linear_algebra.quotient
⟷
Mathlib.LinearAlgebra.Quotient
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.
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(last sync)
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -343,7 +343,7 @@ theorem subsingleton_quotient_iff_eq_top : Subsingleton (M ⧸ p) ↔ p = ⊤ :=
· rintro h
refine' eq_top_iff.mpr fun x _ => _
have : x - 0 ∈ p := (Submodule.Quotient.eq p).mp (Subsingleton.elim _ _)
- rwa [sub_zero] at this
+ rwa [sub_zero] at this
· rintro rfl
infer_instance
#align submodule.subsingleton_quotient_iff_eq_top Submodule.subsingleton_quotient_iff_eq_top
@@ -630,9 +630,9 @@ theorem span_preimage_eq [RingHomSurjective τ₁₂] {f : M →ₛₗ[τ₁₂]
have hk : ker f ≤ span R (f ⁻¹' s) :=
by
let y := Classical.choose h₀; have hy : y ∈ s := Classical.choose_spec h₀
- rw [ker_le_iff]; use y, h₁ hy; rw [← Set.singleton_subset_iff] at hy
+ rw [ker_le_iff]; use y, h₁ hy; rw [← Set.singleton_subset_iff] at hy
exact Set.Subset.trans subset_span (span_mono (Set.preimage_mono hy))
- rw [← left_eq_sup] at hk ; rw [f.range_coe] at h₁
+ rw [← left_eq_sup] at hk; rw [f.range_coe] at h₁
rw [hk, ← LinearMap.map_le_map_iff, map_span, map_comap_eq, Set.image_preimage_eq_of_subset h₁]
exact inf_le_right
#align submodule.span_preimage_eq Submodule.span_preimage_eq
@@ -653,7 +653,7 @@ def Quotient.equiv {N : Type _} [AddCommGroup N] [Module R N] (P : Submodule R M
invFun :=
Q.mapQ P (f.symm : N →ₗ[R] M) fun x hx =>
by
- rw [← hf, Submodule.mem_map] at hx
+ rw [← hf, Submodule.mem_map] at hx
obtain ⟨y, hy, rfl⟩ := hx
simpa
left_inv := fun x => Quotient.inductionOn' x (by simp)
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Kevin Buzzard, Yury Kudryashov
-/
-import Mathbin.GroupTheory.QuotientGroup
-import Mathbin.LinearAlgebra.Span
+import GroupTheory.QuotientGroup
+import LinearAlgebra.Span
#align_import linear_algebra.quotient from "leanprover-community/mathlib"@"23aa88e32dcc9d2a24cca7bc23268567ed4cd7d6"
mathlib commit https://github.com/leanprover-community/mathlib/commit/63721b2c3eba6c325ecf8ae8cca27155a4f6306f
@@ -147,19 +147,19 @@ section SMul
variable {S : Type _} [SMul S R] [SMul S M] [IsScalarTower S R M] (P : Submodule R M)
-#print Submodule.Quotient.hasSmul' /-
-instance hasSmul' : SMul S (M ⧸ P) :=
+#print Submodule.Quotient.instSMul' /-
+instance instSMul' : SMul S (M ⧸ P) :=
⟨fun a =>
Quotient.map' ((· • ·) a) fun x y h =>
leftRel_apply.mpr <| by simpa [smul_sub] using P.smul_mem (a • 1 : R) (left_rel_apply.mp h)⟩
-#align submodule.quotient.has_smul' Submodule.Quotient.hasSmul'
+#align submodule.quotient.has_smul' Submodule.Quotient.instSMul'
-/
-#print Submodule.Quotient.hasSmul /-
+#print Submodule.Quotient.instSMul /-
/-- Shortcut to help the elaborator in the common case. -/
-instance hasSmul : SMul R (M ⧸ P) :=
- Quotient.hasSmul' P
-#align submodule.quotient.has_smul Submodule.Quotient.hasSmul
+instance instSMul : SMul R (M ⧸ P) :=
+ Quotient.instSMul' P
+#align submodule.quotient.has_smul Submodule.Quotient.instSMul
-/
#print Submodule.Quotient.mk_smul /-
@@ -222,18 +222,18 @@ instance smulZeroClass (P : Submodule R M) : SMulZeroClass R (M ⧸ P) :=
#align submodule.quotient.smul_zero_class Submodule.Quotient.smulZeroClass
-/
-#print Submodule.Quotient.distribSmul' /-
-instance distribSmul' [SMul S R] [DistribSMul S M] [IsScalarTower S R M] (P : Submodule R M) :
+#print Submodule.Quotient.distribSMul' /-
+instance distribSMul' [SMul S R] [DistribSMul S M] [IsScalarTower S R M] (P : Submodule R M) :
DistribSMul S (M ⧸ P) :=
Function.Surjective.distribSMul ⟨mk, rfl, fun _ _ => rfl⟩ (surjective_quot_mk _)
P.Quotient.mk_smul
-#align submodule.quotient.distrib_smul' Submodule.Quotient.distribSmul'
+#align submodule.quotient.distrib_smul' Submodule.Quotient.distribSMul'
-/
-#print Submodule.Quotient.distribSmul /-
-instance distribSmul (P : Submodule R M) : DistribSMul R (M ⧸ P) :=
- Quotient.distribSmul' P
-#align submodule.quotient.distrib_smul Submodule.Quotient.distribSmul
+#print Submodule.Quotient.distribSMul /-
+instance distribSMul (P : Submodule R M) : DistribSMul R (M ⧸ P) :=
+ Quotient.distribSMul' P
+#align submodule.quotient.distrib_smul Submodule.Quotient.distribSMul
-/
#print Submodule.Quotient.distribMulAction' /-
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Kevin Buzzard, Yury Kudryashov
-
-! This file was ported from Lean 3 source module linear_algebra.quotient
-! leanprover-community/mathlib commit 23aa88e32dcc9d2a24cca7bc23268567ed4cd7d6
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.GroupTheory.QuotientGroup
import Mathbin.LinearAlgebra.Span
+#align_import linear_algebra.quotient from "leanprover-community/mathlib"@"23aa88e32dcc9d2a24cca7bc23268567ed4cd7d6"
+
/-!
# Quotients by submodules
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -44,9 +44,11 @@ def quotientRel : Setoid M :=
#align submodule.quotient_rel Submodule.quotientRel
-/
+#print Submodule.quotientRel_r_def /-
theorem quotientRel_r_def {x y : M} : @Setoid.r _ p.quotientRel x y ↔ x - y ∈ p :=
Iff.trans (by rw [left_rel_apply, sub_eq_add_neg, neg_add, neg_neg]; rfl) neg_mem_iff
#align submodule.quotient_rel_r_def Submodule.quotientRel_r_def
+-/
#print Submodule.hasQuotient /-
/-- The quotient of a module `M` by a submodule `p ⊆ M`. -/
@@ -65,28 +67,38 @@ def mk {p : Submodule R M} : M → M ⧸ p :=
#align submodule.quotient.mk Submodule.Quotient.mk
-/
+#print Submodule.Quotient.mk'_eq_mk' /-
@[simp]
theorem mk'_eq_mk' {p : Submodule R M} (x : M) : @Quotient.mk' _ (quotientRel p) x = mk x :=
rfl
#align submodule.quotient.mk_eq_mk Submodule.Quotient.mk'_eq_mk'
+-/
+#print Submodule.Quotient.mk''_eq_mk /-
@[simp]
theorem mk''_eq_mk {p : Submodule R M} (x : M) : (Quotient.mk'' x : M ⧸ p) = mk x :=
rfl
#align submodule.quotient.mk'_eq_mk Submodule.Quotient.mk''_eq_mk
+-/
+#print Submodule.Quotient.quot_mk_eq_mk /-
@[simp]
theorem quot_mk_eq_mk {p : Submodule R M} (x : M) : (Quot.mk _ x : M ⧸ p) = mk x :=
rfl
#align submodule.quotient.quot_mk_eq_mk Submodule.Quotient.quot_mk_eq_mk
+-/
+#print Submodule.Quotient.eq' /-
protected theorem eq' {x y : M} : (mk x : M ⧸ p) = mk y ↔ -x + y ∈ p :=
QuotientAddGroup.eq
#align submodule.quotient.eq' Submodule.Quotient.eq'
+-/
+#print Submodule.Quotient.eq /-
protected theorem eq {x y : M} : (mk x : M ⧸ p) = mk y ↔ x - y ∈ p :=
p.Quotient.eq''.trans (leftRel_apply.symm.trans p.quotientRel_r_def)
#align submodule.quotient.eq Submodule.Quotient.eq
+-/
instance : Zero (M ⧸ p) :=
⟨mk 0⟩
@@ -94,14 +106,18 @@ instance : Zero (M ⧸ p) :=
instance : Inhabited (M ⧸ p) :=
⟨0⟩
+#print Submodule.Quotient.mk_zero /-
@[simp]
theorem mk_zero : mk 0 = (0 : M ⧸ p) :=
rfl
#align submodule.quotient.mk_zero Submodule.Quotient.mk_zero
+-/
+#print Submodule.Quotient.mk_eq_zero /-
@[simp]
theorem mk_eq_zero : (mk x : M ⧸ p) = 0 ↔ x ∈ p := by simpa using (Quotient.eq' p : mk x = 0 ↔ _)
#align submodule.quotient.mk_eq_zero Submodule.Quotient.mk_eq_zero
+-/
#print Submodule.Quotient.addCommGroup /-
instance addCommGroup : AddCommGroup (M ⧸ p) :=
@@ -109,20 +125,26 @@ instance addCommGroup : AddCommGroup (M ⧸ p) :=
#align submodule.quotient.add_comm_group Submodule.Quotient.addCommGroup
-/
+#print Submodule.Quotient.mk_add /-
@[simp]
theorem mk_add : (mk (x + y) : M ⧸ p) = mk x + mk y :=
rfl
#align submodule.quotient.mk_add Submodule.Quotient.mk_add
+-/
+#print Submodule.Quotient.mk_neg /-
@[simp]
theorem mk_neg : (mk (-x) : M ⧸ p) = -mk x :=
rfl
#align submodule.quotient.mk_neg Submodule.Quotient.mk_neg
+-/
+#print Submodule.Quotient.mk_sub /-
@[simp]
theorem mk_sub : (mk (x - y) : M ⧸ p) = mk x - mk y :=
rfl
#align submodule.quotient.mk_sub Submodule.Quotient.mk_sub
+-/
section SMul
@@ -143,10 +165,12 @@ instance hasSmul : SMul R (M ⧸ P) :=
#align submodule.quotient.has_smul Submodule.Quotient.hasSmul
-/
+#print Submodule.Quotient.mk_smul /-
@[simp]
theorem mk_smul (r : S) (x : M) : (mk (r • x) : M ⧸ p) = r • mk x :=
rfl
#align submodule.quotient.mk_smul Submodule.Quotient.mk_smul
+-/
#print Submodule.Quotient.smulCommClass /-
instance smulCommClass (T : Type _) [SMul T R] [SMul T M] [IsScalarTower T R M]
@@ -182,24 +206,32 @@ instance mulAction' [Monoid S] [SMul S R] [MulAction S M] [IsScalarTower S R M]
#align submodule.quotient.mul_action' Submodule.Quotient.mulAction'
-/
+#print Submodule.Quotient.mulAction /-
instance mulAction (P : Submodule R M) : MulAction R (M ⧸ P) :=
Quotient.mulAction' P
#align submodule.quotient.mul_action Submodule.Quotient.mulAction
+-/
+#print Submodule.Quotient.smulZeroClass' /-
instance smulZeroClass' [SMul S R] [SMulZeroClass S M] [IsScalarTower S R M] (P : Submodule R M) :
SMulZeroClass S (M ⧸ P) :=
ZeroHom.smulZeroClass ⟨mk, mk_zero _⟩ P.Quotient.mk_smul
#align submodule.quotient.smul_zero_class' Submodule.Quotient.smulZeroClass'
+-/
+#print Submodule.Quotient.smulZeroClass /-
instance smulZeroClass (P : Submodule R M) : SMulZeroClass R (M ⧸ P) :=
Quotient.smulZeroClass' P
#align submodule.quotient.smul_zero_class Submodule.Quotient.smulZeroClass
+-/
+#print Submodule.Quotient.distribSmul' /-
instance distribSmul' [SMul S R] [DistribSMul S M] [IsScalarTower S R M] (P : Submodule R M) :
DistribSMul S (M ⧸ P) :=
Function.Surjective.distribSMul ⟨mk, rfl, fun _ _ => rfl⟩ (surjective_quot_mk _)
P.Quotient.mk_smul
#align submodule.quotient.distrib_smul' Submodule.Quotient.distribSmul'
+-/
#print Submodule.Quotient.distribSmul /-
instance distribSmul (P : Submodule R M) : DistribSMul R (M ⧸ P) :=
@@ -207,15 +239,19 @@ instance distribSmul (P : Submodule R M) : DistribSMul R (M ⧸ P) :=
#align submodule.quotient.distrib_smul Submodule.Quotient.distribSmul
-/
+#print Submodule.Quotient.distribMulAction' /-
instance distribMulAction' [Monoid S] [SMul S R] [DistribMulAction S M] [IsScalarTower S R M]
(P : Submodule R M) : DistribMulAction S (M ⧸ P) :=
Function.Surjective.distribMulAction ⟨mk, rfl, fun _ _ => rfl⟩ (surjective_quot_mk _)
P.Quotient.mk_smul
#align submodule.quotient.distrib_mul_action' Submodule.Quotient.distribMulAction'
+-/
+#print Submodule.Quotient.distribMulAction /-
instance distribMulAction (P : Submodule R M) : DistribMulAction R (M ⧸ P) :=
Quotient.distribMulAction' P
#align submodule.quotient.distrib_mul_action Submodule.Quotient.distribMulAction
+-/
#print Submodule.Quotient.module' /-
instance module' [Semiring S] [SMul S R] [Module S M] [IsScalarTower S R M] (P : Submodule R M) :
@@ -246,17 +282,21 @@ def restrictScalarsEquiv [Ring S] [SMul S R] [Module S M] [IsScalarTower S R M]
#align submodule.quotient.restrict_scalars_equiv Submodule.Quotient.restrictScalarsEquiv
-/
+#print Submodule.Quotient.restrictScalarsEquiv_mk /-
@[simp]
theorem restrictScalarsEquiv_mk [Ring S] [SMul S R] [Module S M] [IsScalarTower S R M]
(P : Submodule R M) (x : M) : restrictScalarsEquiv S P (mk x) = mk x :=
rfl
#align submodule.quotient.restrict_scalars_equiv_mk Submodule.Quotient.restrictScalarsEquiv_mk
+-/
+#print Submodule.Quotient.restrictScalarsEquiv_symm_mk /-
@[simp]
theorem restrictScalarsEquiv_symm_mk [Ring S] [SMul S R] [Module S M] [IsScalarTower S R M]
(P : Submodule R M) (x : M) : (restrictScalarsEquiv S P).symm (mk x) = mk x :=
rfl
#align submodule.quotient.restrict_scalars_equiv_symm_mk Submodule.Quotient.restrictScalarsEquiv_symm_mk
+-/
end Module
@@ -265,32 +305,41 @@ theorem mk_surjective : Function.Surjective (@mk _ _ _ _ _ p) := by rintro ⟨x
#align submodule.quotient.mk_surjective Submodule.Quotient.mk_surjective
-/
+#print Submodule.Quotient.nontrivial_of_lt_top /-
theorem nontrivial_of_lt_top (h : p < ⊤) : Nontrivial (M ⧸ p) :=
by
obtain ⟨x, _, not_mem_s⟩ := SetLike.exists_of_lt h
refine' ⟨⟨mk x, 0, _⟩⟩
simpa using not_mem_s
#align submodule.quotient.nontrivial_of_lt_top Submodule.Quotient.nontrivial_of_lt_top
+-/
end Quotient
+#print Submodule.QuotientBot.infinite /-
instance QuotientBot.infinite [Infinite M] : Infinite (M ⧸ (⊥ : Submodule R M)) :=
Infinite.of_injective Submodule.Quotient.mk fun x y h =>
sub_eq_zero.mp <| (Submodule.Quotient.eq ⊥).mp h
#align submodule.quotient_bot.infinite Submodule.QuotientBot.infinite
+-/
+#print Submodule.QuotientTop.unique /-
instance QuotientTop.unique : Unique (M ⧸ (⊤ : Submodule R M))
where
default := 0
uniq x := Quotient.inductionOn' x fun x => (Submodule.Quotient.eq ⊤).mpr Submodule.mem_top
#align submodule.quotient_top.unique Submodule.QuotientTop.unique
+-/
+#print Submodule.QuotientTop.fintype /-
instance QuotientTop.fintype : Fintype (M ⧸ (⊤ : Submodule R M)) :=
Fintype.ofSubsingleton 0
#align submodule.quotient_top.fintype Submodule.QuotientTop.fintype
+-/
variable {p}
+#print Submodule.subsingleton_quotient_iff_eq_top /-
theorem subsingleton_quotient_iff_eq_top : Subsingleton (M ⧸ p) ↔ p = ⊤ :=
by
constructor
@@ -301,11 +350,14 @@ theorem subsingleton_quotient_iff_eq_top : Subsingleton (M ⧸ p) ↔ p = ⊤ :=
· rintro rfl
infer_instance
#align submodule.subsingleton_quotient_iff_eq_top Submodule.subsingleton_quotient_iff_eq_top
+-/
+#print Submodule.unique_quotient_iff_eq_top /-
theorem unique_quotient_iff_eq_top : Nonempty (Unique (M ⧸ p)) ↔ p = ⊤ :=
⟨fun ⟨h⟩ => subsingleton_quotient_iff_eq_top.mp (@Unique.subsingleton h), by rintro rfl;
exact ⟨quotient_top.unique⟩⟩
#align submodule.unique_quotient_iff_eq_top Submodule.unique_quotient_iff_eq_top
+-/
variable (p)
@@ -328,10 +380,12 @@ section
variable {M₂ : Type _} [AddCommGroup M₂] [Module R M₂]
+#print Submodule.quot_hom_ext /-
theorem quot_hom_ext ⦃f g : M ⧸ p →ₗ[R] M₂⦄ (h : ∀ x, f (Quotient.mk x) = g (Quotient.mk x)) :
f = g :=
LinearMap.ext fun x => Quotient.inductionOn' x h
#align submodule.quot_hom_ext Submodule.quot_hom_ext
+-/
#print Submodule.mkQ /-
/-- The map from a module `M` to the quotient of `M` by a submodule `p` as a linear map. -/
@@ -342,19 +396,24 @@ def mkQ : M →ₗ[R] M ⧸ p where
#align submodule.mkq Submodule.mkQ
-/
+#print Submodule.mkQ_apply /-
@[simp]
theorem mkQ_apply (x : M) : p.mkQ x = Quotient.mk x :=
rfl
#align submodule.mkq_apply Submodule.mkQ_apply
+-/
+#print Submodule.mkQ_surjective /-
theorem mkQ_surjective (A : Submodule R M) : Function.Surjective A.mkQ := by
rintro ⟨x⟩ <;> exact ⟨x, rfl⟩
#align submodule.mkq_surjective Submodule.mkQ_surjective
+-/
end
variable {R₂ M₂ : Type _} [Ring R₂] [AddCommGroup M₂] [Module R₂ M₂] {τ₁₂ : R →+* R₂}
+#print Submodule.linearMap_qext /-
/-- Two `linear_map`s from a quotient module are equal if their compositions with
`submodule.mkq` are equal.
