiv f₂) :=
   LinearEquiv.ext <| mapRange_comp (fun i x => f₂ i x) (fun i x => f i x)
     (fun i => (f₂ i).map_zero) (fun i => (f i).map_zero) (by simp)
-#align dfinsupp.map_range.linear_equiv_trans Dfinsupp.mapRange.linearEquiv_trans
+#align dfinsupp.map_range.linear_equiv_trans DFinsupp.mapRange.linearEquiv_trans
 
 @[simp]
 theorem mapRange.linearEquiv_symm (e : ∀ i, β₁ i ≃ₗ[R] β₂ i) :
     (mapRange.linearEquiv e).symm = mapRange.linearEquiv fun i => (e i).symm :=
   rfl
-#align dfinsupp.map_range.linear_equiv_symm Dfinsupp.mapRange.linearEquiv_symm
+#align dfinsupp.map_range.linear_equiv_symm DFinsupp.mapRange.linearEquiv_symm
 
 end mapRange
 
@@ -267,15 +267,15 @@ This is the map coming from the universal property of `Π₀ i, M i` as the copr
 See also `LinearMap.coprod` for the binary product version. -/
 noncomputable def coprodMap (f : ∀ i : ι, M i →ₗ[R] N) : (Π₀ i, M i) →ₗ[R] N :=
   (Finsupp.lsum ℕ fun _ : ι => LinearMap.id) ∘ₗ
-    (@finsuppLequivDfinsupp ι R N _ _ _ _ _).symm.toLinearMap ∘ₗ Dfinsupp.mapRange.linearMap f
-#align dfinsupp.coprod_map Dfinsupp.coprodMap
+    (@finsuppLequivDFinsupp ι R N _ _ _ _ _).symm.toLinearMap ∘ₗ DFinsupp.mapRange.linearMap f
+#align dfinsupp.coprod_map DFinsupp.coprodMap
 
 theorem coprodMap_apply (f : ∀ i : ι, M i →ₗ[R] N) (x : Π₀ i, M i) :
     coprodMap f x =
       Finsupp.sum (mapRange (fun i => f i) (fun _ => LinearMap.map_zero _) x).toFinsupp fun _ =>
         id :=
   rfl
-#align dfinsupp.coprod_map_apply Dfinsupp.coprodMap_apply
+#align dfinsupp.coprod_map_apply DFinsupp.coprodMap_apply
 
 theorem coprodMap_apply_single (f : ∀ i : ι, M i →ₗ[R] N) (i : ι) (x : M i) :
     coprodMap f (single i x) = f i x := by
@@ -287,22 +287,22 @@ section Basis
 
 /-- The direct sum of free modules is free.
 
-Note that while this is stated for `Dfinsupp` not `DirectSum`, the types are defeq. -/
+Note that while this is stated for `DFinsupp` not `DirectSum`, the types are defeq. -/
 noncomputable def basis {η : ι → Type _} (b : ∀ i, Basis (η i) R (M i)) :
     Basis (Σi, η i) R (Π₀ i, M i) :=
   .ofRepr
-    ((mapRange.linearEquiv fun i => (b i).repr).trans (sigmaFinsuppLequivDfinsupp R).symm)
-#align dfinsupp.basis Dfinsupp.basis
+    ((mapRange.linearEquiv fun i => (b i).repr).trans (sigmaFinsuppLequivDFinsupp R).symm)
+#align dfinsupp.basis DFinsupp.basis
 
 end Basis
 
-end Dfinsupp
+end DFinsupp
 
 namespace Submodule
 
 variable [Semiring R] [AddCommMonoid N] [Module R N]
 
-open Dfinsupp
+open DFinsupp
 
 theorem dfinsupp_sum_mem {β : ι → Type _} [∀ i, Zero (β i)] [∀ (i) (x : β i), Decidable (x ≠ 0)]
     (S : Submodule R N) (f : Π₀ i, β i) (g : ∀ i, β i → N) (h : ∀ c, f c ≠ 0 → g c (f c) ∈ S) :
@@ -312,36 +312,36 @@ theorem dfinsupp_sum_mem {β : ι → Type _} [∀ i, Zero (β i)] [∀ (i) (x :
 
 theorem dfinsupp_sumAddHom_mem {β : ι → Type _} [∀ i, AddZeroClass (β i)] (S : Submodule R N)
     (f : Π₀ i, β i) (g : ∀ i, β i →+ N) (h : ∀ c, f c ≠ 0 → g c (f c) ∈ S) :
-    Dfinsupp.sumAddHom g f ∈ S :=
+    DFinsupp.sumAddHom g f ∈ S :=
   _root_.dfinsupp_sumAddHom_mem S f g h
 #align submodule.dfinsupp_sum_add_hom_mem Submodule.dfinsupp_sumAddHom_mem
 
-/-- The supremum of a family of submodules is equal to the range of `Dfinsupp.lsum`; that is
+/-- The supremum of a family of submodules is equal to the range of `DFinsupp.lsum`; that is
 every element in the `iSup` can be produced from taking a finite number of non-zero elements
 of `p i`, coercing them to `N`, and summing them. -/
 theorem iSup_eq_range_dfinsupp_lsum (p : ι → Submodule R N) :
-    iSup p = LinearMap.range (Dfinsupp.lsum ℕ (M := fun i ↦ ↥(p i)) fun i => (p i).subtype) := by
+    iSup p = LinearMap.range (DFinsupp.lsum ℕ (M := fun i ↦ ↥(p i)) fun i => (p i).subtype) := by
   apply le_antisymm
   · apply iSup_le _
     intro i y hy
     simp only [LinearMap.mem_range, lsum_apply_apply]
-    exact ⟨Dfinsupp.single i ⟨y, hy⟩, Dfinsupp.sumAddHom_single _ _ _⟩
+    exact ⟨DFinsupp.single i ⟨y, hy⟩, DFinsupp.sumAddHom_single _ _ _⟩
   · rintro x ⟨v, rfl⟩
     exact dfinsupp_sumAddHom_mem _ v _ fun i _ => (le_iSup p i : p i ≤ _) (v i).2
 #align submodule.supr_eq_range_dfinsupp_lsum Submodule.iSup_eq_range_dfinsupp_lsum
 