@@ -363,39 +422,52 @@ See note [partially-applied ext lemmas]. -/
theorem linearMap_qext ⦃f g : M ⧸ p →ₛₗ[τ₁₂] M₂⦄ (h : f.comp p.mkQ = g.comp p.mkQ) : f = g :=
LinearMap.ext fun x => Quotient.inductionOn' x <| (LinearMap.congr_fun h : _)
#align submodule.linear_map_qext Submodule.linearMap_qext
+-/
+#print Submodule.liftQ /-
/-- The map from the quotient of `M` by a submodule `p` to `M₂` induced by a linear map `f : M → M₂`
vanishing on `p`, as a linear map. -/
def liftQ (f : M →ₛₗ[τ₁₂] M₂) (h : p ≤ f.ker) : M ⧸ p →ₛₗ[τ₁₂] M₂ :=
{ QuotientAddGroup.lift p.toAddSubgroup f.toAddMonoidHom h with
map_smul' := by rintro a ⟨x⟩ <;> exact f.map_smulₛₗ a x }
#align submodule.liftq Submodule.liftQ
+-/
+#print Submodule.liftQ_apply /-
@[simp]
theorem liftQ_apply (f : M →ₛₗ[τ₁₂] M₂) {h} (x : M) : p.liftQ f h (Quotient.mk x) = f x :=
rfl
#align submodule.liftq_apply Submodule.liftQ_apply
+-/
+#print Submodule.liftQ_mkQ /-
@[simp]
theorem liftQ_mkQ (f : M →ₛₗ[τ₁₂] M₂) (h) : (p.liftQ f h).comp p.mkQ = f := by ext <;> rfl
#align submodule.liftq_mkq Submodule.liftQ_mkQ
+-/
+#print Submodule.liftQSpanSingleton /-
/-- Special case of `liftq` when `p` is the span of `x`. In this case, the condition on `f` simply
becomes vanishing at `x`.-/
def liftQSpanSingleton (x : M) (f : M →ₛₗ[τ₁₂] M₂) (h : f x = 0) : (M ⧸ R ∙ x) →ₛₗ[τ₁₂] M₂ :=
(R ∙ x).liftQ f <| by rw [span_singleton_le_iff_mem, LinearMap.mem_ker, h]
#align submodule.liftq_span_singleton Submodule.liftQSpanSingleton
+-/
+#print Submodule.liftQSpanSingleton_apply /-
@[simp]
theorem liftQSpanSingleton_apply (x : M) (f : M →ₛₗ[τ₁₂] M₂) (h : f x = 0) (y : M) :
liftQSpanSingleton x f h (Quotient.mk y) = f y :=
rfl
#align submodule.liftq_span_singleton_apply Submodule.liftQSpanSingleton_apply
+-/
+#print Submodule.range_mkQ /-
@[simp]
theorem range_mkQ : p.mkQ.range = ⊤ :=
eq_top_iff'.2 <| by rintro ⟨x⟩ <;> exact ⟨x, rfl⟩
#align submodule.range_mkq Submodule.range_mkQ
+-/
#print Submodule.ker_mkQ /-
@[simp]
@@ -403,47 +475,64 @@ theorem ker_mkQ : p.mkQ.ker = p := by ext <;> simp
#align submodule.ker_mkq Submodule.ker_mkQ
-/
+#print Submodule.le_comap_mkQ /-
theorem le_comap_mkQ (p' : Submodule R (M ⧸ p)) : p ≤ comap p.mkQ p' := by
simpa using (comap_mono bot_le : p.mkq.ker ≤ comap p.mkq p')
#align submodule.le_comap_mkq Submodule.le_comap_mkQ
+-/
+#print Submodule.mkQ_map_self /-
@[simp]
theorem mkQ_map_self : map p.mkQ p = ⊥ := by
rw [eq_bot_iff, map_le_iff_le_comap, comap_bot, ker_mkq] <;> exact le_rfl
#align submodule.mkq_map_self Submodule.mkQ_map_self
+-/
+#print Submodule.comap_map_mkQ /-
@[simp]
theorem comap_map_mkQ : comap p.mkQ (map p.mkQ p') = p ⊔ p' := by simp [comap_map_eq, sup_comm]
#align submodule.comap_map_mkq Submodule.comap_map_mkQ
+-/
+#print Submodule.map_mkQ_eq_top /-
@[simp]
theorem map_mkQ_eq_top : map p.mkQ p' = ⊤ ↔ p ⊔ p' = ⊤ := by
simp only [map_eq_top_iff p.range_mkq, sup_comm, ker_mkq]
#align submodule.map_mkq_eq_top Submodule.map_mkQ_eq_top
+-/
variable (q : Submodule R₂ M₂)
+#print Submodule.mapQ /-
/-- The map from the quotient of `M` by submodule `p` to the quotient of `M₂` by submodule `q` along
`f : M → M₂` is linear. -/
def mapQ (f : M →ₛₗ[τ₁₂] M₂) (h : p ≤ comap f q) : M ⧸ p →ₛₗ[τ₁₂] M₂ ⧸ q :=
p.liftQ (q.mkQ.comp f) <| by simpa [ker_comp] using h
#align submodule.mapq Submodule.mapQ
+-/
+#print Submodule.mapQ_apply /-
@[simp]
theorem mapQ_apply (f : M →ₛₗ[τ₁₂] M₂) {h} (x : M) :
mapQ p q f h (Quotient.mk x) = Quotient.mk (f x) :=
rfl
#align submodule.mapq_apply Submodule.mapQ_apply
+-/
+#print Submodule.mapQ_mkQ /-
theorem mapQ_mkQ (f : M →ₛₗ[τ₁₂] M₂) {h} : (mapQ p q f h).comp p.mkQ = q.mkQ.comp f := by
ext x <;> rfl
#align submodule.mapq_mkq Submodule.mapQ_mkQ
+-/
+#print Submodule.mapQ_zero /-
@[simp]
theorem mapQ_zero (h : p ≤ q.comap (0 : M →ₛₗ[τ₁₂] M₂) := (by simp)) :
p.mapQ q (0 : M →ₛₗ[τ₁₂] M₂) h = 0 := by ext; simp
#align submodule.mapq_zero Submodule.mapQ_zero
+-/
+#print Submodule.mapQ_comp /-
/-- Given submodules `p ⊆ M`, `p₂ ⊆ M₂`, `p₃ ⊆ M₃` and maps `f : M → M₂`, `g : M₂ → M₃` inducing
`mapq f : M ⧸ p → M₂ ⧸ p₂` and `mapq g : M₂ ⧸ p₂ → M₃ ⧸ p₃` then
`mapq (g ∘ f) = (mapq g) ∘ (mapq f)`. -/
@@ -453,12 +542,16 @@ theorem mapQ_comp {R₃ M₃ : Type _} [Ring R₃] [AddCommGroup M₃] [Module R
(h := hf.trans (comap_mono hg)) :
p.mapQ p₃ (g.comp f) h = (p₂.mapQ p₃ g hg).comp (p.mapQ p₂ f hf) := by ext; simp
#align submodule.mapq_comp Submodule.mapQ_comp
+-/
+#print Submodule.mapQ_id /-
@[simp]
theorem mapQ_id (h : p ≤ p.comap LinearMap.id := (by rw [comap_id]; exact le_refl _)) :
p.mapQ p LinearMap.id h = LinearMap.id := by ext; simp
#align submodule.mapq_id Submodule.mapQ_id
+-/
+#print Submodule.mapQ_pow /-
theorem mapQ_pow {f : M →ₗ[R] M} (h : p ≤ p.comap f) (k : ℕ)
(h' : p ≤ p.comap (f ^ k) := p.le_comap_pow_of_le_comap h k) :
p.mapQ p (f ^ k) h' = p.mapQ p f h ^ k :=
@@ -468,30 +561,42 @@ theorem mapQ_pow {f : M →ₗ[R] M} (h : p ≤ p.comap f) (k : ℕ)
· simp only [LinearMap.iterate_succ, ← ih]
apply p.mapq_comp
#align submodule.mapq_pow Submodule.mapQ_pow
+-/
+#print Submodule.comap_liftQ /-
theorem comap_liftQ (f : M →ₛₗ[τ₁₂] M₂) (h) : q.comap (p.liftQ f h) = (q.comap f).map (mkQ p) :=
le_antisymm (by rintro ⟨x⟩ hx <;> exact ⟨_, hx, rfl⟩)
(by rw [map_le_iff_le_comap, ← comap_comp, liftq_mkq] <;> exact le_rfl)
#align submodule.comap_liftq Submodule.comap_liftQ
+-/
+#print Submodule.map_liftQ /-
theorem map_liftQ [RingHomSurjective τ₁₂] (f : M →ₛₗ[τ₁₂] M₂) (h) (q : Submodule R (M ⧸ p)) :
q.map (p.liftQ f h) = (q.comap p.mkQ).map f :=
le_antisymm (by rintro _ ⟨⟨x⟩, hxq, rfl⟩ <;> exact ⟨x, hxq, rfl⟩)
(by rintro _ ⟨x, hxq, rfl⟩ <;> exact ⟨Quotient.mk' x, hxq, rfl⟩)
#align submodule.map_liftq Submodule.map_liftQ
+-/
+#print Submodule.ker_liftQ /-
theorem ker_liftQ (f : M →ₛₗ[τ₁₂] M₂) (h) : ker (p.liftQ f h) = (ker f).map (mkQ p) :=
comap_liftQ _ _ _ _
#align submodule.ker_liftq Submodule.ker_liftQ
+-/
+#print Submodule.range_liftQ /-
theorem range_liftQ [RingHomSurjective τ₁₂] (f : M →ₛₗ[τ₁₂] M₂) (h) :
range (p.liftQ f h) = range f := by simpa only [range_eq_map] using map_liftq _ _ _ _
#align submodule.range_liftq Submodule.range_liftQ
+-/
+#print Submodule.ker_liftQ_eq_bot /-
theorem ker_liftQ_eq_bot (f : M →ₛₗ[τ₁₂] M₂) (h) (h' : ker f ≤ p) : ker (p.liftQ f h) = ⊥ := by
rw [ker_liftq, le_antisymm h h', mkq_map_self]
#align submodule.ker_liftq_eq_bot Submodule.ker_liftQ_eq_bot
+-/
+#print Submodule.comapMkQRelIso /-
/-- The correspondence theorem for modules: there is an order isomorphism between submodules of the
quotient of `M` by `p`, and submodules of `M` larger than `p`. -/
def Submodule.comapMkQRelIso : Submodule R (M ⧸ p) ≃o { p' : Submodule R M // p ≤ p' }
@@ -502,19 +607,25 @@ def Submodule.comapMkQRelIso : Submodule R (M ⧸ p) ≃o { p' : Submodule R M /
right_inv := fun ⟨q, hq⟩ => Subtype.ext_val <| by simpa [comap_map_mkq p]
map_rel_iff' p₁ p₂ := comap_le_comap_iff <| range_mkQ _
#align submodule.comap_mkq.rel_iso Submodule.comapMkQRelIso
+-/
+#print Submodule.comapMkQOrderEmbedding /-
/-- The ordering on submodules of the quotient of `M` by `p` embeds into the ordering on submodules
of `M`. -/
def Submodule.comapMkQOrderEmbedding : Submodule R (M ⧸ p) ↪o Submodule R M :=
(RelIso.toRelEmbedding <| Submodule.comapMkQRelIso p).trans (Subtype.relEmbedding _ _)
#align submodule.comap_mkq.order_embedding Submodule.comapMkQOrderEmbedding
+-/
+#print Submodule.comapMkQOrderEmbedding_eq /-
@[simp]
theorem comapMkQOrderEmbedding_eq (p' : Submodule R (M ⧸ p)) :
Submodule.comapMkQOrderEmbedding p p' = comap p.mkQ p' :=
rfl
#align submodule.comap_mkq_embedding_eq Submodule.comapMkQOrderEmbedding_eq
+-/
+#print Submodule.span_preimage_eq /-
theorem span_preimage_eq [RingHomSurjective τ₁₂] {f : M →ₛₗ[τ₁₂] M₂} {s : Set M₂} (h₀ : s.Nonempty)
(h₁ : s ⊆ range f) : span R (f ⁻¹' s) = (span R₂ s).comap f :=
by
@@ -528,7 +639,9 @@ theorem span_preimage_eq [RingHomSurjective τ₁₂] {f : M →ₛₗ[τ₁₂]
rw [hk, ← LinearMap.map_le_map_iff, map_span, map_comap_eq, Set.image_preimage_eq_of_subset h₁]
exact inf_le_right
#align submodule.span_preimage_eq Submodule.span_preimage_eq
+-/
+#print Submodule.Quotient.equiv /-
/-- If `P` is a submodule of `M` and `Q` a submodule of `N`,
and `f : M ≃ₗ N` maps `P` to `Q`, then `M ⧸ P` is equivalent to `N ⧸ Q`. -/
@[simps]
@@ -549,7 +662,9 @@ def Quotient.equiv {N : Type _} [AddCommGroup N] [Module R N] (P : Submodule R M
left_inv := fun x => Quotient.inductionOn' x (by simp)
right_inv := fun x => Quotient.inductionOn' x (by simp) }
#align submodule.quotient.equiv Submodule.Quotient.equiv
+-/
+#print Submodule.Quotient.equiv_symm /-
@[simp]
theorem Quotient.equiv_symm {R M N : Type _} [CommRing R] [AddCommGroup M] [Module R M]
[AddCommGroup N] [Module R N] (P : Submodule R M) (Q : Submodule R N) (f : M ≃ₗ[R] N)
@@ -558,7 +673,9 @@ theorem Quotient.equiv_symm {R M N : Type _} [CommRing R] [AddCommGroup M] [Modu
Quotient.equiv Q P f.symm ((Submodule.map_symm_eq_iff f).mpr hf) :=
rfl
#align submodule.quotient.equiv_symm Submodule.Quotient.equiv_symm
+-/
+#print Submodule.Quotient.equiv_trans /-
@[simp]
theorem Quotient.equiv_trans {N O : Type _} [AddCommGroup N] [Module R N] [AddCommGroup O]
[Module R O] (P : Submodule R M) (Q : Submodule R N) (S : Submodule R O) (e : M ≃ₗ[R] N)
@@ -572,6 +689,7 @@ theorem Quotient.equiv_trans {N O : Type _} [AddCommGroup N] [Module R N] [AddCo
-- `rw` can deal with `mapq_comp` needing extra hypotheses coming from the RHS
rw [mapq_comp, LinearMap.comp_apply]
#align submodule.quotient.equiv_trans Submodule.Quotient.equiv_trans
+-/
end Submodule
@@ -593,15 +711,20 @@ variable {τ₁₂ : R →+* R₂} {τ₂₃ : R₂ →+* R₃} {τ₁₃ : R
variable [RingHomCompTriple τ₁₂ τ₂₃ τ₁₃] [RingHomSurjective τ₁₂]
+#print LinearMap.range_mkQ_comp /-
theorem range_mkQ_comp (f : M →ₛₗ[τ₁₂] M₂) : f.range.mkQ.comp f = 0 :=
LinearMap.ext fun x => by simp
#align linear_map.range_mkq_comp LinearMap.range_mkQ_comp
+-/
+#print LinearMap.ker_le_range_iff /-
theorem ker_le_range_iff {f : M →ₛₗ[τ₁₂] M₂} {g : M₂ →ₛₗ[τ₂₃] M₃} :
g.ker ≤ f.range ↔ f.range.mkQ.comp g.ker.Subtype = 0 := by
rw [← range_le_ker_iff, Submodule.ker_mkQ, Submodule.range_subtype]
#align linear_map.ker_le_range_iff LinearMap.ker_le_range_iff
+-/
+#print LinearMap.range_eq_top_of_cancel /-
/-- An epimorphism is surjective. -/
theorem range_eq_top_of_cancel {f : M →ₛₗ[τ₁₂] M₂}
(h : ∀ u v : M₂ →ₗ[R₂] M₂ ⧸ f.range, u.comp f = v.comp f → u = v) : f.range = ⊤ :=
@@ -610,6 +733,7 @@ theorem range_eq_top_of_cancel {f : M →ₛₗ[τ₁₂] M₂}
rw [← Submodule.ker_mkQ f.range, ← h 0 f.range.mkq (Eq.trans h₁ (range_mkq_comp _).symm)]
exact ker_zero
#align linear_map.range_eq_top_of_cancel LinearMap.range_eq_top_of_cancel
+-/
end Ring
@@ -623,29 +747,37 @@ variable {R M : Type _} {r : R} {x y : M} [Ring R] [AddCommGroup M] [Module R M]
variable (p p' : Submodule R M)
+#print Submodule.quotEquivOfEqBot /-
/-- If `p = ⊥`, then `M / p ≃ₗ[R] M`. -/
def quotEquivOfEqBot (hp : p = ⊥) : (M ⧸ p) ≃ₗ[R] M :=
LinearEquiv.ofLinear (p.liftQ id <| hp.symm ▸ bot_le) p.mkQ (liftQ_mkQ _ _ _) <|
p.quot_hom_ext fun x => rfl
#align submodule.quot_equiv_of_eq_bot Submodule.quotEquivOfEqBot
+-/
+#print Submodule.quotEquivOfEqBot_apply_mk /-
@[simp]
theorem quotEquivOfEqBot_apply_mk (hp : p = ⊥) (x : M) :
p.quotEquivOfEqBot hp (Quotient.mk x) = x :=
rfl
#align submodule.quot_equiv_of_eq_bot_apply_mk Submodule.quotEquivOfEqBot_apply_mk
+-/
+#print Submodule.quotEquivOfEqBot_symm_apply /-
@[simp]
theorem quotEquivOfEqBot_symm_apply (hp : p = ⊥) (x : M) :
(p.quotEquivOfEqBot hp).symm x = Quotient.mk x :=
rfl
#align submodule.quot_equiv_of_eq_bot_symm_apply Submodule.quotEquivOfEqBot_symm_apply
+-/
+#print Submodule.coe_quotEquivOfEqBot_symm /-
@[simp]
theorem coe_quotEquivOfEqBot_symm (hp : p = ⊥) :
((p.quotEquivOfEqBot hp).symm : M →ₗ[R] M ⧸ p) = p.mkQ :=
rfl
#align submodule.coe_quot_equiv_of_eq_bot_symm Submodule.coe_quotEquivOfEqBot_symm
+-/
#print Submodule.quotEquivOfEq /-
/-- Quotienting by equal submodules gives linearly equivalent quotients. -/
@@ -658,18 +790,22 @@ def quotEquivOfEq (h : p = p') : (M ⧸ p) ≃ₗ[R] M ⧸ p' :=
#align submodule.quot_equiv_of_eq Submodule.quotEquivOfEq
-/
+#print Submodule.quotEquivOfEq_mk /-
@[simp]
theorem quotEquivOfEq_mk (h : p = p') (x : M) :
Submodule.quotEquivOfEq p p' h (Submodule.Quotient.mk x) = Submodule.Quotient.mk x :=
rfl
#align submodule.quot_equiv_of_eq_mk Submodule.quotEquivOfEq_mk
+-/
+#print Submodule.Quotient.equiv_refl /-
@[simp]
theorem Quotient.equiv_refl (P : Submodule R M) (Q : Submodule R M)
(hf : P.map (LinearEquiv.refl R M : M →ₗ[R] M) = Q) :
Quotient.equiv P Q (LinearEquiv.refl R M) hf = quotEquivOfEq _ _ (by simpa using hf) :=
rfl
#align submodule.quotient.equiv_refl Submodule.Quotient.equiv_refl
+-/
end Submodule
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -297,7 +297,7 @@ theorem subsingleton_quotient_iff_eq_top : Subsingleton (M ⧸ p) ↔ p = ⊤ :=
· rintro h
refine' eq_top_iff.mpr fun x _ => _
have : x - 0 ∈ p := (Submodule.Quotient.eq p).mp (Subsingleton.elim _ _)
- rwa [sub_zero] at this
+ rwa [sub_zero] at this
· rintro rfl
infer_instance
#align submodule.subsingleton_quotient_iff_eq_top Submodule.subsingleton_quotient_iff_eq_top
@@ -522,9 +522,9 @@ theorem span_preimage_eq [RingHomSurjective τ₁₂] {f : M →ₛₗ[τ₁₂]
have hk : ker f ≤ span R (f ⁻¹' s) :=
by
let y := Classical.choose h₀; have hy : y ∈ s := Classical.choose_spec h₀
- rw [ker_le_iff]; use y, h₁ hy; rw [← Set.singleton_subset_iff] at hy
+ rw [ker_le_iff]; use y, h₁ hy; rw [← Set.singleton_subset_iff] at hy
exact Set.Subset.trans subset_span (span_mono (Set.preimage_mono hy))
- rw [← left_eq_sup] at hk; rw [f.range_coe] at h₁
+ rw [← left_eq_sup] at hk ; rw [f.range_coe] at h₁
rw [hk, ← LinearMap.map_le_map_iff, map_span, map_comap_eq, Set.image_preimage_eq_of_subset h₁]
exact inf_le_right
#align submodule.span_preimage_eq Submodule.span_preimage_eq
@@ -543,7 +543,7 @@ def Quotient.equiv {N : Type _} [AddCommGroup N] [Module R N] (P : Submodule R M
invFun :=
Q.mapQ P (f.symm : N →ₗ[R] M) fun x hx =>
by
- rw [← hf, Submodule.mem_map] at hx
+ rw [← hf, Submodule.mem_map] at hx
obtain ⟨y, hy, rfl⟩ := hx
simpa
left_inv := fun x => Quotient.inductionOn' x (by simp)
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -44,12 +44,6 @@ def quotientRel : Setoid M :=
#align submodule.quotient_rel Submodule.quotientRel
-/
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theorem quotientRel_r_def {x y : M} : @Setoid.r _ p.quotientRel x y ↔ x - y ∈ p :=
Iff.trans (by rw [left_rel_apply, sub_eq_add_neg, neg_add, neg_neg]; rfl) neg_mem_iff
#align submodule.quotient_rel_r_def Submodule.quotientRel_r_def
@@ -71,55 +65,25 @@ def mk {p : Submodule R M} : M → M ⧸ p :=
#align submodule.quotient.mk Submodule.Quotient.mk
-/
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@[simp]
theorem mk'_eq_mk' {p : Submodule R M} (x : M) : @Quotient.mk' _ (quotientRel p) x = mk x :=
rfl
#align submodule.quotient.mk_eq_mk Submodule.Quotient.mk'_eq_mk'
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@[simp]
theorem mk''_eq_mk {p : Submodule R M} (x : M) : (Quotient.mk'' x : M ⧸ p) = mk x :=
rfl
#align submodule.quotient.mk'_eq_mk Submodule.Quotient.mk''_eq_mk
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@[simp]
theorem quot_mk_eq_mk {p : Submodule R M} (x : M) : (Quot.mk _ x : M ⧸ p) = mk x :=
rfl
#align submodule.quotient.quot_mk_eq_mk Submodule.Quotient.quot_mk_eq_mk
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protected theorem eq' {x y : M} : (mk x : M ⧸ p) = mk y ↔ -x + y ∈ p :=
QuotientAddGroup.eq
#align submodule.quotient.eq' Submodule.Quotient.eq'
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-Case conversion may be inaccurate. Consider using '#align submodule.quotient.eq Submodule.Quotient.eqₓ'. -/
protected theorem eq {x y : M} : (mk x : M ⧸ p) = mk y ↔ x - y ∈ p :=