 /-- The bounded supremum of a family of commutative additive submonoids is equal to the range of
-`Dfinsupp.sumAddHom` composed with `Dfinsupp.filter_add_monoid_hom`; that is, every element in the
+`DFinsupp.sumAddHom` composed with `DFinsupp.filter_add_monoid_hom`; that is, every element in the
 bounded `iSup` can be produced from taking a finite number of non-zero elements from the `S i` that
 satisfy `p i`, coercing them to `γ`, and summing them. -/
 theorem biSup_eq_range_dfinsupp_lsum (p : ι → Prop) [DecidablePred p] (S : ι → Submodule R N) :
     ⨆ (i) (_ : p i), S i =
       LinearMap.range
         (LinearMap.comp
-          (Dfinsupp.lsum ℕ (M := fun i ↦ ↥(S i)) (fun i => (S i).subtype))
-            (Dfinsupp.filterLinearMap R _ p)) := by
+          (DFinsupp.lsum ℕ (M := fun i ↦ ↥(S i)) (fun i => (S i).subtype))
+            (DFinsupp.filterLinearMap R _ p)) := by
   apply le_antisymm
-  · refine' iSup₂_le fun i hi y hy => ⟨Dfinsupp.single i ⟨y, hy⟩, _⟩
+  · refine' iSup₂_le fun i hi y hy => ⟨DFinsupp.single i ⟨y, hy⟩, _⟩
     rw [LinearMap.comp_apply, filterLinearMap_apply, filter_single_pos _ _ hi]
     simp only [lsum_apply_apply, sumAddHom_single, LinearMap.toAddMonoidHom_coe, coeSubtype]
   · rintro x ⟨v, rfl⟩
@@ -354,7 +354,7 @@ theorem biSup_eq_range_dfinsupp_lsum (p : ι → Prop) [DecidablePred p] (S : ι
 
 theorem mem_iSup_iff_exists_dfinsupp (p : ι → Submodule R N) (x : N) :
     x ∈ iSup p ↔
-      ∃ f : Π₀ i, p i, Dfinsupp.lsum ℕ (M := fun i ↦ ↥(p i)) (fun i => (p i).subtype) f = x :=
+      ∃ f : Π₀ i, p i, DFinsupp.lsum ℕ (M := fun i ↦ ↥(p i)) (fun i => (p i).subtype) f = x :=
   SetLike.ext_iff.mp (iSup_eq_range_dfinsupp_lsum p) x
 #align submodule.mem_supr_iff_exists_dfinsupp Submodule.mem_iSup_iff_exists_dfinsupp
 
@@ -362,7 +362,7 @@ theorem mem_iSup_iff_exists_dfinsupp (p : ι → Submodule R N) (x : N) :
 theorem mem_iSup_iff_exists_dfinsupp' (p : ι → Submodule R N) [∀ (i) (x : p i), Decidable (x ≠ 0)]
     (x : N) : x ∈ iSup p ↔ ∃ f : Π₀ i, p i, (f.sum fun i xi => ↑xi) = x := by
   rw [mem_iSup_iff_exists_dfinsupp]
-  simp_rw [Dfinsupp.lsum_apply_apply, Dfinsupp.sumAddHom_apply,
+  simp_rw [DFinsupp.lsum_apply_apply, DFinsupp.sumAddHom_apply,
     LinearMap.toAddMonoidHom_coe, coeSubtype]
 #align submodule.mem_supr_iff_exists_dfinsupp' Submodule.mem_iSup_iff_exists_dfinsupp'
 
@@ -370,7 +370,7 @@ theorem mem_biSup_iff_exists_dfinsupp (p : ι → Prop) [DecidablePred p] (S : 
     (x : N) :
     (x ∈ ⨆ (i) (_ : p i), S i) ↔
       ∃ f : Π₀ i, S i,
-        Dfinsupp.lsum ℕ (M := fun i ↦ ↥(S i)) (fun i => (S i).subtype) (f.filter p) = x :=
+        DFinsupp.lsum ℕ (M := fun i ↦ ↥(S i)) (fun i => (S i).subtype) (f.filter p) = x :=
   SetLike.ext_iff.mp (biSup_eq_range_dfinsupp_lsum p S) x
 #align submodule.mem_bsupr_iff_exists_dfinsupp Submodule.mem_biSup_iff_exists_dfinsupp
 
@@ -398,13 +398,13 @@ theorem mem_iSup_finset_iff_exists_sum {s : Finset ι} (p : ι → Submodule R N
         rw [mem_support_iff, not_ne_iff] at hx
         rw [hx]
         rfl
-    · refine' ⟨Dfinsupp.mk s _, _⟩
+    · refine' ⟨DFinsupp.mk s _, _⟩
       · rintro ⟨i, hi⟩
         refine' ⟨μ i, _⟩
         rw [iSup_pos]
         · exact coe_mem _
         · exact hi
-      simp only [Dfinsupp.sum]
+      simp only [DFinsupp.sum]
       rw [Finset.sum_subset support_mk_subset, ← hμ]
       exact Finset.sum_congr rfl fun x hx => congr_arg Subtype.val <| mk_of_mem hx
       · intro x _ hx
@@ -417,13 +417,13 @@ end Submodule
 
 namespace CompleteLattice
 
-open Dfinsupp
+open DFinsupp
 
 section Semiring
 
 variable [Semiring R] [AddCommMonoid N] [Module R N]
 
-/-- Independence of a family of submodules can be expressed as a quantifier over `Dfinsupp`s.
+/-- Independence of a family of submodules can be expressed as a quantifier over `DFinsupp`s.
 
 This is an intermediate result used to prove
 `CompleteLattice.independent_of_dfinsupp_lsum_injective` and
@@ -438,7 +438,7 @@ theorem independent_iff_forall_dfinsupp (p : ι → Submodule R N) :
   simp_rw [Submodule.coe_eq_zero]
 #align complete_lattice.independent_iff_forall_dfinsupp CompleteLattice.independent_iff_forall_dfinsupp
 
-/- If `Dfinsupp.lsum` applied with `Submodule.subtype` is injective then the submodules are
+/- If `DFinsupp.lsum` applied with `Submodule.subtype` is injective then the submodules are
 independent. -/
 theorem independent_of_dfinsupp_lsum_injective (p : ι → Submodule R N)
     (h : Function.Injective (lsum ℕ (M := fun i ↦ ↥(p i)) fun i => (p i).subtype)) :
@@ -453,7 +453,7 @@ theorem independent_of_dfinsupp_lsum_injective (p : ι → Submodule R N)
   simpa [eq_comm] using this
 #align complete_lattice.independent_of_dfinsupp_lsum_injective CompleteLattice.independent_of_dfinsupp_lsum_injective
 
-/- If `Dfinsupp.sumAddHom` applied with `AddSubmonoid.subtype` is injective then the additive
+/- If `DFinsupp.sumAddHom` applied with `AddSubmonoid.subtype` is injective then the additive
 submonoids are independent. -/
 theorem independent_of_dfinsupp_sumAddHom_injective (p : ι → AddSubmonoid N)
     (h : Function.Injective (sumAddHom fun i => (p i).subtype)) : Independent p := by
@@ -461,13 +461,13 @@ theorem independent_of_dfinsupp_sumAddHom_injective (p : ι → AddSubmonoid N)
   exact independent_of_dfinsupp_lsum_injective _ h
 #align complete_lattice.independent_of_dfinsupp_sum_add_hom_injective CompleteLattice.independent_of_dfinsupp_sumAddHom_injective
 