p.Quotient.eq''.trans (leftRel_apply.symm.trans p.quotientRel_r_def)
#align submodule.quotient.eq Submodule.Quotient.eq
@@ -130,23 +94,11 @@ instance : Zero (M ⧸ p) :=
instance : Inhabited (M ⧸ p) :=
⟨0⟩
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@[simp]
theorem mk_zero : mk 0 = (0 : M ⧸ p) :=
rfl
#align submodule.quotient.mk_zero Submodule.Quotient.mk_zero
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-Case conversion may be inaccurate. Consider using '#align submodule.quotient.mk_eq_zero Submodule.Quotient.mk_eq_zeroₓ'. -/
@[simp]
theorem mk_eq_zero : (mk x : M ⧸ p) = 0 ↔ x ∈ p := by simpa using (Quotient.eq' p : mk x = 0 ↔ _)
#align submodule.quotient.mk_eq_zero Submodule.Quotient.mk_eq_zero
@@ -157,34 +109,16 @@ instance addCommGroup : AddCommGroup (M ⧸ p) :=
#align submodule.quotient.add_comm_group Submodule.Quotient.addCommGroup
-/
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@[simp]
theorem mk_add : (mk (x + y) : M ⧸ p) = mk x + mk y :=
rfl
#align submodule.quotient.mk_add Submodule.Quotient.mk_add
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@[simp]
theorem mk_neg : (mk (-x) : M ⧸ p) = -mk x :=
rfl
#align submodule.quotient.mk_neg Submodule.Quotient.mk_neg
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-Case conversion may be inaccurate. Consider using '#align submodule.quotient.mk_sub Submodule.Quotient.mk_subₓ'. -/
@[simp]
theorem mk_sub : (mk (x - y) : M ⧸ p) = mk x - mk y :=
rfl
@@ -209,12 +143,6 @@ instance hasSmul : SMul R (M ⧸ P) :=
#align submodule.quotient.has_smul Submodule.Quotient.hasSmul
-/
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-Case conversion may be inaccurate. Consider using '#align submodule.quotient.mk_smul Submodule.Quotient.mk_smulₓ'. -/
@[simp]
theorem mk_smul (r : S) (x : M) : (mk (r • x) : M ⧸ p) = r • mk x :=
rfl
@@ -254,43 +182,19 @@ instance mulAction' [Monoid S] [SMul S R] [MulAction S M] [IsScalarTower S R M]
#align submodule.quotient.mul_action' Submodule.Quotient.mulAction'
-/
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-Case conversion may be inaccurate. Consider using '#align submodule.quotient.mul_action Submodule.Quotient.mulActionₓ'. -/
instance mulAction (P : Submodule R M) : MulAction R (M ⧸ P) :=
Quotient.mulAction' P
#align submodule.quotient.mul_action Submodule.Quotient.mulAction
-/- warning: submodule.quotient.smul_zero_class' -> Submodule.Quotient.smulZeroClass' is a dubious translation:
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- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {S : Type.{u3}} [_inst_4 : SMul.{u3, u1} S R] [_inst_5 : SMulZeroClass.{u3, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)))))] [_inst_6 : IsScalarTower.{u3, u1, u2} S R M _inst_4 (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (SMulZeroClass.toHasSmul.{u3, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2))))) _inst_5)] (P : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), SMulZeroClass.{u3, u2} S (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.HasQuotient.Quotient.hasZero.{u1, u2} R M _inst_1 _inst_2 _inst_3 P)
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- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {S : Type.{u3}} [_inst_4 : SMul.{u3, u1} S R] [_inst_5 : SMulZeroClass.{u3, u2} S M (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2)))))] [_inst_6 : IsScalarTower.{u3, u1, u2} S R M _inst_4 (SMulZeroClass.toSMul.{u1, u2} R M (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (SMulZeroClass.toSMul.{u3, u2} S M (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) _inst_5)] (P : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), SMulZeroClass.{u3, u2} S (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.instZeroQuotientSubmoduleToSemiringToAddCommMonoidHasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3 P)
-Case conversion may be inaccurate. Consider using '#align submodule.quotient.smul_zero_class' Submodule.Quotient.smulZeroClass'ₓ'. -/
instance smulZeroClass' [SMul S R] [SMulZeroClass S M] [IsScalarTower S R M] (P : Submodule R M) :
SMulZeroClass S (M ⧸ P) :=
ZeroHom.smulZeroClass ⟨mk, mk_zero _⟩ P.Quotient.mk_smul
#align submodule.quotient.smul_zero_class' Submodule.Quotient.smulZeroClass'
-/- warning: submodule.quotient.smul_zero_class -> Submodule.Quotient.smulZeroClass is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (P : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), SMulZeroClass.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.HasQuotient.Quotient.hasZero.{u1, u2} R M _inst_1 _inst_2 _inst_3 P)
-but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (P : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), SMulZeroClass.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.instZeroQuotientSubmoduleToSemiringToAddCommMonoidHasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3 P)
-Case conversion may be inaccurate. Consider using '#align submodule.quotient.smul_zero_class Submodule.Quotient.smulZeroClassₓ'. -/
instance smulZeroClass (P : Submodule R M) : SMulZeroClass R (M ⧸ P) :=
Quotient.smulZeroClass' P
#align submodule.quotient.smul_zero_class Submodule.Quotient.smulZeroClass
-/- warning: submodule.quotient.distrib_smul' -> Submodule.Quotient.distribSmul' is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {S : Type.{u3}} [_inst_4 : SMul.{u3, u1} S R] [_inst_5 : DistribSMul.{u3, u2} S M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2))))] [_inst_6 : IsScalarTower.{u3, u1, u2} S R M _inst_4 (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (SMulZeroClass.toHasSmul.{u3, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2))))) (DistribSMul.toSmulZeroClass.{u3, u2} S M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)))) _inst_5))] (P : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), DistribSMul.{u3, u2} S (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (AddMonoid.toAddZeroClass.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (SubNegMonoid.toAddMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (AddGroup.toSubNegMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (AddCommGroup.toAddGroup.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 P)))))
-but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {S : Type.{u3}} [_inst_4 : SMul.{u3, u1} S R] [_inst_5 : DistribSMul.{u3, u2} S M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2))))] [_inst_6 : IsScalarTower.{u3, u1, u2} S R M _inst_4 (SMulZeroClass.toSMul.{u1, u2} R M (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (SMulZeroClass.toSMul.{u3, u2} S M (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u2} S M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)))) _inst_5))] (P : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), DistribSMul.{u3, u2} S (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (AddMonoid.toAddZeroClass.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (SubNegMonoid.toAddMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (AddGroup.toSubNegMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (AddCommGroup.toAddGroup.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 P)))))
-Case conversion may be inaccurate. Consider using '#align submodule.quotient.distrib_smul' Submodule.Quotient.distribSmul'ₓ'. -/
instance distribSmul' [SMul S R] [DistribSMul S M] [IsScalarTower S R M] (P : Submodule R M) :
DistribSMul S (M ⧸ P) :=
Function.Surjective.distribSMul ⟨mk, rfl, fun _ _ => rfl⟩ (surjective_quot_mk _)
@@ -303,24 +207,12 @@ instance distribSmul (P : Submodule R M) : DistribSMul R (M ⧸ P) :=
#align submodule.quotient.distrib_smul Submodule.Quotient.distribSmul
-/
-/- warning: submodule.quotient.distrib_mul_action' -> Submodule.Quotient.distribMulAction' is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {S : Type.{u3}} [_inst_4 : Monoid.{u3} S] [_inst_5 : SMul.{u3, u1} S R] [_inst_6 : DistribMulAction.{u3, u2} S M _inst_4 (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)))] [_inst_7 : IsScalarTower.{u3, u1, u2} S R M _inst_5 (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (SMulZeroClass.toHasSmul.{u3, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2))))) (DistribSMul.toSmulZeroClass.{u3, u2} S M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u2} S M _inst_4 (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2))) _inst_6)))] (P : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), DistribMulAction.{u3, u2} S (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) _inst_4 (SubNegMonoid.toAddMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (AddGroup.toSubNegMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (AddCommGroup.toAddGroup.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 P))))
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- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {S : Type.{u3}} [_inst_4 : Monoid.{u3} S] [_inst_5 : SMul.{u3, u1} S R] [_inst_6 : DistribMulAction.{u3, u2} S M _inst_4 (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)))] [_inst_7 : IsScalarTower.{u3, u1, u2} S R M _inst_5 (SMulZeroClass.toSMul.{u1, u2} R M (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (SMulZeroClass.toSMul.{u3, u2} S M (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u2} S M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u2} S M _inst_4 (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2))) _inst_6)))] (P : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), DistribMulAction.{u3, u2} S (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) _inst_4 (SubNegMonoid.toAddMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (AddGroup.toSubNegMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (AddCommGroup.toAddGroup.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 P))))
-Case conversion may be inaccurate. Consider using '#align submodule.quotient.distrib_mul_action' Submodule.Quotient.distribMulAction'ₓ'. -/
instance distribMulAction' [Monoid S] [SMul S R] [DistribMulAction S M] [IsScalarTower S R M]
(P : Submodule R M) : DistribMulAction S (M ⧸ P) :=
Function.Surjective.distribMulAction ⟨mk, rfl, fun _ _ => rfl⟩ (surjective_quot_mk _)
P.Quotient.mk_smul
#align submodule.quotient.distrib_mul_action' Submodule.Quotient.distribMulAction'
-/- warning: submodule.quotient.distrib_mul_action -> Submodule.Quotient.distribMulAction is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align submodule.quotient.distrib_mul_action Submodule.Quotient.distribMulActionₓ'. -/
instance distribMulAction (P : Submodule R M) : DistribMulAction R (M ⧸ P) :=
Quotient.distribMulAction' P
#align submodule.quotient.distrib_mul_action Submodule.Quotient.distribMulAction
@@ -354,18 +246,12 @@ def restrictScalarsEquiv [Ring S] [SMul S R] [Module S M] [IsScalarTower S R M]
#align submodule.quotient.restrict_scalars_equiv Submodule.Quotient.restrictScalarsEquiv
-/
-/- warning: submodule.quotient.restrict_scalars_equiv_mk -> Submodule.Quotient.restrictScalarsEquiv_mk is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.quotient.restrict_scalars_equiv_mk Submodule.Quotient.restrictScalarsEquiv_mkₓ'. -/
@[simp]
theorem restrictScalarsEquiv_mk [Ring S] [SMul S R] [Module S M] [IsScalarTower S R M]
(P : Submodule R M) (x : M) : restrictScalarsEquiv S P (mk x) = mk x :=
rfl
#align submodule.quotient.restrict_scalars_equiv_mk Submodule.Quotient.restrictScalarsEquiv_mk
-/- warning: submodule.quotient.restrict_scalars_equiv_symm_mk -> Submodule.Quotient.restrictScalarsEquiv_symm_mk is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.quotient.restrict_scalars_equiv_symm_mk Submodule.Quotient.restrictScalarsEquiv_symm_mkₓ'. -/
@[simp]
theorem restrictScalarsEquiv_symm_mk [Ring S] [SMul S R] [Module S M] [IsScalarTower S R M]
(P : Submodule R M) (x : M) : (restrictScalarsEquiv S P).symm (mk x) = mk x :=
@@ -379,12 +265,6 @@ theorem mk_surjective : Function.Surjective (@mk _ _ _ _ _ p) := by rintro ⟨x
#align submodule.quotient.mk_surjective Submodule.Quotient.mk_surjective
-/
-/- warning: submodule.quotient.nontrivial_of_lt_top -> Submodule.Quotient.nontrivial_of_lt_top 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 submodule.quotient.nontrivial_of_lt_top Submodule.Quotient.nontrivial_of_lt_topₓ'. -/
theorem nontrivial_of_lt_top (h : p < ⊤) : Nontrivial (M ⧸ p) :=
by
obtain ⟨x, _, not_mem_s⟩ := SetLike.exists_of_lt h
@@ -394,47 +274,23 @@ theorem nontrivial_of_lt_top (h : p < ⊤) : Nontrivial (M ⧸ p) :=
end Quotient
-/- warning: submodule.quotient_bot.infinite -> Submodule.QuotientBot.infinite is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align submodule.quotient_bot.infinite Submodule.QuotientBot.infiniteₓ'. -/
instance QuotientBot.infinite [Infinite M] : Infinite (M ⧸ (⊥ : Submodule R M)) :=
Infinite.of_injective Submodule.Quotient.mk fun x y h =>
sub_eq_zero.mp <| (Submodule.Quotient.eq ⊥).mp h
#align submodule.quotient_bot.infinite Submodule.QuotientBot.infinite
-/- warning: submodule.quotient_top.unique -> Submodule.QuotientTop.unique is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align submodule.quotient_top.unique Submodule.QuotientTop.uniqueₓ'. -/
instance QuotientTop.unique : Unique (M ⧸ (⊤ : Submodule R M))
where
default := 0
uniq x := Quotient.inductionOn' x fun x => (Submodule.Quotient.eq ⊤).mpr Submodule.mem_top
#align submodule.quotient_top.unique Submodule.QuotientTop.unique
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instance QuotientTop.fintype : Fintype (M ⧸ (⊤ : Submodule R M)) :=
Fintype.ofSubsingleton 0
#align submodule.quotient_top.fintype Submodule.QuotientTop.fintype
variable {p}
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-Case conversion may be inaccurate. Consider using '#align submodule.subsingleton_quotient_iff_eq_top Submodule.subsingleton_quotient_iff_eq_topₓ'. -/
theorem subsingleton_quotient_iff_eq_top : Subsingleton (M ⧸ p) ↔ p = ⊤ :=
by
constructor
@@ -446,12 +302,6 @@ theorem subsingleton_quotient_iff_eq_top : Subsingleton (M ⧸ p) ↔ p = ⊤ :=
infer_instance
#align submodule.subsingleton_quotient_iff_eq_top Submodule.subsingleton_quotient_iff_eq_top
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-Case conversion may be inaccurate. Consider using '#align submodule.unique_quotient_iff_eq_top Submodule.unique_quotient_iff_eq_topₓ'. -/
theorem unique_quotient_iff_eq_top : Nonempty (Unique (M ⧸ p)) ↔ p = ⊤ :=
⟨fun ⟨h⟩ => subsingleton_quotient_iff_eq_top.mp (@Unique.subsingleton h), by rintro rfl;
exact ⟨quotient_top.unique⟩⟩
@@ -478,9 +328,6 @@ section
variable {M₂ : Type _} [AddCommGroup M₂] [Module R M₂]
-/- warning: submodule.quot_hom_ext -> Submodule.quot_hom_ext is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.quot_hom_ext Submodule.quot_hom_extₓ'. -/
theorem quot_hom_ext ⦃f g : M ⧸ p →ₗ[R] M₂⦄ (h : ∀ x, f (Quotient.mk x) = g (Quotient.mk x)) :
f = g :=
LinearMap.ext fun x => Quotient.inductionOn' x h
@@ -495,23 +342,11 @@ def mkQ : M →ₗ[R] M ⧸ p where
#align submodule.mkq Submodule.mkQ
-/
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@[simp]
theorem mkQ_apply (x : M) : p.mkQ x = Quotient.mk x :=
rfl
#align submodule.mkq_apply Submodule.mkQ_apply
-/- warning: submodule.mkq_surjective -> Submodule.mkQ_surjective is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align submodule.mkq_surjective Submodule.mkQ_surjectiveₓ'. -/
theorem mkQ_surjective (A : Submodule R M) : Function.Surjective A.mkQ := by
rintro ⟨x⟩ <;> exact ⟨x, rfl⟩
#align submodule.mkq_surjective Submodule.mkQ_surjective
@@ -520,9 +355,6 @@ end
variable {R₂ M₂ : Type _} [Ring R₂] [AddCommGroup M₂] [Module R₂ M₂] {τ₁₂ : R →+* R₂}
-/- warning: submodule.linear_map_qext -> Submodule.linearMap_qext is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.linear_map_qext Submodule.linearMap_qextₓ'. -/
/-- Two `linear_map`s from a quotient module are equal if their compositions with
`submodule.mkq` are equal.