-/-- Combining `Dfinsupp.lsum` with `LinearMap.toSpanSingleton` is the same as `Finsupp.total` -/
+/-- Combining `DFinsupp.lsum` with `LinearMap.toSpanSingleton` is the same as `Finsupp.total` -/
 theorem lsum_comp_mapRange_toSpanSingleton [∀ m : R, Decidable (m ≠ 0)] (p : ι → Submodule R N)
     {v : ι → N} (hv : ∀ i : ι, v i ∈ p i) :
     (lsum ℕ (M := fun i ↦ ↥(p i)) fun i => (p i).subtype : _ →ₗ[R] _).comp
         ((mapRange.linearMap fun i => LinearMap.toSpanSingleton R (↥(p i)) ⟨v i, hv i⟩ :
               _ →ₗ[R] _).comp
-          (finsuppLequivDfinsupp R : (ι →₀ R) ≃ₗ[R] _).toLinearMap) =
+          (finsuppLequivDFinsupp R : (ι →₀ R) ≃ₗ[R] _).toLinearMap) =
       Finsupp.total ι N R v := by
   ext
   simp
@@ -479,7 +479,7 @@ section Ring
 
 variable [Ring R] [AddCommGroup N] [Module R N]
 
-/- If `Dfinsupp.sumAddHom` applied with `AddSubmonoid.subtype` is injective then the additive
+/- If `DFinsupp.sumAddHom` applied with `AddSubmonoid.subtype` is injective then the additive
 subgroups are independent. -/
 theorem independent_of_dfinsupp_sumAddHom_injective' (p : ι → AddSubgroup N)
     (h : Function.Injective (sumAddHom fun i => (p i).subtype)) : Independent p := by
@@ -507,7 +507,7 @@ theorem Independent.dfinsupp_lsum_injective {p : ι → Submodule R N} (h : Inde
   intro m hm
   ext i : 1
   -- split `m` into the piece at `i` and the pieces elsewhere, to match `h`
-  rw [Dfinsupp.zero_apply, ← neg_eq_zero]
+  rw [DFinsupp.zero_apply, ← neg_eq_zero]
   refine' h i (-m i) m _
   rwa [← erase_add_single i m, LinearMap.map_add, lsum_single, Submodule.subtype_apply,
     add_eq_zero_iff_eq_neg, ← Submodule.coe_neg] at hm
@@ -521,7 +521,7 @@ theorem Independent.dfinsupp_sumAddHom_injective {p : ι → AddSubgroup N} (h :
   exact h.dfinsupp_lsum_injective
 #align complete_lattice.independent.dfinsupp_sum_add_hom_injective CompleteLattice.Independent.dfinsupp_sumAddHom_injective
 
-/-- A family of submodules over an additive group are independent if and only iff `Dfinsupp.lsum`
+/-- A family of submodules over an additive group are independent if and only iff `DFinsupp.lsum`
 applied with `Submodule.subtype` is injective.
 
 Note that this is not generally true for `[Semiring R]`; see
@@ -532,7 +532,7 @@ theorem independent_iff_dfinsupp_lsum_injective (p : ι → Submodule R N) :
 #align complete_lattice.independent_iff_dfinsupp_lsum_injective CompleteLattice.independent_iff_dfinsupp_lsum_injective
 
 /-- A family of additive subgroups over an additive group are independent if and only if
-`Dfinsupp.sumAddHom` applied with `AddSubgroup.subtype` is injective. -/
+`DFinsupp.sumAddHom` applied with `AddSubgroup.subtype` is injective. -/
 theorem independent_iff_dfinsupp_sumAddHom_injective (p : ι → AddSubgroup N) :
     Independent p ↔ Function.Injective (sumAddHom fun i => (p i).subtype) :=
   ⟨Independent.dfinsupp_sumAddHom_injective, independent_of_dfinsupp_sumAddHom_injective' p⟩
@@ -550,8 +550,8 @@ theorem Independent.linearIndependent [NoZeroSMulDivisors R N] (p : ι → Submo
   rw [linearIndependent_iff]
   intro l hl
   let a :=
-    Dfinsupp.mapRange.linearMap (fun i => LinearMap.toSpanSingleton R (p i) ⟨v i, hv i⟩)
-      l.toDfinsupp
+    DFinsupp.mapRange.linearMap (fun i => LinearMap.toSpanSingleton R (p i) ⟨v i, hv i⟩)
+      l.toDFinsupp
   have ha : a = 0 := by
     apply hp.dfinsupp_lsum_injective
     rwa [← lsum_comp_mapRange_toSpanSingleton _ hv] at hl

a148d797

fix: precedences of ⨆⋃⋂⨅ (#5614)

e3c8f983

Diff

@@ -335,7 +335,7 @@ theorem iSup_eq_range_dfinsupp_lsum (p : ι → Submodule R N) :
 bounded `iSup` can be produced from taking a finite number of non-zero elements from the `S i` that
 satisfy `p i`, coercing them to `γ`, and summing them. -/
 theorem biSup_eq_range_dfinsupp_lsum (p : ι → Prop) [DecidablePred p] (S : ι → Submodule R N) :
-    (⨆ (i) (_ : p i), S i) =
+    ⨆ (i) (_ : p i), S i =
       LinearMap.range
         (LinearMap.comp
           (Dfinsupp.lsum ℕ (M := fun i ↦ ↥(S i)) (fun i => (S i).subtype))

a148d797

style: allow _ for an argument in notation3 & replace _foo with _ in notation3 (#4652)

e2b5ca37

Diff

@@ -335,7 +335,7 @@ theorem iSup_eq_range_dfinsupp_lsum (p : ι → Submodule R N) :
 bounded `iSup` can be produced from taking a finite number of non-zero elements from the `S i` that
 satisfy `p i`, coercing them to `γ`, and summing them. -/
 theorem biSup_eq_range_dfinsupp_lsum (p : ι → Prop) [DecidablePred p] (S : ι → Submodule R N) :
-    (⨆ (i) (_h : p i), S i) =
+    (⨆ (i) (_ : p i), S i) =
       LinearMap.range
         (LinearMap.comp
           (Dfinsupp.lsum ℕ (M := fun i ↦ ↥(S i)) (fun i => (S i).subtype))
@@ -368,7 +368,7 @@ theorem mem_iSup_iff_exists_dfinsupp' (p : ι → Submodule R N) [∀ (i) (x : p
 
 theorem mem_biSup_iff_exists_dfinsupp (p : ι → Prop) [DecidablePred p] (S : ι → Submodule R N)
     (x : N) :
-    (x ∈ ⨆ (i) (_h : p i), S i) ↔
+    (x ∈ ⨆ (i) (_ : p i), S i) ↔
       ∃ f : Π₀ i, S i,
         Dfinsupp.lsum ℕ (M := fun i ↦ ↥(S i)) (fun i => (S i).subtype) (f.filter p) = x :=
   SetLike.ext_iff.mp (biSup_eq_range_dfinsupp_lsum p S) x
@@ -391,7 +391,7 @@ theorem mem_iSup_finset_iff_exists_sum {s : Finset ι} (p : ι → Submodule R N
         rw [mem_support_iff, not_ne_iff]
         ext
         rw [coe_zero, ← mem_bot R]
-        suffices : ⊥ = ⨆ (_H : x ∈ s), p x
+        suffices : ⊥ = ⨆ (_ : x ∈ s), p x
         · exact this.symm ▸ coe_mem (μ x)
         exact (iSup_neg hx).symm
       · intro x _ hx

a148d797

chore: fix upper/lowercase in comments (#4360)

Run a non-interactive version of fix-comments.py on all files.
Go through the diff and manually add/discard/edit chunks.