@@ -532,12 +364,6 @@ theorem linearMap_qext ⦃f g : M ⧸ p →ₛₗ[τ₁₂] M₂⦄ (h : f.comp
LinearMap.ext fun x => Quotient.inductionOn' x <| (LinearMap.congr_fun h : _)
#align submodule.linear_map_qext Submodule.linearMap_qext
-/- warning: submodule.liftq -> Submodule.liftQ is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align submodule.liftq Submodule.liftQₓ'. -/
/-- The map from the quotient of `M` by a submodule `p` to `M₂` induced by a linear map `f : M → M₂`
vanishing on `p`, as a linear map. -/
def liftQ (f : M →ₛₗ[τ₁₂] M₂) (h : p ≤ f.ker) : M ⧸ p →ₛₗ[τ₁₂] M₂ :=
@@ -545,42 +371,27 @@ def liftQ (f : M →ₛₗ[τ₁₂] M₂) (h : p ≤ f.ker) : M ⧸ p →ₛₗ
map_smul' := by rintro a ⟨x⟩ <;> exact f.map_smulₛₗ a x }
#align submodule.liftq Submodule.liftQ
-/- warning: submodule.liftq_apply -> Submodule.liftQ_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.liftq_apply Submodule.liftQ_applyₓ'. -/
@[simp]
theorem liftQ_apply (f : M →ₛₗ[τ₁₂] M₂) {h} (x : M) : p.liftQ f h (Quotient.mk x) = f x :=
rfl
#align submodule.liftq_apply Submodule.liftQ_apply
-/- warning: submodule.liftq_mkq -> Submodule.liftQ_mkQ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.liftq_mkq Submodule.liftQ_mkQₓ'. -/
@[simp]
theorem liftQ_mkQ (f : M →ₛₗ[τ₁₂] M₂) (h) : (p.liftQ f h).comp p.mkQ = f := by ext <;> rfl
#align submodule.liftq_mkq Submodule.liftQ_mkQ
-/- warning: submodule.liftq_span_singleton -> Submodule.liftQSpanSingleton is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.liftq_span_singleton Submodule.liftQSpanSingletonₓ'. -/
/-- Special case of `liftq` when `p` is the span of `x`. In this case, the condition on `f` simply
becomes vanishing at `x`.-/
def liftQSpanSingleton (x : M) (f : M →ₛₗ[τ₁₂] M₂) (h : f x = 0) : (M ⧸ R ∙ x) →ₛₗ[τ₁₂] M₂ :=
(R ∙ x).liftQ f <| by rw [span_singleton_le_iff_mem, LinearMap.mem_ker, h]
#align submodule.liftq_span_singleton Submodule.liftQSpanSingleton
-/- warning: submodule.liftq_span_singleton_apply -> Submodule.liftQSpanSingleton_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.liftq_span_singleton_apply Submodule.liftQSpanSingleton_applyₓ'. -/
@[simp]
theorem liftQSpanSingleton_apply (x : M) (f : M →ₛₗ[τ₁₂] M₂) (h : f x = 0) (y : M) :
liftQSpanSingleton x f h (Quotient.mk y) = f y :=
rfl
#align submodule.liftq_span_singleton_apply Submodule.liftQSpanSingleton_apply
-/- warning: submodule.range_mkq -> Submodule.range_mkQ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.range_mkq Submodule.range_mkQₓ'. -/
@[simp]
theorem range_mkQ : p.mkQ.range = ⊤ :=
eq_top_iff'.2 <| by rintro ⟨x⟩ <;> exact ⟨x, rfl⟩
@@ -592,34 +403,19 @@ theorem ker_mkQ : p.mkQ.ker = p := by ext <;> simp
#align submodule.ker_mkq Submodule.ker_mkQ
-/
-/- warning: submodule.le_comap_mkq -> Submodule.le_comap_mkQ is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (p' : Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)), LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) p')
-but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (p : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (p' : Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)), LE.le.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) p (Submodule.comap.{u2, u2, u1, u1, u1} R R M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} 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))) M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.mkQ.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) p')
-Case conversion may be inaccurate. Consider using '#align submodule.le_comap_mkq Submodule.le_comap_mkQₓ'. -/
theorem le_comap_mkQ (p' : Submodule R (M ⧸ p)) : p ≤ comap p.mkQ p' := by
simpa using (comap_mono bot_le : p.mkq.ker ≤ comap p.mkq p')
#align submodule.le_comap_mkq Submodule.le_comap_mkQ
-/- warning: submodule.mkq_map_self -> Submodule.mkQ_map_self is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.mkq_map_self Submodule.mkQ_map_selfₓ'. -/
@[simp]
theorem mkQ_map_self : map p.mkQ p = ⊥ := by
rw [eq_bot_iff, map_le_iff_le_comap, comap_bot, ker_mkq] <;> exact le_rfl
#align submodule.mkq_map_self Submodule.mkQ_map_self
-/- warning: submodule.comap_map_mkq -> Submodule.comap_map_mkQ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.comap_map_mkq Submodule.comap_map_mkQₓ'. -/
@[simp]
theorem comap_map_mkQ : comap p.mkQ (map p.mkQ p') = p ⊔ p' := by simp [comap_map_eq, sup_comm]
#align submodule.comap_map_mkq Submodule.comap_map_mkQ
-/- warning: submodule.map_mkq_eq_top -> Submodule.map_mkQ_eq_top is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.map_mkq_eq_top Submodule.map_mkQ_eq_topₓ'. -/
@[simp]
theorem map_mkQ_eq_top : map p.mkQ p' = ⊤ ↔ p ⊔ p' = ⊤ := by
simp only [map_eq_top_iff p.range_mkq, sup_comm, ker_mkq]
@@ -627,42 +423,27 @@ theorem map_mkQ_eq_top : map p.mkQ p' = ⊤ ↔ p ⊔ p' = ⊤ := by
variable (q : Submodule R₂ M₂)
-/- warning: submodule.mapq -> Submodule.mapQ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.mapq Submodule.mapQₓ'. -/
/-- The map from the quotient of `M` by submodule `p` to the quotient of `M₂` by submodule `q` along
`f : M → M₂` is linear. -/
def mapQ (f : M →ₛₗ[τ₁₂] M₂) (h : p ≤ comap f q) : M ⧸ p →ₛₗ[τ₁₂] M₂ ⧸ q :=
p.liftQ (q.mkQ.comp f) <| by simpa [ker_comp] using h
#align submodule.mapq Submodule.mapQ
-/- warning: submodule.mapq_apply -> Submodule.mapQ_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.mapq_apply Submodule.mapQ_applyₓ'. -/
@[simp]
theorem mapQ_apply (f : M →ₛₗ[τ₁₂] M₂) {h} (x : M) :
mapQ p q f h (Quotient.mk x) = Quotient.mk (f x) :=
rfl
#align submodule.mapq_apply Submodule.mapQ_apply
-/- warning: submodule.mapq_mkq -> Submodule.mapQ_mkQ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.mapq_mkq Submodule.mapQ_mkQₓ'. -/
theorem mapQ_mkQ (f : M →ₛₗ[τ₁₂] M₂) {h} : (mapQ p q f h).comp p.mkQ = q.mkQ.comp f := by
ext x <;> rfl
#align submodule.mapq_mkq Submodule.mapQ_mkQ
-/- warning: submodule.mapq_zero -> Submodule.mapQ_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.mapq_zero Submodule.mapQ_zeroₓ'. -/
@[simp]
theorem mapQ_zero (h : p ≤ q.comap (0 : M →ₛₗ[τ₁₂] M₂) := (by simp)) :
p.mapQ q (0 : M →ₛₗ[τ₁₂] M₂) h = 0 := by ext; simp
#align submodule.mapq_zero Submodule.mapQ_zero
-/- warning: submodule.mapq_comp -> Submodule.mapQ_comp is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.mapq_comp Submodule.mapQ_compₓ'. -/
/-- Given submodules `p ⊆ M`, `p₂ ⊆ M₂`, `p₃ ⊆ M₃` and maps `f : M → M₂`, `g : M₂ → M₃` inducing
`mapq f : M ⧸ p → M₂ ⧸ p₂` and `mapq g : M₂ ⧸ p₂ → M₃ ⧸ p₃` then
`mapq (g ∘ f) = (mapq g) ∘ (mapq f)`. -/
@@ -673,17 +454,11 @@ theorem mapQ_comp {R₃ M₃ : Type _} [Ring R₃] [AddCommGroup M₃] [Module R
p.mapQ p₃ (g.comp f) h = (p₂.mapQ p₃ g hg).comp (p.mapQ p₂ f hf) := by ext; simp
#align submodule.mapq_comp Submodule.mapQ_comp
-/- warning: submodule.mapq_id -> Submodule.mapQ_id is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.mapq_id Submodule.mapQ_idₓ'. -/
@[simp]
theorem mapQ_id (h : p ≤ p.comap LinearMap.id := (by rw [comap_id]; exact le_refl _)) :
p.mapQ p LinearMap.id h = LinearMap.id := by ext; simp
#align submodule.mapq_id Submodule.mapQ_id
-/- warning: submodule.mapq_pow -> Submodule.mapQ_pow is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.mapq_pow Submodule.mapQ_powₓ'. -/
theorem mapQ_pow {f : M →ₗ[R] M} (h : p ≤ p.comap f) (k : ℕ)
(h' : p ≤ p.comap (f ^ k) := p.le_comap_pow_of_le_comap h k) :
p.mapQ p (f ^ k) h' = p.mapQ p f h ^ k :=
@@ -694,47 +469,29 @@ theorem mapQ_pow {f : M →ₗ[R] M} (h : p ≤ p.comap f) (k : ℕ)
apply p.mapq_comp
#align submodule.mapq_pow Submodule.mapQ_pow
-/- warning: submodule.comap_liftq -> Submodule.comap_liftQ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.comap_liftq Submodule.comap_liftQₓ'. -/
theorem comap_liftQ (f : M →ₛₗ[τ₁₂] M₂) (h) : q.comap (p.liftQ f h) = (q.comap f).map (mkQ p) :=
le_antisymm (by rintro ⟨x⟩ hx <;> exact ⟨_, hx, rfl⟩)
(by rw [map_le_iff_le_comap, ← comap_comp, liftq_mkq] <;> exact le_rfl)
#align submodule.comap_liftq Submodule.comap_liftQ
-/- warning: submodule.map_liftq -> Submodule.map_liftQ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.map_liftq Submodule.map_liftQₓ'. -/
theorem map_liftQ [RingHomSurjective τ₁₂] (f : M →ₛₗ[τ₁₂] M₂) (h) (q : Submodule R (M ⧸ p)) :
q.map (p.liftQ f h) = (q.comap p.mkQ).map f :=
le_antisymm (by rintro _ ⟨⟨x⟩, hxq, rfl⟩ <;> exact ⟨x, hxq, rfl⟩)
(by rintro _ ⟨x, hxq, rfl⟩ <;> exact ⟨Quotient.mk' x, hxq, rfl⟩)
#align submodule.map_liftq Submodule.map_liftQ
-/- warning: submodule.ker_liftq -> Submodule.ker_liftQ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.ker_liftq Submodule.ker_liftQₓ'. -/
theorem ker_liftQ (f : M →ₛₗ[τ₁₂] M₂) (h) : ker (p.liftQ f h) = (ker f).map (mkQ p) :=
comap_liftQ _ _ _ _
#align submodule.ker_liftq Submodule.ker_liftQ
-/- warning: submodule.range_liftq -> Submodule.range_liftQ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.range_liftq Submodule.range_liftQₓ'. -/
theorem range_liftQ [RingHomSurjective τ₁₂] (f : M →ₛₗ[τ₁₂] M₂) (h) :
range (p.liftQ f h) = range f := by simpa only [range_eq_map] using map_liftq _ _ _ _
#align submodule.range_liftq Submodule.range_liftQ
-/- warning: submodule.ker_liftq_eq_bot -> Submodule.ker_liftQ_eq_bot is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.ker_liftq_eq_bot Submodule.ker_liftQ_eq_botₓ'. -/
theorem ker_liftQ_eq_bot (f : M →ₛₗ[τ₁₂] M₂) (h) (h' : ker f ≤ p) : ker (p.liftQ f h) = ⊥ := by
rw [ker_liftq, le_antisymm h h', mkq_map_self]
#align submodule.ker_liftq_eq_bot Submodule.ker_liftQ_eq_bot
-/- warning: submodule.comap_mkq.rel_iso -> Submodule.comapMkQRelIso is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.comap_mkq.rel_iso Submodule.comapMkQRelIsoₓ'. -/
/-- The correspondence theorem for modules: there is an order isomorphism between submodules of the
quotient of `M` by `p`, and submodules of `M` larger than `p`. -/
def Submodule.comapMkQRelIso : Submodule R (M ⧸ p) ≃o { p' : Submodule R M // p ≤ p' }
@@ -746,30 +503,18 @@ def Submodule.comapMkQRelIso : Submodule R (M ⧸ p) ≃o { p' : Submodule R M /
map_rel_iff' p₁ p₂ := comap_le_comap_iff <| range_mkQ _
#align submodule.comap_mkq.rel_iso Submodule.comapMkQRelIso
-/- warning: submodule.comap_mkq.order_embedding -> Submodule.comapMkQOrderEmbedding is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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(Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) 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M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)))))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) 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-Case conversion may be inaccurate. Consider using '#align submodule.comap_mkq.order_embedding Submodule.comapMkQOrderEmbeddingₓ'. -/
/-- The ordering on submodules of the quotient of `M` by `p` embeds into the ordering on submodules
of `M`. -/
def Submodule.comapMkQOrderEmbedding : Submodule R (M ⧸ p) ↪o Submodule R M :=
(RelIso.toRelEmbedding <| Submodule.comapMkQRelIso p).trans (Subtype.relEmbedding _ _)
#align submodule.comap_mkq.order_embedding Submodule.comapMkQOrderEmbedding
-/- warning: submodule.comap_mkq_embedding_eq -> Submodule.comapMkQOrderEmbedding_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.comap_mkq_embedding_eq Submodule.comapMkQOrderEmbedding_eqₓ'. -/
@[simp]
theorem comapMkQOrderEmbedding_eq (p' : Submodule R (M ⧸ p)) :
Submodule.comapMkQOrderEmbedding p p' = comap p.mkQ p' :=
rfl
#align submodule.comap_mkq_embedding_eq Submodule.comapMkQOrderEmbedding_eq
-/- warning: submodule.span_preimage_eq -> Submodule.span_preimage_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.span_preimage_eq Submodule.span_preimage_eqₓ'. -/
theorem span_preimage_eq [RingHomSurjective τ₁₂] {f : M →ₛₗ[τ₁₂] M₂} {s : Set M₂} (h₀ : s.Nonempty)
(h₁ : s ⊆ range f) : span R (f ⁻¹' s) = (span R₂ s).comap f :=
by
@@ -784,9 +529,6 @@ theorem span_preimage_eq [RingHomSurjective τ₁₂] {f : M →ₛₗ[τ₁₂]
exact inf_le_right
#align submodule.span_preimage_eq Submodule.span_preimage_eq
-/- warning: submodule.quotient.equiv -> Submodule.Quotient.equiv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.quotient.equiv Submodule.Quotient.equivₓ'. -/
/-- If `P` is a submodule of `M` and `Q` a submodule of `N`,
and `f : M ≃ₗ N` maps `P` to `Q`, then `M ⧸ P` is equivalent to `N ⧸ Q`. -/
@[simps]
@@ -808,9 +550,6 @@ def Quotient.equiv {N : Type _} [AddCommGroup N] [Module R N] (P : Submodule R M
right_inv := fun x => Quotient.inductionOn' x (by simp) }
#align submodule.quotient.equiv Submodule.Quotient.equiv
-/- warning: submodule.quotient.equiv_symm -> Submodule.Quotient.equiv_symm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.quotient.equiv_symm Submodule.Quotient.equiv_symmₓ'. -/
@[simp]
theorem Quotient.equiv_symm {R M N : Type _} [CommRing R] [AddCommGroup M] [Module R M]
[AddCommGroup N] [Module R N] (P : Submodule R M) (Q : Submodule R N) (f : M ≃ₗ[R] N)
@@ -820,9 +559,6 @@ theorem Quotient.equiv_symm {R M N : Type _} [CommRing R] [AddCommGroup M] [Modu
rfl
#align submodule.quotient.equiv_symm Submodule.Quotient.equiv_symm
-/- warning: submodule.quotient.equiv_trans -> Submodule.Quotient.equiv_trans is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.quotient.equiv_trans Submodule.Quotient.equiv_transₓ'. -/
@[simp]
theorem Quotient.equiv_trans {N O : Type _} [AddCommGroup N] [Module R N] [AddCommGroup O]
[Module R O] (P : Submodule R M) (Q : Submodule R N) (S : Submodule R O) (e : M ≃ₗ[R] N)
@@ -857,24 +593,15 @@ variable {τ₁₂ : R →+* R₂} {τ₂₃ : R₂ →+* R₃} {τ₁₃ : R
variable [RingHomCompTriple τ₁₂ τ₂₃ τ₁₃] [RingHomSurjective τ₁₂]
-/- warning: linear_map.range_mkq_comp -> LinearMap.range_mkQ_comp is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.range_mkq_comp LinearMap.range_mkQ_compₓ'. -/
theorem range_mkQ_comp (f : M →ₛₗ[τ₁₂] M₂) : f.range.mkQ.comp f = 0 :=
LinearMap.ext fun x => by simp
#align linear_map.range_mkq_comp LinearMap.range_mkQ_comp
-/- warning: linear_map.ker_le_range_iff -> LinearMap.ker_le_range_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.ker_le_range_iff LinearMap.ker_le_range_iffₓ'. -/
theorem ker_le_range_iff {f : M →ₛₗ[τ₁₂] M₂} {g : M₂ →ₛₗ[τ₂₃] M₃} :
g.ker ≤ f.range ↔ f.range.mkQ.comp g.ker.Subtype = 0 := by
rw [← range_le_ker_iff, Submodule.ker_mkQ, Submodule.range_subtype]
#align linear_map.ker_le_range_iff LinearMap.ker_le_range_iff
-/- warning: linear_map.range_eq_top_of_cancel -> LinearMap.range_eq_top_of_cancel is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.range_eq_top_of_cancel LinearMap.range_eq_top_of_cancelₓ'. -/
/-- An epimorphism is surjective. -/
theorem range_eq_top_of_cancel {f : M →ₛₗ[τ₁₂] M₂}
(h : ∀ u v : M₂ →ₗ[R₂] M₂ ⧸ f.range, u.comp f = v.comp f → u = v) : f.range = ⊤ :=
@@ -896,39 +623,24 @@ variable {R M : Type _} {r : R} {x y : M} [Ring R] [AddCommGroup M] [Module R M]
variable (p p' : Submodule R M)
-/- warning: submodule.quot_equiv_of_eq_bot -> Submodule.quotEquivOfEqBot is a dubious translation:
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- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p (Bot.bot.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasBot.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) -> (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Submodule.quotEquivOfEqBot._proof_1.{u1} R _inst_1) (Submodule.quotEquivOfEqBot._proof_2.{u1} R _inst_1) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_3)
-but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p (Bot.bot.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instBotSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) -> (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_3)
-Case conversion may be inaccurate. Consider using '#align submodule.quot_equiv_of_eq_bot Submodule.quotEquivOfEqBotₓ'. -/
/-- If `p = ⊥`, then `M / p ≃ₗ[R] M`. -/
def quotEquivOfEqBot (hp : p = ⊥) : (M ⧸ p) ≃ₗ[R] M :=
LinearEquiv.ofLinear (p.liftQ id <| hp.symm ▸ bot_le) p.mkQ (liftQ_mkQ _ _ _) <|
p.quot_hom_ext fun x => rfl
#align submodule.quot_equiv_of_eq_bot Submodule.quotEquivOfEqBot
-/- warning: submodule.quot_equiv_of_eq_bot_apply_mk -> Submodule.quotEquivOfEqBot_apply_mk is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.quot_equiv_of_eq_bot_apply_mk Submodule.quotEquivOfEqBot_apply_mkₓ'. -/
@[simp]
theorem quotEquivOfEqBot_apply_mk (hp : p = ⊥) (x : M) :
p.quotEquivOfEqBot hp (Quotient.mk x) = x :=
rfl
#align submodule.quot_equiv_of_eq_bot_apply_mk Submodule.quotEquivOfEqBot_apply_mk
-/- warning: submodule.quot_equiv_of_eq_bot_symm_apply -> Submodule.quotEquivOfEqBot_symm_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.quot_equiv_of_eq_bot_symm_apply Submodule.quotEquivOfEqBot_symm_applyₓ'. -/
@[simp]
theorem quotEquivOfEqBot_symm_apply (hp : p = ⊥) (x : M) :
(p.quotEquivOfEqBot hp).symm x = Quotient.mk x :=
rfl
#align submodule.quot_equiv_of_eq_bot_symm_apply Submodule.quotEquivOfEqBot_symm_apply
-/- warning: submodule.coe_quot_equiv_of_eq_bot_symm -> Submodule.coe_quotEquivOfEqBot_symm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.coe_quot_equiv_of_eq_bot_symm Submodule.coe_quotEquivOfEqBot_symmₓ'. -/