27d257fc

Diff

@@ -287,7 +287,7 @@ section Basis
 
 /-- The direct sum of free modules is free.
 
-Note that while this is stated for `Dfinsupp` not `direct_sum`, the types are defeq. -/
+Note that while this is stated for `Dfinsupp` not `DirectSum`, the types are defeq. -/
 noncomputable def basis {η : ι → Type _} (b : ∀ i, Basis (η i) R (M i)) :
     Basis (Σi, η i) R (Π₀ i, M i) :=
   .ofRepr
@@ -317,7 +317,7 @@ theorem dfinsupp_sumAddHom_mem {β : ι → Type _} [∀ i, AddZeroClass (β i)]
 #align submodule.dfinsupp_sum_add_hom_mem Submodule.dfinsupp_sumAddHom_mem
 
 /-- The supremum of a family of submodules is equal to the range of `Dfinsupp.lsum`; that is
-every element in the `supr` can be produced from taking a finite number of non-zero elements
+every element in the `iSup` can be produced from taking a finite number of non-zero elements
 of `p i`, coercing them to `N`, and summing them. -/
 theorem iSup_eq_range_dfinsupp_lsum (p : ι → Submodule R N) :
     iSup p = LinearMap.range (Dfinsupp.lsum ℕ (M := fun i ↦ ↥(p i)) fun i => (p i).subtype) := by
@@ -332,7 +332,7 @@ theorem iSup_eq_range_dfinsupp_lsum (p : ι → Submodule R N) :
 
 /-- The bounded supremum of a family of commutative additive submonoids is equal to the range of
 `Dfinsupp.sumAddHom` composed with `Dfinsupp.filter_add_monoid_hom`; that is, every element in the
-bounded `supr` can be produced from taking a finite number of non-zero elements from the `S i` that
+bounded `iSup` can be produced from taking a finite number of non-zero elements from the `S i` that
 satisfy `p i`, coercing them to `γ`, and summing them. -/
 theorem biSup_eq_range_dfinsupp_lsum (p : ι → Prop) [DecidablePred p] (S : ι → Submodule R N) :
     (⨆ (i) (_h : p i), S i) =
@@ -479,7 +479,7 @@ section Ring
 
 variable [Ring R] [AddCommGroup N] [Module R N]
 
-/- If `Dfinsupp.sumAddHom` applied with `add_submonoid.subtype` is injective then the additive
+/- If `Dfinsupp.sumAddHom` applied with `AddSubmonoid.subtype` is injective then the additive
 subgroups are independent. -/
 theorem independent_of_dfinsupp_sumAddHom_injective' (p : ι → AddSubgroup N)
     (h : Function.Injective (sumAddHom fun i => (p i).subtype)) : Independent p := by

a148d797

chore: delete 2074 references (#4030)

1877b122

Diff

@@ -37,9 +37,6 @@ much more developed, but many lemmas in that file should be eligible to copy ove
 function with finite support, module, linear algebra
 -/
 
--- Porting note: TODO Erase this line. Workaround for lean4#2074.
-attribute [-instance] Ring.toNonAssocRing
-
 variable {ι : Type _} {R : Type _} {S : Type _} {M : ι → Type _} {N : Type _}
 
 variable [dec_ι : DecidableEq ι]

a148d797

chore: reenable eta, bump to nightly 2023-05-16 (#3414)

Now that leanprover/lean4#2210 has been merged, this PR:

removes all the set_option synthInstance.etaExperiment true commands (and some etaExperiment% term elaborators)
removes many but not quite all set_option maxHeartbeats commands
makes various other changes required to cope with leanprover/lean4#2210.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Matthew Ballard <matt@mrb.email>

a6e1045f

Diff

@@ -541,7 +541,6 @@ theorem independent_iff_dfinsupp_sumAddHom_injective (p : ι → AddSubgroup N)
   ⟨Independent.dfinsupp_sumAddHom_injective, independent_of_dfinsupp_sumAddHom_injective' p⟩
 #align complete_lattice.independent_iff_dfinsupp_sum_add_hom_injective CompleteLattice.independent_iff_dfinsupp_sumAddHom_injective
 
-set_option synthInstance.etaExperiment true in
 /-- If a family of submodules is `Independent`, then a choice of nonzero vector from each submodule
 forms a linearly independent family.

a148d797

chore: Rename to sSup/iSup (#3938)

As discussed on Zulip

Renames

supₛ → sSup
infₛ → sInf
supᵢ → iSup
infᵢ → iInf
bsupₛ → bsSup
binfₛ → bsInf
bsupᵢ → biSup
binfᵢ → biInf
csupₛ → csSup
cinfₛ → csInf
csupᵢ → ciSup
cinfᵢ → ciInf
unionₛ → sUnion
interₛ → sInter
unionᵢ → iUnion
interᵢ → iInter
bunionₛ → bsUnion
binterₛ → bsInter
bunionᵢ → biUnion
binterᵢ → biInter

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

d1eb6264

Diff

@@ -322,69 +322,69 @@ theorem dfinsupp_sumAddHom_mem {β : ι → Type _} [∀ i, AddZeroClass (β i)]
 /-- The supremum of a family of submodules is equal to the range of `Dfinsupp.lsum`; that is
 every element in the `supr` can be produced from taking a finite number of non-zero elements
 of `p i`, coercing them to `N`, and summing them. -/
-theorem supᵢ_eq_range_dfinsupp_lsum (p : ι → Submodule R N) :
-    supᵢ p = LinearMap.range (Dfinsupp.lsum ℕ (M := fun i ↦ ↥(p i)) fun i => (p i).subtype) := by
+theorem iSup_eq_range_dfinsupp_lsum (p : ι → Submodule R N) :
+    iSup p = LinearMap.range (Dfinsupp.lsum ℕ (M := fun i ↦ ↥(p i)) fun i => (p i).subtype) := by
   apply le_antisymm
-  · apply supᵢ_le _
+  · apply iSup_le _
     intro i y hy
     simp only [LinearMap.mem_range, lsum_apply_apply]
     exact ⟨Dfinsupp.single i ⟨y, hy⟩, Dfinsupp.sumAddHom_single _ _ _⟩
   · rintro x ⟨v, rfl⟩
-    exact dfinsupp_sumAddHom_mem _ v _ fun i _ => (le_supᵢ p i : p i ≤ _) (v i).2
-#align submodule.supr_eq_range_dfinsupp_lsum Submodule.supᵢ_eq_range_dfinsupp_lsum
+    exact dfinsupp_sumAddHom_mem _ v _ fun i _ => (le_iSup p i : p i ≤ _) (v i).2
+#align submodule.supr_eq_range_dfinsupp_lsum Submodule.iSup_eq_range_dfinsupp_lsum
 
 /-- The bounded supremum of a family of commutative additive submonoids is equal to the range of
 `Dfinsupp.sumAddHom` composed with `Dfinsupp.filter_add_monoid_hom`; that is, every element in the
 bounded `supr` can be produced from taking a finite number of non-zero elements from the `S i` that
 satisfy `p i`, coercing them to `γ`, and summing them. -/
-theorem bsupᵢ_eq_range_dfinsupp_lsum (p : ι → Prop) [DecidablePred p] (S : ι → Submodule R N) :
+theorem biSup_eq_range_dfinsupp_lsum (p : ι → Prop) [DecidablePred p] (S : ι → Submodule R N) :
     (⨆ (i) (_h : p i), S i) =
       LinearMap.range
         (LinearMap.comp
           (Dfinsupp.lsum ℕ (M := fun i ↦ ↥(S i)) (fun i => (S i).subtype))
             (Dfinsupp.filterLinearMap R _ p)) := by
   apply le_antisymm
-  · refine' supᵢ₂_le fun i hi y hy => ⟨Dfinsupp.single i ⟨y, hy⟩, _⟩
+  · refine' iSup₂_le fun i hi y hy => ⟨Dfinsupp.single i ⟨y, hy⟩, _⟩
     rw [LinearMap.comp_apply, filterLinearMap_apply, filter_single_pos _ _ hi]
     simp only [lsum_apply_apply, sumAddHom_single, LinearMap.toAddMonoidHom_coe, coeSubtype]
   · rintro x ⟨v, rfl⟩
     refine' dfinsupp_sumAddHom_mem _ _ _ fun i _ => _
-    refine' mem_supᵢ_of_mem i _
+    refine' mem_iSup_of_mem i _
     by_cases hp : p i
     · simp [hp]
     · simp [hp]
-#align submodule.bsupr_eq_range_dfinsupp_lsum Submodule.bsupᵢ_eq_range_dfinsupp_lsum
+#align submodule.bsupr_eq_range_dfinsupp_lsum Submodule.biSup_eq_range_dfinsupp_lsum
 
-theorem mem_supᵢ_iff_exists_dfinsupp (p : ι → Submodule R N) (x : N) :
-    x ∈ supᵢ p ↔
+theorem mem_iSup_iff_exists_dfinsupp (p : ι → Submodule R N) (x : N) :
+    x ∈ iSup p ↔
       ∃ f : Π₀ i, p i, Dfinsupp.lsum ℕ (M := fun i ↦ ↥(p i)) (fun i => (p i).subtype) f = x :=
-  SetLike.ext_iff.mp (supᵢ_eq_range_dfinsupp_lsum p) x
-#align submodule.mem_supr_iff_exists_dfinsupp Submodule.mem_supᵢ_iff_exists_dfinsupp
+  SetLike.ext_iff.mp (iSup_eq_range_dfinsupp_lsum p) x
+#align submodule.mem_supr_iff_exists_dfinsupp Submodule.mem_iSup_iff_exists_dfinsupp
 
-/-- A variant of `Submodule.mem_supᵢ_iff_exists_dfinsupp` with the RHS fully unfolded. -/
-theorem mem_supᵢ_iff_exists_dfinsupp' (p : ι → Submodule R N) [∀ (i) (x : p i), Decidable (x ≠ 0)]
-    (x : N) : x ∈ supᵢ p ↔ ∃ f : Π₀ i, p i, (f.sum fun i xi => ↑xi) = x := by
-  rw [mem_supᵢ_iff_exists_dfinsupp]
+/-- A variant of `Submodule.mem_iSup_iff_exists_dfinsupp` with the RHS fully unfolded. -/
+theorem mem_iSup_iff_exists_dfinsupp' (p : ι → Submodule R N) [∀ (i) (x : p i), Decidable (x ≠ 0)]
+    (x : N) : x ∈ iSup p ↔ ∃ f : Π₀ i, p i, (f.sum fun i xi => ↑xi) = x := by
+  rw [mem_iSup_iff_exists_dfinsupp]
   simp_rw [Dfinsupp.lsum_apply_apply, Dfinsupp.sumAddHom_apply,
     LinearMap.toAddMonoidHom_coe, coeSubtype]
-#align submodule.mem_supr_iff_exists_dfinsupp' Submodule.mem_supᵢ_iff_exists_dfinsupp'
+#align submodule.mem_supr_iff_exists_dfinsupp' Submodule.mem_iSup_iff_exists_dfinsupp'
 
-theorem mem_bsupᵢ_iff_exists_dfinsupp (p : ι → Prop) [DecidablePred p] (S : ι → Submodule R N)
+theorem mem_biSup_iff_exists_dfinsupp (p : ι → Prop) [DecidablePred p] (S : ι → Submodule R N)
     (x : N) :
     (x ∈ ⨆ (i) (_h : p i), S i) ↔
       ∃ f : Π₀ i, S i,
         Dfinsupp.lsum ℕ (M := fun i ↦ ↥(S i)) (fun i => (S i).subtype) (f.filter p) = x :=
-  SetLike.ext_iff.mp (bsupᵢ_eq_range_dfinsupp_lsum p S) x
-#align submodule.mem_bsupr_iff_exists_dfinsupp Submodule.mem_bsupᵢ_iff_exists_dfinsupp
+  SetLike.ext_iff.mp (biSup_eq_range_dfinsupp_lsum p S) x
+#align submodule.mem_bsupr_iff_exists_dfinsupp Submodule.mem_biSup_iff_exists_dfinsupp
 
 open BigOperators
 
-theorem mem_supᵢ_finset_iff_exists_sum {s : Finset ι} (p : ι → Submodule R N) (a : N) :
+theorem mem_iSup_finset_iff_exists_sum {s : Finset ι} (p : ι → Submodule R N) (a : N) :
     (a ∈ ⨆ i ∈ s, p i) ↔ ∃ μ : ∀ i, p i, (∑ i in s, (μ i : N)) = a := by
   classical
-    rw [Submodule.mem_supᵢ_iff_exists_dfinsupp']
+    rw [Submodule.mem_iSup_iff_exists_dfinsupp']
     constructor <;> rintro ⟨μ, hμ⟩
-    · use fun i => ⟨μ i, (supᵢ_const_le : _ ≤ p i) (coe_mem <| μ i)⟩
+    · use fun i => ⟨μ i, (iSup_const_le : _ ≤ p i) (coe_mem <| μ i)⟩
       rw [← hμ]
       symm
       apply Finset.sum_subset
@@ -396,7 +396,7 @@ theorem mem_supᵢ_finset_iff_exists_sum {s : Finset ι} (p : ι → Submodule R
         rw [coe_zero, ← mem_bot R]
         suffices : ⊥ = ⨆ (_H : x ∈ s), p x
         · exact this.symm ▸ coe_mem (μ x)
-        exact (supᵢ_neg hx).symm
+        exact (iSup_neg hx).symm
       · intro x _ hx
         rw [mem_support_iff, not_ne_iff] at hx
         rw [hx]
@@ -404,7 +404,7 @@ theorem mem_supᵢ_finset_iff_exists_sum {s : Finset ι} (p : ι → Submodule R
     · refine' ⟨Dfinsupp.mk s _, _⟩
       · rintro ⟨i, hi⟩
         refine' ⟨μ i, _⟩
-        rw [supᵢ_pos]
+        rw [iSup_pos]
         · exact coe_mem _
         · exact hi
       simp only [Dfinsupp.sum]
@@ -414,7 +414,7 @@ theorem mem_supᵢ_finset_iff_exists_sum {s : Finset ι} (p : ι → Submodule R
         rw [mem_support_iff, not_ne_iff] at hx
         rw [hx]
         rfl
-#align submodule.mem_supr_finset_iff_exists_sum Submodule.mem_supᵢ_finset_iff_exists_sum
+#align submodule.mem_supr_finset_iff_exists_sum Submodule.mem_iSup_finset_iff_exists_sum
 