@[simp]
theorem coe_quotEquivOfEqBot_symm (hp : p = ⊥) :
((p.quotEquivOfEqBot hp).symm : M →ₗ[R] M ⧸ p) = p.mkQ :=
@@ -946,18 +658,12 @@ def quotEquivOfEq (h : p = p') : (M ⧸ p) ≃ₗ[R] M ⧸ p' :=
#align submodule.quot_equiv_of_eq Submodule.quotEquivOfEq
-/
-/- warning: submodule.quot_equiv_of_eq_mk -> Submodule.quotEquivOfEq_mk is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.quot_equiv_of_eq_mk Submodule.quotEquivOfEq_mkₓ'. -/
@[simp]
theorem quotEquivOfEq_mk (h : p = p') (x : M) :
Submodule.quotEquivOfEq p p' h (Submodule.Quotient.mk x) = Submodule.Quotient.mk x :=
rfl
#align submodule.quot_equiv_of_eq_mk Submodule.quotEquivOfEq_mk
-/- warning: submodule.quotient.equiv_refl -> Submodule.Quotient.equiv_refl is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.quotient.equiv_refl Submodule.Quotient.equiv_reflₓ'. -/
@[simp]
theorem Quotient.equiv_refl (P : Submodule R M) (Q : Submodule R M)
(hf : P.map (LinearEquiv.refl R M : M →ₗ[R] M) = Q) :
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -51,11 +51,7 @@ but is expected to have type
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {x : M} {y : M}, Iff (Setoid.r.{succ u2} M (Submodule.quotientRel.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) x y) (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HSub.hSub.{u2, u2, u2} M M M (instHSub.{u2} M (SubNegMonoid.toSub.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)))) x y) p)
Case conversion may be inaccurate. Consider using '#align submodule.quotient_rel_r_def Submodule.quotientRel_r_defₓ'. -/
theorem quotientRel_r_def {x y : M} : @Setoid.r _ p.quotientRel x y ↔ x - y ∈ p :=
- Iff.trans
- (by
- rw [left_rel_apply, sub_eq_add_neg, neg_add, neg_neg]
- rfl)
- neg_mem_iff
+ Iff.trans (by rw [left_rel_apply, sub_eq_add_neg, neg_add, neg_neg]; rfl) neg_mem_iff
#align submodule.quotient_rel_r_def Submodule.quotientRel_r_def
#print Submodule.hasQuotient /-
@@ -379,10 +375,7 @@ theorem restrictScalarsEquiv_symm_mk [Ring S] [SMul S R] [Module S M] [IsScalarT
end Module
#print Submodule.Quotient.mk_surjective /-
-theorem mk_surjective : Function.Surjective (@mk _ _ _ _ _ p) :=
- by
- rintro ⟨x⟩
- exact ⟨x, rfl⟩
+theorem mk_surjective : Function.Surjective (@mk _ _ _ _ _ p) := by rintro ⟨x⟩; exact ⟨x, rfl⟩
#align submodule.quotient.mk_surjective Submodule.Quotient.mk_surjective
-/
@@ -460,9 +453,7 @@ but is expected to have type
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3}, Iff (Nonempty.{succ u2} (Unique.{succ u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p))) (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))
Case conversion may be inaccurate. Consider using '#align submodule.unique_quotient_iff_eq_top Submodule.unique_quotient_iff_eq_topₓ'. -/
theorem unique_quotient_iff_eq_top : Nonempty (Unique (M ⧸ p)) ↔ p = ⊤ :=
- ⟨fun ⟨h⟩ => subsingleton_quotient_iff_eq_top.mp (@Unique.subsingleton h),
- by
- rintro rfl
+ ⟨fun ⟨h⟩ => subsingleton_quotient_iff_eq_top.mp (@Unique.subsingleton h), by rintro rfl;
exact ⟨quotient_top.unique⟩⟩
#align submodule.unique_quotient_iff_eq_top Submodule.unique_quotient_iff_eq_top
@@ -666,9 +657,7 @@ theorem mapQ_mkQ (f : M →ₛₗ[τ₁₂] M₂) {h} : (mapQ p q f h).comp p.mk
Case conversion may be inaccurate. Consider using '#align submodule.mapq_zero Submodule.mapQ_zeroₓ'. -/
@[simp]
theorem mapQ_zero (h : p ≤ q.comap (0 : M →ₛₗ[τ₁₂] M₂) := (by simp)) :
- p.mapQ q (0 : M →ₛₗ[τ₁₂] M₂) h = 0 := by
- ext
- simp
+ p.mapQ q (0 : M →ₛₗ[τ₁₂] M₂) h = 0 := by ext; simp
#align submodule.mapq_zero Submodule.mapQ_zero
/- warning: submodule.mapq_comp -> Submodule.mapQ_comp is a dubious translation:
@@ -681,24 +670,15 @@ theorem mapQ_comp {R₃ M₃ : Type _} [Ring R₃] [AddCommGroup M₃] [Module R
(p₃ : Submodule R₃ M₃) {τ₂₃ : R₂ →+* R₃} {τ₁₃ : R →+* R₃} [RingHomCompTriple τ₁₂ τ₂₃ τ₁₃]
(f : M →ₛₗ[τ₁₂] M₂) (g : M₂ →ₛₗ[τ₂₃] M₃) (hf : p ≤ p₂.comap f) (hg : p₂ ≤ p₃.comap g)
(h := hf.trans (comap_mono hg)) :
- p.mapQ p₃ (g.comp f) h = (p₂.mapQ p₃ g hg).comp (p.mapQ p₂ f hf) :=
- by
- ext
- simp
+ p.mapQ p₃ (g.comp f) h = (p₂.mapQ p₃ g hg).comp (p.mapQ p₂ f hf) := by ext; simp
#align submodule.mapq_comp Submodule.mapQ_comp
/- warning: submodule.mapq_id -> Submodule.mapQ_id is a dubious translation:
<too large>
Case conversion may be inaccurate. Consider using '#align submodule.mapq_id Submodule.mapQ_idₓ'. -/
@[simp]
-theorem mapQ_id
- (h : p ≤ p.comap LinearMap.id :=
- (by
- rw [comap_id]
- exact le_refl _)) :
- p.mapQ p LinearMap.id h = LinearMap.id := by
- ext
- simp
+theorem mapQ_id (h : p ≤ p.comap LinearMap.id := (by rw [comap_id]; exact le_refl _)) :
+ p.mapQ p LinearMap.id h = LinearMap.id := by ext; simp
#align submodule.mapq_id Submodule.mapQ_id
/- warning: submodule.mapq_pow -> Submodule.mapQ_pow is a dubious translation:
@@ -796,14 +776,10 @@ theorem span_preimage_eq [RingHomSurjective τ₁₂] {f : M →ₛₗ[τ₁₂]
suffices (span R₂ s).comap f ≤ span R (f ⁻¹' s) by exact le_antisymm (span_preimage_le f s) this
have hk : ker f ≤ span R (f ⁻¹' s) :=
by
- let y := Classical.choose h₀
- have hy : y ∈ s := Classical.choose_spec h₀
- rw [ker_le_iff]
- use y, h₁ hy
- rw [← Set.singleton_subset_iff] at hy
+ let y := Classical.choose h₀; have hy : y ∈ s := Classical.choose_spec h₀
+ rw [ker_le_iff]; use y, h₁ hy; rw [← Set.singleton_subset_iff] at hy
exact Set.Subset.trans subset_span (span_mono (Set.preimage_mono hy))
- rw [← left_eq_sup] at hk
- rw [f.range_coe] at h₁
+ rw [← left_eq_sup] at hk; rw [f.range_coe] at h₁
rw [hk, ← LinearMap.map_le_map_iff, map_span, map_comap_eq, Set.image_preimage_eq_of_subset h₁]
exact inf_le_right
#align submodule.span_preimage_eq Submodule.span_preimage_eq
@@ -963,16 +939,10 @@ theorem coe_quotEquivOfEqBot_symm (hp : p = ⊥) :
/-- Quotienting by equal submodules gives linearly equivalent quotients. -/
def quotEquivOfEq (h : p = p') : (M ⧸ p) ≃ₗ[R] M ⧸ p' :=
{
- @Quotient.congr _ _ (quotientRel p) (quotientRel p') (Equiv.refl _) fun a b =>
- by
- subst h
+ @Quotient.congr _ _ (quotientRel p) (quotientRel p') (Equiv.refl _) fun a b => by subst h;
rfl with
- map_add' := by
- rintro ⟨x⟩ ⟨y⟩
- rfl
- map_smul' := by
- rintro x ⟨y⟩
- rfl }
+ map_add' := by rintro ⟨x⟩ ⟨y⟩; rfl
+ map_smul' := by rintro x ⟨y⟩; rfl }
#align submodule.quot_equiv_of_eq Submodule.quotEquivOfEq
-/
@@ -1012,12 +982,8 @@ the natural map $\{f ∈ Hom(M, M₂) | f(p) ⊆ q \} \to Hom(M/p, M₂/q)$ is l
def mapQLinear : compatibleMaps p q →ₗ[R] M ⧸ p →ₗ[R] M₂ ⧸ q
where
toFun f := mapQ _ _ f.val f.property
- map_add' x y := by
- ext
- rfl
- map_smul' c f := by
- ext
- rfl
+ map_add' x y := by ext; rfl
+ map_smul' c f := by ext; rfl
#align submodule.mapq_linear Submodule.mapQLinear
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -359,10 +359,7 @@ def restrictScalarsEquiv [Ring S] [SMul S R] [Module S M] [IsScalarTower S R M]
-/
/- warning: submodule.quotient.restrict_scalars_equiv_mk -> Submodule.Quotient.restrictScalarsEquiv_mk is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (S : Type.{u3}) [_inst_4 : Ring.{u3} S] [_inst_5 : SMul.{u3, u1} S R] [_inst_6 : Module.{u3, u2} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_7 : IsScalarTower.{u3, u1, u2} S R M _inst_5 (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (SMulZeroClass.toHasSmul.{u3, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u3, u2} S M (MulZeroClass.toHasZero.{u3} S (MulZeroOneClass.toMulZeroClass.{u3} S (MonoidWithZero.toMulZeroOneClass.{u3} S (Semiring.toMonoidWithZero.{u3} S (Ring.toSemiring.{u3} S _inst_4))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u3, u2} S M (Semiring.toMonoidWithZero.{u3} S (Ring.toSemiring.{u3} S _inst_4)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u3, u2} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_6))))] (P : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (x : M), Eq.{succ u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (coeFn.{succ u2, succ u2} (LinearEquiv.{u3, u3, u2, u2} S S (Ring.toSemiring.{u3} S _inst_4) (Ring.toSemiring.{u3} S _inst_4) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) 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_inst_5 _inst_7 P)) -> (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P)) (LinearEquiv.hasCoeToFun.{u3, u3, u2, u2} S S (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u2} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (Ring.toSemiring.{u3} S _inst_4) (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u2} 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_inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P) x)) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 P x)
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M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (SMulZeroClass.toSMul.{u3, u1} S M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u1} S M (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u1} S M (Semiring.toMonoidWithZero.{u3} S (Ring.toSemiring.{u3} S _inst_4)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6))))] (P : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u1} S M 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(AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u1} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.addCommGroup.{u3, u1} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P))) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 P)) (Submodule.Quotient.module.{u3, u1} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u2, u1} S R 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(RingHomInvPair.ids.{u3} S (Ring.toSemiring.{u3} S _inst_4)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u3, u3, u1, u1} S S (HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u1} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (Ring.toSemiring.{u3} S _inst_4) (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) 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+<too large>
Case conversion may be inaccurate. Consider using '#align submodule.quotient.restrict_scalars_equiv_mk Submodule.Quotient.restrictScalarsEquiv_mkₓ'. -/
@[simp]
theorem restrictScalarsEquiv_mk [Ring S] [SMul S R] [Module S M] [IsScalarTower S R M]
@@ -371,10 +368,7 @@ theorem restrictScalarsEquiv_mk [Ring S] [SMul S R] [Module S M] [IsScalarTower
#align submodule.quotient.restrict_scalars_equiv_mk Submodule.Quotient.restrictScalarsEquiv_mk
/- warning: submodule.quotient.restrict_scalars_equiv_symm_mk -> Submodule.Quotient.restrictScalarsEquiv_symm_mk is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (S : Type.{u3}) [_inst_4 : Ring.{u3} S] [_inst_5 : SMul.{u3, u1} S R] [_inst_6 : Module.{u3, u2} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_7 : IsScalarTower.{u3, u1, u2} S R M _inst_5 (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (SMulZeroClass.toHasSmul.{u3, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u3, u2} S M (MulZeroClass.toHasZero.{u3} S (MulZeroOneClass.toMulZeroClass.{u3} S (MonoidWithZero.toMulZeroOneClass.{u3} S (Semiring.toMonoidWithZero.{u3} S (Ring.toSemiring.{u3} S _inst_4))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u3, u2} S M 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R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.addCommGroup.{u3, u2} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P))) (Submodule.Quotient.module'.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 S (Ring.toSemiring.{u3} S _inst_4) _inst_5 _inst_6 _inst_7 P) (Submodule.Quotient.module.{u3, u2} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P))) => (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) -> (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u2} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P))) (LinearEquiv.hasCoeToFun.{u3, u3, u2, u2} S S (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u2} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M 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u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P))) (Submodule.Quotient.module'.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 S (Ring.toSemiring.{u3} S _inst_4) _inst_5 _inst_6 _inst_7 P) (Submodule.Quotient.module.{u3, u2} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (Submodule.Quotient.restrictScalarsEquiv._proof_2.{u3} S _inst_4) (Submodule.Quotient.restrictScalarsEquiv._proof_1.{u3} S _inst_4)) (LinearEquiv.symm.{u3, u3, u2, u2} S S (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u2} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (Ring.toSemiring.{u3} S _inst_4) (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u2} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.addCommGroup.{u3, u2} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P))) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 P)) (Submodule.Quotient.module.{u3, u2} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.module'.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 S (Ring.toSemiring.{u3} S _inst_4) _inst_5 _inst_6 _inst_7 P) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (Submodule.Quotient.restrictScalarsEquiv._proof_1.{u3} S _inst_4) (Submodule.Quotient.restrictScalarsEquiv._proof_2.{u3} S _inst_4) (Submodule.Quotient.restrictScalarsEquiv.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6 _inst_7 P)) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 P x)) (Submodule.Quotient.mk.{u3, u2} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P) x)
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- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (S : Type.{u3}) [_inst_4 : Ring.{u3} S] [_inst_5 : SMul.{u3, u2} S R] [_inst_6 : Module.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_7 : IsScalarTower.{u3, u2, u1} S R M _inst_5 (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (SMulZeroClass.toSMul.{u3, u1} S M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u1} S M (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u1} S M (Semiring.toMonoidWithZero.{u3} S (Ring.toSemiring.{u3} S _inst_4)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6))))] (P : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) => HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u1} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.mk.{u2, u1} R M _inst_1 _inst_2 _inst_3 P x)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearEquiv.{u3, u3, u1, u1} S S (Ring.toSemiring.{u3} S _inst_4) (Ring.toSemiring.{u3} S _inst_4) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHomInvPair.ids.{u3} S (Ring.toSemiring.{u3} S _inst_4)) (RingHomInvPair.ids.{u3} S (Ring.toSemiring.{u3} S _inst_4)) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u1} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 P)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) 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(Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHomInvPair.ids.{u3} S (Ring.toSemiring.{u3} S _inst_4)) (RingHomInvPair.ids.{u3} S (Ring.toSemiring.{u3} S _inst_4))))))) (LinearEquiv.symm.{u3, u3, u1, u1} S S (HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u1} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (Ring.toSemiring.{u3} S _inst_4) (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u1} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.addCommGroup.{u3, u1} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P))) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 P)) (Submodule.Quotient.module.{u3, u1} S M _inst_4 _inst_2 _inst_6 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+<too large>
Case conversion may be inaccurate. Consider using '#align submodule.quotient.restrict_scalars_equiv_symm_mk Submodule.Quotient.restrictScalarsEquiv_symm_mkₓ'. -/
@[simp]
theorem restrictScalarsEquiv_symm_mk [Ring S] [SMul S R] [Module S M] [IsScalarTower S R M]
@@ -494,10 +488,7 @@ section
variable {M₂ : Type _} [AddCommGroup M₂] [Module R M₂]
/- warning: submodule.quot_hom_ext -> Submodule.quot_hom_ext is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {M₂ : Type.{u3}} [_inst_4 : AddCommGroup.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4)] {{f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5}} {{g : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5}}, (forall (x : M), Eq.{succ u3} M₂ (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 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Case conversion may be inaccurate. Consider using '#align submodule.quot_hom_ext Submodule.quot_hom_extₓ'. -/
theorem quot_hom_ext ⦃f g : M ⧸ p →ₗ[R] M₂⦄ (h : ∀ x, f (Quotient.mk x) = g (Quotient.mk x)) :
f = g :=
@@ -539,10 +530,7 @@ end
variable {R₂ M₂ : Type _} [Ring R₂] [AddCommGroup M₂] [Module R₂ M₂] {τ₁₂ : R →+* R₂}
/- warning: submodule.linear_map_qext -> Submodule.linearMap_qext is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align submodule.linear_map_qext Submodule.linearMap_qextₓ'. -/
/-- Two `linear_map`s from a quotient module are equal if their compositions with
`submodule.mkq` are equal.