 end Submodule
 
@@ -436,7 +436,7 @@ theorem independent_iff_forall_dfinsupp (p : ι → Submodule R N) :
       ∀ (i) (x : p i) (v : Π₀ i : ι, ↥(p i)),
         lsum ℕ (M := fun i ↦ ↥(p i)) (fun i => (p i).subtype) (erase i v) = x → x = 0 := by
   simp_rw [CompleteLattice.independent_def, Submodule.disjoint_def,
-    Submodule.mem_bsupᵢ_iff_exists_dfinsupp, exists_imp, filter_ne_eq_erase]
+    Submodule.mem_biSup_iff_exists_dfinsupp, exists_imp, filter_ne_eq_erase]
   refine' forall_congr' fun i => Subtype.forall'.trans _
   simp_rw [Submodule.coe_eq_zero]
 #align complete_lattice.independent_iff_forall_dfinsupp CompleteLattice.independent_iff_forall_dfinsupp

a148d797

chore: bye-bye, solo bys! (#3825)

This PR puts, with one exception, every single remaining by that lies all by itself on its own line to the previous line, thus matching the current behaviour of start-port.sh. The exception is when the by begins the second or later argument to a tuple or anonymous constructor; see https://github.com/leanprover-community/mathlib4/pull/3825#discussion_r1186702599.

Essentially this is s/\n *by$/ by/g, but with manual editing to satisfy the linter's max-100-char-line requirement. The Python style linter is also modified to catch these "isolated bys".

14167e48

Diff

@@ -501,8 +501,7 @@ theorem Independent.dfinsupp_lsum_injective {p : ι → Submodule R N} (h : Inde
     Function.Injective (lsum ℕ (M := fun i ↦ ↥(p i)) fun i => (p i).subtype) := by
   -- simplify everything down to binders over equalities in `N`
   rw [independent_iff_forall_dfinsupp] at h
-  suffices LinearMap.ker (lsum ℕ (M := fun i ↦ ↥(p i)) fun i => (p i).subtype) = ⊥
-    by
+  suffices LinearMap.ker (lsum ℕ (M := fun i ↦ ↥(p i)) fun i => (p i).subtype) = ⊥ by
     -- Lean can't find this without our help
     letI thisI : AddCommGroup (Π₀ i, p i) := inferInstance
     rw [LinearMap.ker_eq_bot] at this

a148d797

feat: port LinearAlgebra.ProjectiveSpace.Independence (#3728)

Co-authored-by: ChrisHughes24 <chrishughes24@gmail.com>

8c309869

Diff

@@ -550,24 +550,26 @@ See also `CompleteLattice.Independent.linearIndependent'`. -/
 theorem Independent.linearIndependent [NoZeroSMulDivisors R N] (p : ι → Submodule R N)
     (hp : Independent p) {v : ι → N} (hv : ∀ i, v i ∈ p i) (hv' : ∀ i, v i ≠ 0) :
     LinearIndependent R v := by
-  classical
-    rw [linearIndependent_iff]
-    intro l hl
-    let a :=
-      Dfinsupp.mapRange.linearMap (fun i => LinearMap.toSpanSingleton R (p i) ⟨v i, hv i⟩)
-        l.toDfinsupp
-    have ha : a = 0 := by
-      apply hp.dfinsupp_lsum_injective
-      rwa [← lsum_comp_mapRange_toSpanSingleton _ hv] at hl
-    ext i
-    apply smul_left_injective R (hv' i)
-    have : l i • v i = a i := rfl
-    simp only [coe_zero, Pi.zero_apply, ZeroMemClass.coe_zero, smul_eq_zero, ha] at this
-    simpa
+  let _ := Classical.decEq ι
+  let _ := Classical.decEq R
+  rw [linearIndependent_iff]
+  intro l hl
+  let a :=
+    Dfinsupp.mapRange.linearMap (fun i => LinearMap.toSpanSingleton R (p i) ⟨v i, hv i⟩)
+      l.toDfinsupp
+  have ha : a = 0 := by
+    apply hp.dfinsupp_lsum_injective
+    rwa [← lsum_comp_mapRange_toSpanSingleton _ hv] at hl
+  ext i
+  apply smul_left_injective R (hv' i)
+  have : l i • v i = a i := rfl
+  simp only [coe_zero, Pi.zero_apply, ZeroMemClass.coe_zero, smul_eq_zero, ha] at this
+  simpa
 #align complete_lattice.independent.linear_independent CompleteLattice.Independent.linearIndependent
 
 theorem independent_iff_linearIndependent_of_ne_zero [NoZeroSMulDivisors R N] {v : ι → N}
     (h_ne_zero : ∀ i, v i ≠ 0) : (Independent fun i => R ∙ v i) ↔ LinearIndependent R v :=
+  let _ := Classical.decEq ι
   ⟨fun hv => hv.linearIndependent _ (fun i => Submodule.mem_span_singleton_self <| v i) h_ne_zero,
     fun hv => hv.independent_span_singleton⟩
 #align complete_lattice.independent_iff_linear_independent_of_ne_zero CompleteLattice.independent_iff_linearIndependent_of_ne_zero

a148d797

chore: use etaExperiment rather than hacking with instances (#3668)

This is to fix timeouts in https://github.com/leanprover-community/mathlib4/pull/3552.

See discussion at https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/!4.233552.20.28LinearAlgebra.2EMatrix.2EToLin.29.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

0f225a7f

Diff

@@ -542,6 +542,7 @@ theorem independent_iff_dfinsupp_sumAddHom_injective (p : ι → AddSubgroup N)
   ⟨Independent.dfinsupp_sumAddHom_injective, independent_of_dfinsupp_sumAddHom_injective' p⟩
 #align complete_lattice.independent_iff_dfinsupp_sum_add_hom_injective CompleteLattice.independent_iff_dfinsupp_sumAddHom_injective
 
+set_option synthInstance.etaExperiment true in
 /-- If a family of submodules is `Independent`, then a choice of nonzero vector from each submodule
 forms a linearly independent family.

a148d797

feat: port Algebra.Module.Projective (#3335)

6ab1bde3

Diff

@@ -73,7 +73,7 @@ theorem lhom_ext ⦃φ ψ : (Π₀ i, M i) →ₗ[R] N⦄ (h : ∀ i x, φ (sing
 
 See note [partially-applied ext lemmas].
 After apply this lemma, if `M = R` then it suffices to verify `φ (single a 1) = ψ (single a 1)`. -/
-@[ext]
+@[ext 1100]
 theorem lhom_ext' ⦃φ ψ : (Π₀ i, M i) →ₗ[R] N⦄ (h : ∀ i, φ.comp (lsingle i) = ψ.comp (lsingle i)) :
     φ = ψ :=
   lhom_ext fun i => LinearMap.congr_fun (h i)
@@ -280,6 +280,10 @@ theorem coprodMap_apply (f : ∀ i : ι, M i →ₗ[R] N) (x : Π₀ i, M i) :
   rfl
 #align dfinsupp.coprod_map_apply Dfinsupp.coprodMap_apply
 
+theorem coprodMap_apply_single (f : ∀ i : ι, M i →ₗ[R] N) (i : ι) (x : M i) :
+    coprodMap f (single i x) = f i x := by
+  simp [coprodMap_apply]
+
 end CoprodMap
 
 section Basis

a148d797

chore: tidy various files (#3124)

55209140

Diff

@@ -21,7 +21,7 @@ In this file we define `LinearMap` versions of various maps:
 
 * `Dfinsupp.lsingle a : M →ₗ[R] Π₀ i, M i`: `Dfinsupp.single a` as a linear map;
 
-* `Dfinsupp.lmk s : (Π i : (↑s : set ι), M i) →ₗ[R] Π₀ i, M i`: `Dfinsupp.single a` as a linear map;
+* `Dfinsupp.lmk s : (Π i : (↑s : Set ι), M i) →ₗ[R] Π₀ i, M i`: `Dfinsupp.single a` as a linear map;
 
 * `Dfinsupp.lapply i : (Π₀ i, M i) →ₗ[R] M`: the map `fun f ↦ f i` as a linear map;
 
@@ -51,8 +51,7 @@ variable [Semiring R] [∀ i, AddCommMonoid (M i)] [∀ i, Module R (M i)]
 variable [AddCommMonoid N] [Module R N]
 
 /-- `Dfinsupp.mk` as a `LinearMap`. -/
-def lmk (s : Finset ι) : (∀ i : (↑s : Set ι), M i) →ₗ[R] Π₀ i, M i
-    where
+def lmk (s : Finset ι) : (∀ i : (↑s : Set ι), M i) →ₗ[R] Π₀ i, M i where
   toFun := mk s
   map_add' _ _ := mk_add
   map_smul' c x := mk_smul c x
@@ -81,8 +80,7 @@ theorem lhom_ext' ⦃φ ψ : (Π₀ i, M i) →ₗ[R] N⦄ (h : ∀ i, φ.comp (
 #align dfinsupp.lhom_ext' Dfinsupp.lhom_ext'
 
 /-- Interpret `fun (f : Π₀ i, M i) ↦ f i` as a linear map. -/
-def lapply (i : ι) : (Π₀ i, M i) →ₗ[R] M i
-    where
+def lapply (i : ι) : (Π₀ i, M i) →ₗ[R] M i where
   toFun f := f i
   map_add' f g := add_apply f g i
   map_smul' c f := smul_apply c f i
@@ -128,9 +126,9 @@ variable (S)
 
 
 instance {R : Type _} {S : Type _} [Semiring R] [Semiring S] (σ : R →+* S)
-  {σ' : S →+* R} [RingHomInvPair σ σ'] [RingHomInvPair σ' σ] (M : Type _) (M₂ : Type _)
-  [AddCommMonoid M] [AddCommMonoid M₂] [Module R M] [Module S M₂] :
-      EquivLike (LinearEquiv σ M M₂) M M₂ :=
+    {σ' : S →+* R} [RingHomInvPair σ σ'] [RingHomInvPair σ' σ] (M : Type _) (M₂ : Type _)
+    [AddCommMonoid M] [AddCommMonoid M₂] [Module R M] [Module S M₂] :
+    EquivLike (LinearEquiv σ M M₂) M M₂ :=
   inferInstance
 
 /- Porting note: In every application of lsum that follows, the argument M needs to be explicitly
@@ -140,8 +138,7 @@ supplied, lean does not manage to gather that information itself -/
 See note [bundled maps over different rings] for why separate `R` and `S` semirings are used. -/
 @[simps]
 def lsum [Semiring S] [Module S N] [SMulCommClass R S N] :
-    (∀ i, M i →ₗ[R] N) ≃ₗ[S] (Π₀ i, M i) →ₗ[R] N
-    where
+    (∀ i, M i →ₗ[R] N) ≃ₗ[S] (Π₀ i, M i) →ₗ[R] N where
   toFun F :=
     { toFun := sumAddHom fun i => (F i).toAddMonoidHom
       -- Porting note: needed to (β := M) hint below
@@ -205,9 +202,7 @@ theorem mapRange_smul (f : ∀ i, β₁ i → β₂ i) (hf : ∀ i, f i 0 = 0) (
 /-- `Dfinsupp.mapRange` as a `LinearMap`. -/
 @[simps! apply]
 def mapRange.linearMap (f : ∀ i, β₁ i →ₗ[R] β₂ i) : (Π₀ i, β₁ i) →ₗ[R] Π₀ i, β₂ i :=
-  {
-    mapRange.addMonoidHom fun i =>
-      (f i).toAddMonoidHom with
+  { mapRange.addMonoidHom fun i => (f i).toAddMonoidHom with
     toFun := mapRange (fun i x => f i x) fun i => (f i).map_zero
     map_smul' := fun r => mapRange_smul _ (fun i => (f i).map_zero) _ fun i => (f i).map_smul r }
 #align dfinsupp.map_range.linear_map Dfinsupp.mapRange.linearMap
@@ -239,8 +234,7 @@ theorem sum_mapRange_index.linearMap [∀ (i : ι) (x : β₁ i), Decidable (x 
 @[simps apply]
 def mapRange.linearEquiv (e : ∀ i, β₁ i ≃ₗ[R] β₂ i) : (Π₀ i, β₁ i) ≃ₗ[R] Π₀ i, β₂ i :=
   { mapRange.addEquiv fun i => (e i).toAddEquiv,
-    mapRange.linearMap fun i =>
-      (e i).toLinearMap with
+    mapRange.linearMap fun i => (e i).toLinearMap with
     toFun := mapRange (fun i x => e i x) fun i => (e i).map_zero
     invFun := mapRange (fun i x => (e i).symm x) fun i => (e i).symm.map_zero }
 #align dfinsupp.map_range.linear_equiv Dfinsupp.mapRange.linearEquiv
@@ -321,7 +315,6 @@ theorem dfinsupp_sumAddHom_mem {β : ι → Type _} [∀ i, AddZeroClass (β i)]
   _root_.dfinsupp_sumAddHom_mem S f g h
 #align submodule.dfinsupp_sum_add_hom_mem Submodule.dfinsupp_sumAddHom_mem
 