@@ -567,10 +555,7 @@ def liftQ (f : M →ₛₗ[τ₁₂] M₂) (h : p ≤ f.ker) : M ⧸ p →ₛₗ
#align submodule.liftq Submodule.liftQ
/- warning: submodule.liftq_apply -> Submodule.liftQ_apply is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align submodule.liftq_apply Submodule.liftQ_applyₓ'. -/
@[simp]
theorem liftQ_apply (f : M →ₛₗ[τ₁₂] M₂) {h} (x : M) : p.liftQ f h (Quotient.mk x) = f x :=
@@ -578,20 +563,14 @@ theorem liftQ_apply (f : M →ₛₗ[τ₁₂] M₂) {h} (x : M) : p.liftQ f h (
#align submodule.liftq_apply Submodule.liftQ_apply
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Case conversion may be inaccurate. Consider using '#align submodule.liftq_mkq Submodule.liftQ_mkQₓ'. -/
@[simp]
theorem liftQ_mkQ (f : M →ₛₗ[τ₁₂] M₂) (h) : (p.liftQ f h).comp p.mkQ = f := by ext <;> rfl
#align submodule.liftq_mkq Submodule.liftQ_mkQ
/- warning: submodule.liftq_span_singleton -> Submodule.liftQSpanSingleton is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align submodule.liftq_span_singleton Submodule.liftQSpanSingletonₓ'. -/
/-- Special case of `liftq` when `p` is the span of `x`. In this case, the condition on `f` simply
becomes vanishing at `x`.-/
@@ -600,10 +579,7 @@ def liftQSpanSingleton (x : M) (f : M →ₛₗ[τ₁₂] M₂) (h : f x = 0) :
#align submodule.liftq_span_singleton Submodule.liftQSpanSingleton
/- warning: submodule.liftq_span_singleton_apply -> Submodule.liftQSpanSingleton_apply is a dubious translation:
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(Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x)))) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) _inst_6 τ₁₂) (Submodule.liftQSpanSingleton.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ x f h) (Submodule.Quotient.mk.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x)) y)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ 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+<too large>
Case conversion may be inaccurate. Consider using '#align submodule.liftq_span_singleton_apply Submodule.liftQSpanSingleton_applyₓ'. -/
@[simp]
theorem liftQSpanSingleton_apply (x : M) (f : M →ₛₗ[τ₁₂] M₂) (h : f x = 0) (y : M) :
@@ -612,10 +588,7 @@ theorem liftQSpanSingleton_apply (x : M) (f : M →ₛₗ[τ₁₂] M₂) (h : f
#align submodule.liftq_span_singleton_apply Submodule.liftQSpanSingleton_apply
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+<too large>
Case conversion may be inaccurate. Consider using '#align submodule.range_mkq Submodule.range_mkQₓ'. -/
@[simp]
theorem range_mkQ : p.mkQ.range = ⊤ :=
@@ -639,10 +612,7 @@ theorem le_comap_mkQ (p' : Submodule R (M ⧸ p)) : p ≤ comap p.mkQ p' := by
#align submodule.le_comap_mkq Submodule.le_comap_mkQ
/- warning: submodule.mkq_map_self -> Submodule.mkQ_map_self is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align submodule.mkq_map_self Submodule.mkQ_map_selfₓ'. -/
@[simp]
theorem mkQ_map_self : map p.mkQ p = ⊥ := by
@@ -650,20 +620,14 @@ theorem mkQ_map_self : map p.mkQ p = ⊥ := by
#align submodule.mkq_map_self Submodule.mkQ_map_self
/- warning: submodule.comap_map_mkq -> Submodule.comap_map_mkQ is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align submodule.comap_map_mkq Submodule.comap_map_mkQₓ'. -/
@[simp]
theorem comap_map_mkQ : comap p.mkQ (map p.mkQ p') = p ⊔ p' := by simp [comap_map_eq, sup_comm]
#align submodule.comap_map_mkq Submodule.comap_map_mkQ
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+<too large>
Case conversion may be inaccurate. Consider using '#align submodule.map_mkq_eq_top Submodule.map_mkQ_eq_topₓ'. -/
@[simp]
theorem map_mkQ_eq_top : map p.mkQ p' = ⊤ ↔ p ⊔ p' = ⊤ := by
@@ -673,10 +637,7 @@ theorem map_mkQ_eq_top : map p.mkQ p' = ⊤ ↔ p ⊔ p' = ⊤ := by
variable (q : Submodule R₂ M₂)
/- warning: submodule.mapq -> Submodule.mapQ is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align submodule.mapq Submodule.mapQₓ'. -/
/-- The map from the quotient of `M` by submodule `p` to the quotient of `M₂` by submodule `q` along
`f : M → M₂` is linear. -/
@@ -685,10 +646,7 @@ def mapQ (f : M →ₛₗ[τ₁₂] M₂) (h : p ≤ comap f q) : M ⧸ p →ₛ
#align submodule.mapq Submodule.mapQ
/- warning: submodule.mapq_apply -> Submodule.mapQ_apply is a dubious translation:
-lean 3 declaration is
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+<too large>
Case conversion may be inaccurate. Consider using '#align submodule.mapq_apply Submodule.mapQ_applyₓ'. -/
@[simp]
theorem mapQ_apply (f : M →ₛₗ[τ₁₂] M₂) {h} (x : M) :
@@ -697,20 +655,14 @@ theorem mapQ_apply (f : M →ₛₗ[τ₁₂] M₂) {h} (x : M) :
#align submodule.mapq_apply Submodule.mapQ_apply
/- warning: submodule.mapq_mkq -> Submodule.mapQ_mkQ is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align submodule.mapq_mkq Submodule.mapQ_mkQₓ'. -/
theorem mapQ_mkQ (f : M →ₛₗ[τ₁₂] M₂) {h} : (mapQ p q f h).comp p.mkQ = q.mkQ.comp f := by
ext x <;> rfl
#align submodule.mapq_mkq Submodule.mapQ_mkQ
/- warning: submodule.mapq_zero -> Submodule.mapQ_zero is a dubious translation:
-lean 3 declaration is
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(Submodule.Quotient.module.{u3, u4} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q) τ₁₂)))
+<too large>
Case conversion may be inaccurate. Consider using '#align submodule.mapq_zero Submodule.mapQ_zeroₓ'. -/
@[simp]
theorem mapQ_zero (h : p ≤ q.comap (0 : M →ₛₗ[τ₁₂] M₂) := (by simp)) :
@@ -720,10 +672,7 @@ theorem mapQ_zero (h : p ≤ q.comap (0 : M →ₛₗ[τ₁₂] M₂) := (by sim
#align submodule.mapq_zero Submodule.mapQ_zero
/- warning: submodule.mapq_comp -> Submodule.mapQ_comp is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} {R₃ : Type.{u5}} {M₃ : Type.{u6}} [_inst_7 : Ring.{u5} R₃] [_inst_8 : AddCommGroup.{u6} M₃] [_inst_9 : Module.{u5, u6} R₃ M₃ (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8)] (p₂ : Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (p₃ : Submodule.{u5, u6} R₃ M₃ (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_9) {τ₂₃ : RingHom.{u3, u5} R₂ R₃ (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4)) (NonAssocRing.toNonAssocSemiring.{u5} R₃ (Ring.toNonAssocRing.{u5} R₃ _inst_7))} {τ₁₃ : RingHom.{u1, u5} R R₃ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u5} R₃ (Ring.toNonAssocRing.{u5} R₃ _inst_7))} [_inst_10 : RingHomCompTriple.{u1, u3, u5} R R₂ R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) τ₁₂ τ₂₃ τ₁₃] (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (g : LinearMap.{u3, u5, u4, u6} R₂ R₃ (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_6 _inst_9) (hf : LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f p₂)) (hg : LE.le.{u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Preorder.toHasLe.{u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (PartialOrder.toPreorder.{u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) 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(AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) (p₃ : Submodule.{u6, u5} R₃ M₃ (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_9) {τ₂₃ : RingHom.{u4, u6} R₂ R₃ (Semiring.toNonAssocSemiring.{u4} R₂ (Ring.toSemiring.{u4} R₂ _inst_4)) (Semiring.toNonAssocSemiring.{u6} R₃ (Ring.toSemiring.{u6} R₃ _inst_7))} {τ₁₃ : RingHom.{u2, u6} R R₃ (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u6} R₃ (Ring.toSemiring.{u6} R₃ _inst_7))} [_inst_10 : RingHomCompTriple.{u2, u4, u6} R R₂ R₃ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) τ₁₂ τ₂₃ τ₁₃] (f : LinearMap.{u2, u4, u1, u3} R R₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6) (g : LinearMap.{u4, u6, u3, u5} R₂ R₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9) (hf : LE.le.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) p (Submodule.comap.{u2, u4, u1, u3, max u1 u3} R R₂ M M₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u2, u4, u1, u3} R R₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u2, u4, u1, u3} R R₂ M M₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f p₂)) (hg : LE.le.{u3} (Submodule.{u4, u3} R₂ M₂ (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) (Preorder.toLE.{u3} (Submodule.{u4, u3} R₂ M₂ (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) (PartialOrder.toPreorder.{u3} (Submodule.{u4, u3} R₂ M₂ (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u4, u3} R₂ M₂ (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u4, u3} R₂ M₂ (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) (Submodule.completeLattice.{u4, u3} R₂ M₂ (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6))))) p₂ (Submodule.comap.{u4, u6, u3, u5, max u3 u5} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9 τ₂₃ (LinearMap.{u4, u6, u3, u5} R₂ R₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9) (LinearMap.semilinearMapClass.{u4, u6, u3, u5} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9 τ₂₃) g p₃)) (h : optParam.{0} (LE.le.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) p (Submodule.comap.{u2, u4, u1, u3, max u1 u3} R R₂ M M₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u2, u4, u1, u3} R R₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u2, u4, u1, u3} R R₂ M M₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f (Submodule.comap.{u4, u6, u3, u5, max u3 u5} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9 τ₂₃ (LinearMap.{u4, u6, u3, u5} R₂ R₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9) (LinearMap.semilinearMapClass.{u4, u6, u3, u5} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9 τ₂₃) g p₃))) (LE.le.trans.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) p (Submodule.comap.{u2, u4, u1, u3, max u1 u3} R R₂ M M₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u2, u4, u1, u3} R R₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u2, u4, u1, u3} R R₂ M M₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f p₂) (Submodule.comap.{u2, u4, u1, u3, max u1 u3} R R₂ M M₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u2, u4, u1, u3} R R₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u2, u4, u1, u3} R R₂ M M₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f (Submodule.comap.{u4, u6, u3, u5, max u3 u5} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9 τ₂₃ (LinearMap.{u4, u6, u3, u5} R₂ R₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9) (LinearMap.semilinearMapClass.{u4, u6, u3, u5} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9 τ₂₃) g p₃)) hf (Submodule.comap_mono.{max u1 u3, u2, u1, u3, u4} R R₂ M M₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u2, u4, u1, u3} R R₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u2, u4, u1, u3} R R₂ M M₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f p₂ (Submodule.comap.{u4, u6, u3, u5, max u3 u5} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9 τ₂₃ (LinearMap.{u4, u6, u3, u5} R₂ R₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9) (LinearMap.semilinearMapClass.{u4, u6, u3, u5} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9 τ₂₃) g p₃) hg))), Eq.{max (succ u1) (succ u5)} (LinearMap.{u2, u6, u1, u5} R R₃ (Ring.toSemiring.{u2} R 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(Submodule.hasQuotient.{u6, u5} R₃ M₃ _inst_7 _inst_8 _inst_9) p₃) (Submodule.Quotient.addCommGroup.{u6, u5} R₃ M₃ _inst_7 _inst_8 _inst_9 p₃)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u6, u5} R₃ M₃ _inst_7 _inst_8 _inst_9 p₃)) (Submodule.mapQ.{u2, u1, u6, u5} R M _inst_1 _inst_2 _inst_3 p R₃ M₃ _inst_7 _inst_8 _inst_9 τ₁₃ p₃ (LinearMap.comp.{u2, u4, u6, u1, u3, u5} R R₂ R₃ M M₂ M₃ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_3 _inst_6 _inst_9 τ₁₂ τ₂₃ τ₁₃ _inst_10 g f) h) (LinearMap.comp.{u2, u4, u6, u1, u3, u5} R R₂ R₃ (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u3, u3} M₂ (Submodule.{u4, u3} R₂ M₂ (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u4, u3} R₂ M₂ _inst_4 _inst_5 _inst_6) p₂) (HasQuotient.Quotient.{u5, u5} M₃ (Submodule.{u6, u5} R₃ M₃ (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_9) (Submodule.hasQuotient.{u6, u5} R₃ M₃ _inst_7 _inst_8 _inst_9) p₃) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u3} (HasQuotient.Quotient.{u3, u3} M₂ (Submodule.{u4, u3} R₂ M₂ (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u4, u3} R₂ M₂ _inst_4 _inst_5 _inst_6) p₂) (Submodule.Quotient.addCommGroup.{u4, u3} R₂ M₂ _inst_4 _inst_5 _inst_6 p₂)) (AddCommGroup.toAddCommMonoid.{u5} (HasQuotient.Quotient.{u5, u5} M₃ (Submodule.{u6, u5} R₃ M₃ (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_9) (Submodule.hasQuotient.{u6, u5} R₃ M₃ _inst_7 _inst_8 _inst_9) p₃) (Submodule.Quotient.addCommGroup.{u6, u5} R₃ M₃ _inst_7 _inst_8 _inst_9 p₃)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u4, u3} R₂ M₂ _inst_4 _inst_5 _inst_6 p₂) (Submodule.Quotient.module.{u6, u5} R₃ M₃ _inst_7 _inst_8 _inst_9 p₃) τ₁₂ τ₂₃ τ₁₃ _inst_10 (Submodule.mapQ.{u4, u3, u6, u5} R₂ M₂ _inst_4 _inst_5 _inst_6 p₂ R₃ M₃ _inst_7 _inst_8 _inst_9 τ₂₃ p₃ g hg) (Submodule.mapQ.{u2, u1, u4, u3} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ p₂ f hf))
+<too large>
Case conversion may be inaccurate. Consider using '#align submodule.mapq_comp Submodule.mapQ_compₓ'. -/
/-- Given submodules `p ⊆ M`, `p₂ ⊆ M₂`, `p₃ ⊆ M₃` and maps `f : M → M₂`, `g : M₂ → M₃` inducing
`mapq f : M ⧸ p → M₂ ⧸ p₂` and `mapq g : M₂ ⧸ p₂ → M₃ ⧸ p₃` then
@@ -739,10 +688,7 @@ theorem mapQ_comp {R₃ M₃ : Type _} [Ring R₃] [AddCommGroup M₃] [Module R
#align submodule.mapq_comp Submodule.mapQ_comp
/- warning: submodule.mapq_id -> Submodule.mapQ_id is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (h : optParam.{0} (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p)) (Eq.mpr.{0} (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p)) (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p p) (id_tag Tactic.IdTag.rw (Eq.{1} Prop (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p)) (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p p)) (Eq.ndrec.{0, succ u2} (Submodule.{u1, u2} R M 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_inst_3) p)) (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p _a)) (rfl.{1} Prop (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p))) p (Submodule.comap_id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 p))) (le_refl.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) p))), Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.mapQ.{u1, u2, u1, u2} R M _inst_1 _inst_2 _inst_3 p R M _inst_1 _inst_2 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) p (LinearMap.id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) h) (LinearMap.id.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p))
-but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (h : optParam.{0} (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (Submodule.comap.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p)) (Eq.mpr.{0} (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (Submodule.comap.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p)) (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p p) (id.{0} (Eq.{1} Prop (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (Submodule.comap.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) 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(Submodule.comap.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p) (fun (_a : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => Eq.{1} Prop (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (Submodule.comap.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p)) (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p _a)) (Eq.refl.{1} Prop 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p))) p (Submodule.comap_id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 p))) (le_refl.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p))), Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.mapQ.{u1, u2, u1, u2} R M _inst_1 _inst_2 _inst_3 p R M _inst_1 _inst_2 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) p (LinearMap.id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) h) (LinearMap.id.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p))
+<too large>
Case conversion may be inaccurate. Consider using '#align submodule.mapq_id Submodule.mapQ_idₓ'. -/
@[simp]
theorem mapQ_id
@@ -756,10 +702,7 @@ theorem mapQ_id
#align submodule.mapq_id Submodule.mapQ_id
/- warning: submodule.mapq_pow -> Submodule.mapQ_pow is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3} (h : LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f p)) (k : Nat) (h' : optParam.{0} (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (HPow.hPow.{u2, 0, u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) Nat (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (instHPow.{u2, 0} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) Nat (Monoid.Pow.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.monoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) f k) p)) (Submodule.le_comap_pow_of_le_comap.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 p f h k)), Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.mapQ.{u1, u2, u1, u2} R M _inst_1 _inst_2 _inst_3 p R M _inst_1 _inst_2 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) p (HPow.hPow.{u2, 0, u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) Nat (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (instHPow.{u2, 0} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) Nat (Monoid.Pow.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.monoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) f k) h') (HPow.hPow.{u2, 0, u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) Nat (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) 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+<too large>
Case conversion may be inaccurate. Consider using '#align submodule.mapq_pow Submodule.mapQ_powₓ'. -/
theorem mapQ_pow {f : M →ₗ[R] M} (h : p ≤ p.comap f) (k : ℕ)
(h' : p ≤ p.comap (f ^ k) := p.le_comap_pow_of_le_comap h k) :
@@ -772,10 +715,7 @@ theorem mapQ_pow {f : M →ₗ[R] M} (h : p ≤ p.comap f) (k : ℕ)
#align submodule.mapq_pow Submodule.mapQ_pow
/- warning: submodule.comap_liftq -> Submodule.comap_liftQ is a dubious translation:
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(AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (h : LE.le.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (LinearMap.ker.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)), Eq.{succ u2} (Submodule.{u4, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) (Submodule.liftQ.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h) q) (Submodule.map.{u4, u4, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (RingHomSurjective.ids.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u2, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f q))
+<too large>
Case conversion may be inaccurate. Consider using '#align submodule.comap_liftq Submodule.comap_liftQₓ'. -/
theorem comap_liftQ (f : M →ₛₗ[τ₁₂] M₂) (h) : q.comap (p.liftQ f h) = (q.comap f).map (mkQ p) :=
le_antisymm (by rintro ⟨x⟩ hx <;> exact ⟨_, hx, rfl⟩)
@@ -783,10 +723,7 @@ theorem comap_liftQ (f : M →ₛₗ[τ₁₂] M₂) (h) : q.comap (p.liftQ f h)
#align submodule.comap_liftq Submodule.comap_liftQ
/- warning: submodule.map_liftq -> Submodule.map_liftQ is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} [_inst_7 : RingHomSurjective.{u1, u3} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂] (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (h : LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)) (q : Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 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_inst_3 (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) (Submodule.mkQ.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) q))
+<too large>
Case conversion may be inaccurate. Consider using '#align submodule.map_liftq Submodule.map_liftQₓ'. -/
theorem map_liftQ [RingHomSurjective τ₁₂] (f : M →ₛₗ[τ₁₂] M₂) (h) (q : Submodule R (M ⧸ p)) :
q.map (p.liftQ f h) = (q.comap p.mkQ).map f :=
@@ -795,40 +732,28 @@ theorem map_liftQ [RingHomSurjective τ₁₂] (f : M →ₛₗ[τ₁₂] M₂)
#align submodule.map_liftq Submodule.map_liftQ
/- warning: submodule.ker_liftq -> Submodule.ker_liftQ is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (h : LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)), Eq.{succ u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) (Submodule.liftQ.{u1, u2, u3, u4} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h)) (Submodule.map.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f))
-but is expected to have type
- forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (h : LE.le.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (LinearMap.ker.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)), Eq.{succ u2} (Submodule.{u4, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.ker.{u4, u3, u2, u1, max u2 u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) 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+<too large>
Case conversion may be inaccurate. Consider using '#align submodule.ker_liftq Submodule.ker_liftQₓ'. -/
theorem ker_liftQ (f : M →ₛₗ[τ₁₂] M₂) (h) : ker (p.liftQ f h) = (ker f).map (mkQ p) :=
comap_liftQ _ _ _ _
#align submodule.ker_liftq Submodule.ker_liftQ
/- warning: submodule.range_liftq -> Submodule.range_liftQ is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align submodule.range_liftq Submodule.range_liftQₓ'. -/
theorem range_liftQ [RingHomSurjective τ₁₂] (f : M →ₛₗ[τ₁₂] M₂) (h) :
range (p.liftQ f h) = range f := by simpa only [range_eq_map] using map_liftq _ _ _ _
#align submodule.range_liftq Submodule.range_liftQ