--- set_option pp.universes true
 /-- The supremum of a family of submodules is equal to the range of `Dfinsupp.lsum`; that is
 every element in the `supr` can be produced from taking a finite number of non-zero elements
 of `p i`, coercing them to `N`, and summing them. -/
@@ -364,7 +357,7 @@ theorem mem_supᵢ_iff_exists_dfinsupp (p : ι → Submodule R N) (x : N) :
   SetLike.ext_iff.mp (supᵢ_eq_range_dfinsupp_lsum p) x
 #align submodule.mem_supr_iff_exists_dfinsupp Submodule.mem_supᵢ_iff_exists_dfinsupp
 
-/-- A variant of `submodule.mem_supr_iff_exists_dfinsupp` with the RHS fully unfolded. -/
+/-- A variant of `Submodule.mem_supᵢ_iff_exists_dfinsupp` with the RHS fully unfolded. -/
 theorem mem_supᵢ_iff_exists_dfinsupp' (p : ι → Submodule R N) [∀ (i) (x : p i), Decidable (x ≠ 0)]
     (x : N) : x ∈ supᵢ p ↔ ∃ f : Π₀ i, p i, (f.sum fun i xi => ↑xi) = x := by
   rw [mem_supᵢ_iff_exists_dfinsupp]
@@ -372,13 +365,13 @@ theorem mem_supᵢ_iff_exists_dfinsupp' (p : ι → Submodule R N) [∀ (i) (x :
     LinearMap.toAddMonoidHom_coe, coeSubtype]
 #align submodule.mem_supr_iff_exists_dfinsupp' Submodule.mem_supᵢ_iff_exists_dfinsupp'
 
-theorem mem_bsupr_iff_exists_dfinsupp (p : ι → Prop) [DecidablePred p] (S : ι → Submodule R N)
+theorem mem_bsupᵢ_iff_exists_dfinsupp (p : ι → Prop) [DecidablePred p] (S : ι → Submodule R N)
     (x : N) :
     (x ∈ ⨆ (i) (_h : p i), S i) ↔
       ∃ f : Π₀ i, S i,
         Dfinsupp.lsum ℕ (M := fun i ↦ ↥(S i)) (fun i => (S i).subtype) (f.filter p) = x :=
   SetLike.ext_iff.mp (bsupᵢ_eq_range_dfinsupp_lsum p S) x
-#align submodule.mem_bsupr_iff_exists_dfinsupp Submodule.mem_bsupr_iff_exists_dfinsupp
+#align submodule.mem_bsupr_iff_exists_dfinsupp Submodule.mem_bsupᵢ_iff_exists_dfinsupp
 
 open BigOperators
 
@@ -439,12 +432,12 @@ theorem independent_iff_forall_dfinsupp (p : ι → Submodule R N) :
       ∀ (i) (x : p i) (v : Π₀ i : ι, ↥(p i)),
         lsum ℕ (M := fun i ↦ ↥(p i)) (fun i => (p i).subtype) (erase i v) = x → x = 0 := by
   simp_rw [CompleteLattice.independent_def, Submodule.disjoint_def,
-    Submodule.mem_bsupr_iff_exists_dfinsupp, exists_imp, filter_ne_eq_erase]
+    Submodule.mem_bsupᵢ_iff_exists_dfinsupp, exists_imp, filter_ne_eq_erase]
   refine' forall_congr' fun i => Subtype.forall'.trans _
   simp_rw [Submodule.coe_eq_zero]
 #align complete_lattice.independent_iff_forall_dfinsupp CompleteLattice.independent_iff_forall_dfinsupp
 
-/- If `Dfinsupp.lsum` applied with `submodule.subtype` is injective then the submodules are
+/- If `Dfinsupp.lsum` applied with `Submodule.subtype` is injective then the submodules are
 independent. -/
 theorem independent_of_dfinsupp_lsum_injective (p : ι → Submodule R N)
     (h : Function.Injective (lsum ℕ (M := fun i ↦ ↥(p i)) fun i => (p i).subtype)) :
@@ -459,7 +452,7 @@ theorem independent_of_dfinsupp_lsum_injective (p : ι → Submodule R N)
   simpa [eq_comm] using this
 #align complete_lattice.independent_of_dfinsupp_lsum_injective CompleteLattice.independent_of_dfinsupp_lsum_injective
 
-/- If `Dfinsupp.sumAddHom` applied with `add_submonoid.subtype` is injective then the additive
+/- If `Dfinsupp.sumAddHom` applied with `AddSubmonoid.subtype` is injective then the additive
 submonoids are independent. -/
 theorem independent_of_dfinsupp_sumAddHom_injective (p : ι → AddSubmonoid N)
     (h : Function.Injective (sumAddHom fun i => (p i).subtype)) : Independent p := by
@@ -529,9 +522,9 @@ theorem Independent.dfinsupp_sumAddHom_injective {p : ι → AddSubgroup N} (h :
 #align complete_lattice.independent.dfinsupp_sum_add_hom_injective CompleteLattice.Independent.dfinsupp_sumAddHom_injective
 
 /-- A family of submodules over an additive group are independent if and only iff `Dfinsupp.lsum`
-applied with `submodule.subtype` is injective.
+applied with `Submodule.subtype` is injective.
 
-Note that this is not generally true for `[semiring R]`; see
+Note that this is not generally true for `[Semiring R]`; see
 `CompleteLattice.Independent.dfinsupp_lsum_injective` for details. -/
 theorem independent_iff_dfinsupp_lsum_injective (p : ι → Submodule R N) :
     Independent p ↔ Function.Injective (lsum ℕ (M := fun i ↦ ↥(p i)) fun i => (p i).subtype) :=

a148d797

chore: fix docs, golf, rename (#3010)

Run fix-comments on Mathlib/LinearAlgebra/Basis.lean.
Rename Basis.of_repr to Basis.ofRepr.
Reflow/minor golf.

4a6b502d

Diff

@@ -295,7 +295,7 @@ section Basis
 Note that while this is stated for `Dfinsupp` not `direct_sum`, the types are defeq. -/
 noncomputable def basis {η : ι → Type _} (b : ∀ i, Basis (η i) R (M i)) :
     Basis (Σi, η i) R (Π₀ i, M i) :=
-  Basis.of_repr
+  .ofRepr
     ((mapRange.linearEquiv fun i => (b i).repr).trans (sigmaFinsuppLequivDfinsupp R).symm)
 #align dfinsupp.basis Dfinsupp.basis

a148d797

feat: port LinearAlgebra.Dfinsupp (#2550)

88902554

`linear_algebra.dfinsupp` ⟷ `Mathlib.LinearAlgebra.DFinsupp`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Dependencies 8 + 421

linear_algebra.dfinsupp ⟷ Mathlib.LinearAlgebra.DFinsupp

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Dependencies 8 + 421

`linear_algebra.dfinsupp` ⟷ `Mathlib.LinearAlgebra.DFinsupp`