/- warning: submodule.ker_liftq_eq_bot -> Submodule.ker_liftQ_eq_bot is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align submodule.ker_liftq_eq_bot Submodule.ker_liftQ_eq_botₓ'. -/
theorem ker_liftQ_eq_bot (f : M →ₛₗ[τ₁₂] M₂) (h) (h' : ker f ≤ p) : ker (p.liftQ f h) = ⊥ := by
rw [ker_liftq, le_antisymm h h', mkq_map_self]
#align submodule.ker_liftq_eq_bot Submodule.ker_liftQ_eq_bot
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(OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (fun (p' : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p p'))
+<too large>
Case conversion may be inaccurate. Consider using '#align submodule.comap_mkq.rel_iso Submodule.comapMkQRelIsoₓ'. -/
/-- The correspondence theorem for modules: there is an order isomorphism between submodules of the
quotient of `M` by `p`, and submodules of `M` larger than `p`. -/
@@ -854,10 +779,7 @@ def Submodule.comapMkQOrderEmbedding : Submodule R (M ⧸ p) ↪o Submodule R M
#align submodule.comap_mkq.order_embedding Submodule.comapMkQOrderEmbedding
/- warning: submodule.comap_mkq_embedding_eq -> Submodule.comapMkQOrderEmbedding_eq is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (p' : Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)), Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} 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u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LE.le.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M 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(Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} 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))) M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 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+<too large>
Case conversion may be inaccurate. Consider using '#align submodule.comap_mkq_embedding_eq Submodule.comapMkQOrderEmbedding_eqₓ'. -/
@[simp]
theorem comapMkQOrderEmbedding_eq (p' : Submodule R (M ⧸ p)) :
@@ -866,10 +788,7 @@ theorem comapMkQOrderEmbedding_eq (p' : Submodule R (M ⧸ p)) :
#align submodule.comap_mkq_embedding_eq Submodule.comapMkQOrderEmbedding_eq
/- warning: submodule.span_preimage_eq -> Submodule.span_preimage_eq is a dubious translation:
-lean 3 declaration is
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Case conversion may be inaccurate. Consider using '#align submodule.span_preimage_eq Submodule.span_preimage_eqₓ'. -/
theorem span_preimage_eq [RingHomSurjective τ₁₂] {f : M →ₛₗ[τ₁₂] M₂} {s : Set M₂} (h₀ : s.Nonempty)
(h₁ : s ⊆ range f) : span R (f ⁻¹' s) = (span R₂ s).comap f :=
@@ -890,10 +809,7 @@ theorem span_preimage_eq [RingHomSurjective τ₁₂] {f : M →ₛₗ[τ₁₂]
#align submodule.span_preimage_eq Submodule.span_preimage_eq
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_inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, u3} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_3 _inst_8 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f P) Q) -> (LinearEquiv.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (HasQuotient.Quotient.{u3, u3} N (Submodule.{u1, u3} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8) (Submodule.hasQuotient.{u1, u3} R N _inst_1 _inst_7 _inst_8) Q) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 P)) (AddCommGroup.toAddCommMonoid.{u3} (HasQuotient.Quotient.{u3, u3} N 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+<too large>
Case conversion may be inaccurate. Consider using '#align submodule.quotient.equiv Submodule.Quotient.equivₓ'. -/
/-- If `P` is a submodule of `M` and `Q` a submodule of `N`,
and `f : M ≃ₗ N` maps `P` to `Q`, then `M ⧸ P` is equivalent to `N ⧸ Q`. -/
@@ -917,10 +833,7 @@ def Quotient.equiv {N : Type _} [AddCommGroup N] [Module R N] (P : Submodule R M
#align submodule.quotient.equiv Submodule.Quotient.equiv
/- warning: submodule.quotient.equiv_symm -> Submodule.Quotient.equiv_symm is a dubious translation:
-lean 3 declaration is
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+<too large>
Case conversion may be inaccurate. Consider using '#align submodule.quotient.equiv_symm Submodule.Quotient.equiv_symmₓ'. -/
@[simp]
theorem Quotient.equiv_symm {R M N : Type _} [CommRing R] [AddCommGroup M] [Module R M]
@@ -932,10 +845,7 @@ theorem Quotient.equiv_symm {R M N : Type _} [CommRing R] [AddCommGroup M] [Modu
#align submodule.quotient.equiv_symm Submodule.Quotient.equiv_symm
/- warning: submodule.quotient.equiv_trans -> Submodule.Quotient.equiv_trans is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {N : Type.{u3}} {O : Type.{u4}} [_inst_7 : AddCommGroup.{u3} N] [_inst_8 : Module.{u1, u3} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7)] [_inst_9 : AddCommGroup.{u4} O] [_inst_10 : Module.{u1, u4} R O (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} O _inst_9)] (P : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Q : Submodule.{u1, u3} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8) (S : Submodule.{u1, u4} R O (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} O _inst_9) _inst_10) (e : LinearEquiv.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_3 _inst_8) (f : LinearEquiv.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) N O (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (AddCommGroup.toAddCommMonoid.{u4} O _inst_9) _inst_8 _inst_10) (he : Eq.{succ u3} (Submodule.{u1, u3} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_3 _inst_8 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearEquiv.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_3 _inst_8) (SemilinearEquivClass.semilinearMapClass.{u1, u1, u2, u3, max u2 u3} R R M N (LinearEquiv.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_3 _inst_8) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_3 _inst_8 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearEquiv.semilinearEquivClass.{u1, u1, u2, u3} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_3 _inst_8 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) e P) Q) (hf : Eq.{succ u4} (Submodule.{u1, u4} R O (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} O _inst_9) _inst_10) (Submodule.map.{u1, u1, u3, u4, max u3 u4} R R N O (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (AddCommGroup.toAddCommMonoid.{u4} O _inst_9) _inst_8 _inst_10 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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(Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) N O (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (AddCommGroup.toAddCommMonoid.{u4} O _inst_9) _inst_8 _inst_10) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (AddCommGroup.toAddCommMonoid.{u4} O _inst_9) _inst_8 _inst_10 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearEquiv.semilinearEquivClass.{u1, u1, u3, u4} R R N O (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (AddCommGroup.toAddCommMonoid.{u4} O _inst_9) _inst_8 _inst_10 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R 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(Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M O (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} O _inst_9) _inst_3 _inst_10) (SemilinearEquivClass.semilinearMapClass.{u1, u1, u2, u4, max u2 u4} R R M O (LinearEquiv.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M O (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} O _inst_9) _inst_3 _inst_10) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) 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+<too large>
Case conversion may be inaccurate. Consider using '#align submodule.quotient.equiv_trans Submodule.Quotient.equiv_transₓ'. -/
@[simp]
theorem Quotient.equiv_trans {N O : Type _} [AddCommGroup N] [Module R N] [AddCommGroup O]
@@ -972,20 +882,14 @@ variable {τ₁₂ : R →+* R₂} {τ₂₃ : R₂ →+* R₃} {τ₁₃ : R
variable [RingHomCompTriple τ₁₂ τ₂₃ τ₁₃] [RingHomSurjective τ₁₂]
/- warning: linear_map.range_mkq_comp -> LinearMap.range_mkQ_comp is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u3} R₂] [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_7 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_8 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_2))} [_inst_11 : RingHomSurjective.{u1, u3} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂] (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8), Eq.{max (succ u2) (succ u4)} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ 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+<too large>
Case conversion may be inaccurate. Consider using '#align linear_map.range_mkq_comp LinearMap.range_mkQ_compₓ'. -/
theorem range_mkQ_comp (f : M →ₛₗ[τ₁₂] M₂) : f.range.mkQ.comp f = 0 :=
LinearMap.ext fun x => by simp
#align linear_map.range_mkq_comp LinearMap.range_mkQ_comp
/- warning: linear_map.ker_le_range_iff -> LinearMap.ker_le_range_iff is a dubious translation:
-lean 3 declaration is
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+<too large>
Case conversion may be inaccurate. Consider using '#align linear_map.ker_le_range_iff LinearMap.ker_le_range_iffₓ'. -/
theorem ker_le_range_iff {f : M →ₛₗ[τ₁₂] M₂} {g : M₂ →ₛₗ[τ₂₃] M₃} :
g.ker ≤ f.range ↔ f.range.mkQ.comp g.ker.Subtype = 0 := by
@@ -993,10 +897,7 @@ theorem ker_le_range_iff {f : M →ₛₗ[τ₁₂] M₂} {g : M₂ →ₛₗ[τ
#align linear_map.ker_le_range_iff LinearMap.ker_le_range_iff
/- warning: linear_map.range_eq_top_of_cancel -> LinearMap.range_eq_top_of_cancel is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u3} R₂] [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_7 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_8 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_2))} [_inst_11 : RingHomSurjective.{u1, u3} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂] {f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8}, (forall (u : LinearMap.{u3, u3, u4, u4} R₂ R₂ (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u3} R₂ _inst_2) (RingHom.id.{u3} 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+<too large>
Case conversion may be inaccurate. Consider using '#align linear_map.range_eq_top_of_cancel LinearMap.range_eq_top_of_cancelₓ'. -/
/-- An epimorphism is surjective. -/
theorem range_eq_top_of_cancel {f : M →ₛₗ[τ₁₂] M₂}
@@ -1032,10 +933,7 @@ def quotEquivOfEqBot (hp : p = ⊥) : (M ⧸ p) ≃ₗ[R] M :=
#align submodule.quot_equiv_of_eq_bot Submodule.quotEquivOfEqBot
/- warning: submodule.quot_equiv_of_eq_bot_apply_mk -> Submodule.quotEquivOfEqBot_apply_mk is a dubious translation:
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_inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (Submodule.quotEquivOfEqBot.{u1, u2} R M _inst_1 _inst_2 _inst_3 p hp) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x)) x
+<too large>
Case conversion may be inaccurate. Consider using '#align submodule.quot_equiv_of_eq_bot_apply_mk Submodule.quotEquivOfEqBot_apply_mkₓ'. -/
@[simp]
theorem quotEquivOfEqBot_apply_mk (hp : p = ⊥) (x : M) :
@@ -1044,10 +942,7 @@ theorem quotEquivOfEqBot_apply_mk (hp : p = ⊥) (x : M) :
#align submodule.quot_equiv_of_eq_bot_apply_mk Submodule.quotEquivOfEqBot_apply_mk
/- warning: submodule.quot_equiv_of_eq_bot_symm_apply -> Submodule.quotEquivOfEqBot_symm_apply is a dubious translation:
-lean 3 declaration is
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(Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.quotEquivOfEqBot.{u1, u2} R M _inst_1 _inst_2 _inst_3 p hp)) x) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x)
+<too large>
Case conversion may be inaccurate. Consider using '#align submodule.quot_equiv_of_eq_bot_symm_apply Submodule.quotEquivOfEqBot_symm_applyₓ'. -/
@[simp]
theorem quotEquivOfEqBot_symm_apply (hp : p = ⊥) (x : M) :
@@ -1056,10 +951,7 @@ theorem quotEquivOfEqBot_symm_apply (hp : p = ⊥) (x : M) :
#align submodule.quot_equiv_of_eq_bot_symm_apply Submodule.quotEquivOfEqBot_symm_apply
/- warning: submodule.coe_quot_equiv_of_eq_bot_symm -> Submodule.coe_quotEquivOfEqBot_symm is a dubious translation:
-lean 3 declaration is
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+<too large>
Case conversion may be inaccurate. Consider using '#align submodule.coe_quot_equiv_of_eq_bot_symm Submodule.coe_quotEquivOfEqBot_symmₓ'. -/
@[simp]
theorem coe_quotEquivOfEqBot_symm (hp : p = ⊥) :
@@ -1085,10 +977,7 @@ def quotEquivOfEq (h : p = p') : (M ⧸ p) ≃ₗ[R] M ⧸ p' :=
-/
/- warning: submodule.quot_equiv_of_eq_mk -> Submodule.quotEquivOfEq_mk is a dubious translation:
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_inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p')) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p')) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (fun (_x : HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) => HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') _x) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p')) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p')) R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (SMulZeroClass.toSMul.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddMonoid.toZero.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommMonoid.toAddMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)))) (DistribSMul.toSMulZeroClass.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddMonoid.toAddZeroClass.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommMonoid.toAddMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)))) (DistribMulAction.toDistribSMul.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p))) (Module.toDistribMulAction.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p))))) (SMulZeroClass.toSMul.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (AddMonoid.toZero.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (AddCommMonoid.toAddMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p')))) (DistribSMul.toSMulZeroClass.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (AddMonoid.toAddZeroClass.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (AddCommMonoid.toAddMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p')))) (DistribMulAction.toDistribSMul.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p'))) (Module.toDistribMulAction.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p')) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p'))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p')) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p')) R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p))) (AddCommMonoid.toAddMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M 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+<too large>
Case conversion may be inaccurate. Consider using '#align submodule.quot_equiv_of_eq_mk Submodule.quotEquivOfEq_mkₓ'. -/
@[simp]
theorem quotEquivOfEq_mk (h : p = p') (x : M) :
@@ -1097,10 +986,7 @@ theorem quotEquivOfEq_mk (h : p = p') (x : M) :
#align submodule.quot_equiv_of_eq_mk Submodule.quotEquivOfEq_mk
/- warning: submodule.quotient.equiv_refl -> Submodule.Quotient.equiv_refl is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (P : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Q : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (hf : Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.map.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 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P)) Q Q (rfl.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Q)) hf)))
-but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (P : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Q : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (hf : Eq.{succ u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.map.{u2, u2, u1, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (LinearEquiv.refl.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) P) Q), Eq.{succ u1} (LinearEquiv.{u2, u2, u1, u1} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) Q) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 P)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) Q) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 Q)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 P) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 Q)) (Submodule.Quotient.equiv.{u2, u1, u1} R M _inst_1 _inst_2 _inst_3 M _inst_2 _inst_3 P Q (LinearEquiv.refl.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) hf) (Submodule.quotEquivOfEq.{u2, u1} R M _inst_1 _inst_2 _inst_3 P Q (Eq.mp.{0} (Eq.{succ u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.map.{u2, u2, u1, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R M M 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+<too large>
Case conversion may be inaccurate. Consider using '#align submodule.quotient.equiv_refl Submodule.Quotient.equiv_reflₓ'. -/
@[simp]
theorem Quotient.equiv_refl (P : Submodule R M) (Q : Submodule R M)
mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b
@@ -362,7 +362,7 @@ def restrictScalarsEquiv [Ring S] [SMul S R] [Module S M] [IsScalarTower S R M]
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (S : Type.{u3}) [_inst_4 : Ring.{u3} S] [_inst_5 : SMul.{u3, u1} S R] [_inst_6 : Module.{u3, u2} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_7 : IsScalarTower.{u3, u1, u2} S R M _inst_5 (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (SMulZeroClass.toHasSmul.{u3, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u3, u2} S M (MulZeroClass.toHasZero.{u3} S (MulZeroOneClass.toMulZeroClass.{u3} S (MonoidWithZero.toMulZeroOneClass.{u3} S (Semiring.toMonoidWithZero.{u3} S (Ring.toSemiring.{u3} S _inst_4))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u3, u2} S M (Semiring.toMonoidWithZero.{u3} S (Ring.toSemiring.{u3} S _inst_4)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u3, u2} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_6))))] (P : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (x : M), Eq.{succ u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (coeFn.{succ u2, succ u2} (LinearEquiv.{u3, u3, u2, u2} S S (Ring.toSemiring.{u3} S _inst_4) (Ring.toSemiring.{u3} S _inst_4) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (Submodule.Quotient.restrictScalarsEquiv._proof_1.{u3} S _inst_4) (Submodule.Quotient.restrictScalarsEquiv._proof_2.{u3} S _inst_4) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u2} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u2} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.addCommGroup.{u3, u2} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P))) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 P)) (Submodule.Quotient.module.{u3, u2} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.module'.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 S (Ring.toSemiring.{u3} S _inst_4) _inst_5 _inst_6 _inst_7 P)) (fun (_x : LinearEquiv.{u3, u3, u2, u2} S S (Ring.toSemiring.{u3} S _inst_4) (Ring.toSemiring.{u3} S _inst_4) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (Submodule.Quotient.restrictScalarsEquiv._proof_1.{u3} S _inst_4) (Submodule.Quotient.restrictScalarsEquiv._proof_2.{u3} S _inst_4) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u2} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u2} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.addCommGroup.{u3, u2} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P))) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 P)) (Submodule.Quotient.module.{u3, u2} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.module'.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 S (Ring.toSemiring.{u3} S _inst_4) _inst_5 _inst_6 _inst_7 P)) => (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u2} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) -> (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P)) (LinearEquiv.hasCoeToFun.{u3, u3, u2, u2} S S (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u2} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (Ring.toSemiring.{u3} S _inst_4) (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u2} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.addCommGroup.{u3, u2} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P))) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 P)) (Submodule.Quotient.module.{u3, u2} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.module'.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 S (Ring.toSemiring.{u3} S _inst_4) _inst_5 _inst_6 _inst_7 P) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (Submodule.Quotient.restrictScalarsEquiv._proof_1.{u3} S _inst_4) (Submodule.Quotient.restrictScalarsEquiv._proof_2.{u3} S _inst_4)) (Submodule.Quotient.restrictScalarsEquiv.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6 _inst_7 P) (Submodule.Quotient.mk.{u3, u2} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P) x)) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 P x)
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (S : Type.{u3}) [_inst_4 : Ring.{u3} S] [_inst_5 : SMul.{u3, u2} S R] [_inst_6 : Module.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_7 : IsScalarTower.{u3, u2, u1} S R M _inst_5 (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (SMulZeroClass.toSMul.{u3, u1} S M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u1} S M (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u1} S M (Semiring.toMonoidWithZero.{u3} S (Ring.toSemiring.{u3} S _inst_4)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6))))] (P : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u1} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) => HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.mk.{u2, u1} R M _inst_1 _inst_2 _inst_3 P x)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearEquiv.{u3, u3, u1, u1} S S (Ring.toSemiring.{u3} S _inst_4) (Ring.toSemiring.{u3} S _inst_4) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHomInvPair.ids.{u3} S (Ring.toSemiring.{u3} S _inst_4)) (RingHomInvPair.ids.{u3} S (Ring.toSemiring.{u3} S _inst_4)) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M 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(AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 P)) (Submodule.Quotient.module.{u3, u1} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.module'.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 S (Ring.toSemiring.{u3} S _inst_4) _inst_5 _inst_6 _inst_7 P)) (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u1} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.addCommGroup.{u3, u1} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P))) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 P)) (Submodule.Quotient.module.{u3, u1} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.module'.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 S (Ring.toSemiring.{u3} S _inst_4) _inst_5 _inst_6 _inst_7 P) (SemilinearEquivClass.instSemilinearMapClass.{u3, u3, u1, u1, u1} S S (HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u1} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (LinearEquiv.{u3, u3, u1, u1} S S (Ring.toSemiring.{u3} S _inst_4) (Ring.toSemiring.{u3} S _inst_4) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHomInvPair.ids.{u3} S (Ring.toSemiring.{u3} S _inst_4)) (RingHomInvPair.ids.{u3} S (Ring.toSemiring.{u3} S _inst_4)) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u1} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u1} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.addCommGroup.{u3, u1} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P))) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 P)) (Submodule.Quotient.module.{u3, u1} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.module'.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 S (Ring.toSemiring.{u3} S _inst_4) _inst_5 _inst_6 _inst_7 P)) (Ring.toSemiring.{u3} S _inst_4) (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u1} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.addCommGroup.{u3, u1} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P))) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 P)) (Submodule.Quotient.module.{u3, u1} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.module'.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 S (Ring.toSemiring.{u3} S _inst_4) _inst_5 _inst_6 _inst_7 P) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHomInvPair.ids.{u3} S (Ring.toSemiring.{u3} S _inst_4)) (RingHomInvPair.ids.{u3} S (Ring.toSemiring.{u3} S _inst_4)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u3, u3, u1, u1} S S (HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u1} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (Ring.toSemiring.{u3} S _inst_4) (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u1} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.addCommGroup.{u3, u1} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P))) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 P)) (Submodule.Quotient.module.{u3, u1} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.module'.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 S (Ring.toSemiring.{u3} S _inst_4) _inst_5 _inst_6 _inst_7 P) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHomInvPair.ids.{u3} S (Ring.toSemiring.{u3} S _inst_4)) (RingHomInvPair.ids.{u3} S (Ring.toSemiring.{u3} S _inst_4))))))) (Submodule.Quotient.restrictScalarsEquiv.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6 _inst_7 P) (Submodule.Quotient.mk.{u2, u1} R M _inst_1 _inst_2 _inst_3 P x)) (Submodule.Quotient.mk.{u2, u1} R M _inst_1 _inst_2 _inst_3 P x)
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (S : Type.{u3}) [_inst_4 : Ring.{u3} S] [_inst_5 : SMul.{u3, u2} S R] [_inst_6 : Module.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_7 : IsScalarTower.{u3, u2, u1} S R M _inst_5 (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (SMulZeroClass.toSMul.{u3, u1} S M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u1} S M (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u1} S M (Semiring.toMonoidWithZero.{u3} S (Ring.toSemiring.{u3} S _inst_4)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6))))] (P : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u1} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) => HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.mk.{u2, u1} R M _inst_1 _inst_2 _inst_3 P x)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearEquiv.{u3, u3, u1, u1} S S (Ring.toSemiring.{u3} S _inst_4) (Ring.toSemiring.{u3} S _inst_4) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHomInvPair.ids.{u3} S (Ring.toSemiring.{u3} S _inst_4)) (RingHomInvPair.ids.{u3} S (Ring.toSemiring.{u3} S _inst_4)) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u1} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u1} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) 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_inst_2 _inst_3) P) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (AddCommMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 P)))) (DistribMulAction.toDistribSMul.{u3, u1} S (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) 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_inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.module'.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 S (Ring.toSemiring.{u3} S _inst_4) _inst_5 _inst_6 _inst_7 P) (SemilinearEquivClass.instSemilinearMapClass.{u3, u3, u1, u1, u1} S S (HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u1} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (LinearEquiv.{u3, u3, u1, u1} S S (Ring.toSemiring.{u3} S _inst_4) (Ring.toSemiring.{u3} S _inst_4) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S 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(AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u1} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.addCommGroup.{u3, u1} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P))) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 P)) (Submodule.Quotient.module.{u3, u1} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.module'.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 S (Ring.toSemiring.{u3} S _inst_4) _inst_5 _inst_6 _inst_7 P)) (Ring.toSemiring.{u3} S _inst_4) (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u1} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.addCommGroup.{u3, u1} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P))) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 P)) (Submodule.Quotient.module.{u3, u1} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.module'.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 S (Ring.toSemiring.{u3} S _inst_4) _inst_5 _inst_6 _inst_7 P) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHomInvPair.ids.{u3} S (Ring.toSemiring.{u3} S _inst_4)) (RingHomInvPair.ids.{u3} S (Ring.toSemiring.{u3} S _inst_4)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u3, u3, u1, u1} S S (HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u1} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (Ring.toSemiring.{u3} S _inst_4) (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u1} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.addCommGroup.{u3, u1} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P))) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 P)) (Submodule.Quotient.module.{u3, u1} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.module'.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 S (Ring.toSemiring.{u3} S _inst_4) _inst_5 _inst_6 _inst_7 P) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHomInvPair.ids.{u3} S (Ring.toSemiring.{u3} S _inst_4)) (RingHomInvPair.ids.{u3} S (Ring.toSemiring.{u3} S _inst_4))))))) (Submodule.Quotient.restrictScalarsEquiv.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6 _inst_7 P) (Submodule.Quotient.mk.{u2, u1} R M _inst_1 _inst_2 _inst_3 P x)) (Submodule.Quotient.mk.{u2, u1} R M _inst_1 _inst_2 _inst_3 P x)
Case conversion may be inaccurate. Consider using '#align submodule.quotient.restrict_scalars_equiv_mk Submodule.Quotient.restrictScalarsEquiv_mkₓ'. -/
@[simp]
theorem restrictScalarsEquiv_mk [Ring S] [SMul S R] [Module S M] [IsScalarTower S R M]
@@ -374,7 +374,7 @@ theorem restrictScalarsEquiv_mk [Ring S] [SMul S R] [Module S M] [IsScalarTower
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (S : Type.{u3}) [_inst_4 : Ring.{u3} S] [_inst_5 : SMul.{u3, u1} S R] [_inst_6 : Module.{u3, u2} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_7 : IsScalarTower.{u3, u1, u2} S R M _inst_5 (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (SMulZeroClass.toHasSmul.{u3, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u3, u2} S M (MulZeroClass.toHasZero.{u3} S (MulZeroOneClass.toMulZeroClass.{u3} S (MonoidWithZero.toMulZeroOneClass.{u3} S (Semiring.toMonoidWithZero.{u3} S (Ring.toSemiring.{u3} S _inst_4))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u3, u2} S M (Semiring.toMonoidWithZero.{u3} S (Ring.toSemiring.{u3} S _inst_4)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u3, u2} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_6))))] (P : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (x : M), Eq.{succ u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u2} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (coeFn.{succ u2, succ u2} (LinearEquiv.{u3, u3, u2, u2} S S (Ring.toSemiring.{u3} S _inst_4) (Ring.toSemiring.{u3} S _inst_4) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (Submodule.Quotient.restrictScalarsEquiv._proof_2.{u3} S _inst_4) (Submodule.Quotient.restrictScalarsEquiv._proof_1.{u3} S _inst_4) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u2} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 P)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u2} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.addCommGroup.{u3, u2} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P))) (Submodule.Quotient.module'.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 S (Ring.toSemiring.{u3} S _inst_4) _inst_5 _inst_6 _inst_7 P) (Submodule.Quotient.module.{u3, u2} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P))) (fun (_x : LinearEquiv.{u3, u3, u2, u2} S S (Ring.toSemiring.{u3} S _inst_4) (Ring.toSemiring.{u3} S _inst_4) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (Submodule.Quotient.restrictScalarsEquiv._proof_2.{u3} S _inst_4) (Submodule.Quotient.restrictScalarsEquiv._proof_1.{u3} S _inst_4) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u2} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 P)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u2} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.addCommGroup.{u3, u2} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P))) (Submodule.Quotient.module'.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 S (Ring.toSemiring.{u3} S _inst_4) _inst_5 _inst_6 _inst_7 P) (Submodule.Quotient.module.{u3, u2} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P))) => (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) -> (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u2} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P))) (LinearEquiv.hasCoeToFun.{u3, u3, u2, u2} S S (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u2} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Ring.toSemiring.{u3} S _inst_4) (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 P)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u2} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.addCommGroup.{u3, u2} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P))) (Submodule.Quotient.module'.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 S (Ring.toSemiring.{u3} S _inst_4) _inst_5 _inst_6 _inst_7 P) (Submodule.Quotient.module.{u3, u2} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (Submodule.Quotient.restrictScalarsEquiv._proof_2.{u3} S _inst_4) (Submodule.Quotient.restrictScalarsEquiv._proof_1.{u3} S _inst_4)) (LinearEquiv.symm.{u3, u3, u2, u2} S S (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u2} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (Ring.toSemiring.{u3} S _inst_4) (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u2} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.addCommGroup.{u3, u2} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P))) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 P)) (Submodule.Quotient.module.{u3, u2} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.module'.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 S (Ring.toSemiring.{u3} S _inst_4) _inst_5 _inst_6 _inst_7 P) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (Submodule.Quotient.restrictScalarsEquiv._proof_1.{u3} S _inst_4) (Submodule.Quotient.restrictScalarsEquiv._proof_2.{u3} S _inst_4) (Submodule.Quotient.restrictScalarsEquiv.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6 _inst_7 P)) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 P x)) (Submodule.Quotient.mk.{u3, u2} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u1, u2} S R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P) x)
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (S : Type.{u3}) [_inst_4 : Ring.{u3} S] [_inst_5 : SMul.{u3, u2} S R] [_inst_6 : Module.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_7 : IsScalarTower.{u3, u2, u1} S R M _inst_5 (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (SMulZeroClass.toSMul.{u3, u1} S M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u1} S M (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u1} S M (Semiring.toMonoidWithZero.{u3} S (Ring.toSemiring.{u3} S _inst_4)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6))))] (P : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) => HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u1} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.mk.{u2, u1} R M _inst_1 _inst_2 _inst_3 P x)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearEquiv.{u3, u3, u1, u1} S S (Ring.toSemiring.{u3} S _inst_4) (Ring.toSemiring.{u3} S _inst_4) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHomInvPair.ids.{u3} S (Ring.toSemiring.{u3} S _inst_4)) (RingHomInvPair.ids.{u3} S (Ring.toSemiring.{u3} S _inst_4)) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u1} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 P)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u1} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.addCommGroup.{u3, u1} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P))) (Submodule.Quotient.module'.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 S (Ring.toSemiring.{u3} S _inst_4) _inst_5 _inst_6 _inst_7 P) (Submodule.Quotient.module.{u3, u1} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P))) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (fun (_x : HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) => HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u1} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) _x) (SMulHomClass.toFunLike.{u1, u3, u1, u1} (LinearEquiv.{u3, u3, u1, u1} S S (Ring.toSemiring.{u3} S _inst_4) (Ring.toSemiring.{u3} S _inst_4) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHomInvPair.ids.{u3} S (Ring.toSemiring.{u3} S _inst_4)) (RingHomInvPair.ids.{u3} S (Ring.toSemiring.{u3} S _inst_4)) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u1} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R 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(AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 P)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u1} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.addCommGroup.{u3, u1} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P))) (Submodule.Quotient.module'.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 S (Ring.toSemiring.{u3} S _inst_4) _inst_5 _inst_6 _inst_7 P) (Submodule.Quotient.module.{u3, u1} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHomInvPair.ids.{u3} S (Ring.toSemiring.{u3} S _inst_4)) (RingHomInvPair.ids.{u3} S (Ring.toSemiring.{u3} S _inst_4)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u3, u3, u1, u1} S S (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u1} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Ring.toSemiring.{u3} S _inst_4) (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 P)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u1} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.addCommGroup.{u3, u1} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P))) (Submodule.Quotient.module'.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 S (Ring.toSemiring.{u3} S _inst_4) _inst_5 _inst_6 _inst_7 P) (Submodule.Quotient.module.{u3, u1} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHomInvPair.ids.{u3} S (Ring.toSemiring.{u3} S _inst_4)) (RingHomInvPair.ids.{u3} S (Ring.toSemiring.{u3} S _inst_4))))))) (LinearEquiv.symm.{u3, u3, u1, u1} S S (HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u1} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (Ring.toSemiring.{u3} S _inst_4) (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u1} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.addCommGroup.{u3, u1} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P))) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 P)) (Submodule.Quotient.module.{u3, u1} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.module'.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 S (Ring.toSemiring.{u3} S _inst_4) _inst_5 _inst_6 _inst_7 P) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHomInvPair.ids.{u3} S (Ring.toSemiring.{u3} S _inst_4)) (RingHomInvPair.ids.{u3} S (Ring.toSemiring.{u3} S _inst_4)) (Submodule.Quotient.restrictScalarsEquiv.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6 _inst_7 P)) (Submodule.Quotient.mk.{u2, u1} R M _inst_1 _inst_2 _inst_3 P x)) (Submodule.Quotient.mk.{u2, u1} R M _inst_1 _inst_2 _inst_3 P x)
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (S : Type.{u3}) [_inst_4 : Ring.{u3} S] [_inst_5 : SMul.{u3, u2} S R] [_inst_6 : Module.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_7 : IsScalarTower.{u3, u2, u1} S R M _inst_5 (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (SMulZeroClass.toSMul.{u3, u1} S M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u1} S M (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u1} S M (Semiring.toMonoidWithZero.{u3} S (Ring.toSemiring.{u3} S _inst_4)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6))))] (P : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) => HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u1} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.mk.{u2, u1} R M _inst_1 _inst_2 _inst_3 P x)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearEquiv.{u3, u3, u1, u1} S S (Ring.toSemiring.{u3} S _inst_4) (Ring.toSemiring.{u3} S _inst_4) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHomInvPair.ids.{u3} S (Ring.toSemiring.{u3} S _inst_4)) (RingHomInvPair.ids.{u3} S (Ring.toSemiring.{u3} S _inst_4)) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u1} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 P)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u1} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.addCommGroup.{u3, u1} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P))) (Submodule.Quotient.module'.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 S (Ring.toSemiring.{u3} S _inst_4) _inst_5 _inst_6 _inst_7 P) (Submodule.Quotient.module.{u3, u1} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P))) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (fun (_x : HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) => HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u1} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) 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_inst_5 _inst_7 P))) (Submodule.Quotient.module'.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 S (Ring.toSemiring.{u3} S _inst_4) _inst_5 _inst_6 _inst_7 P) (Submodule.Quotient.module.{u3, u1} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHomInvPair.ids.{u3} S (Ring.toSemiring.{u3} S _inst_4)) (RingHomInvPair.ids.{u3} S (Ring.toSemiring.{u3} S _inst_4)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u3, u3, u1, u1} S S (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u1} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Ring.toSemiring.{u3} S _inst_4) (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 P)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u1} S M 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(Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHomInvPair.ids.{u3} S (Ring.toSemiring.{u3} S _inst_4)) (RingHomInvPair.ids.{u3} S (Ring.toSemiring.{u3} S _inst_4))))))) (LinearEquiv.symm.{u3, u3, u1, u1} S S (HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u1} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (Ring.toSemiring.{u3} S _inst_4) (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u3, u1} S M (Ring.toSemiring.{u3} S _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_6) (Submodule.hasQuotient.{u3, u1} S M _inst_4 _inst_2 _inst_6) (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.addCommGroup.{u3, u1} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P))) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 P)) (Submodule.Quotient.module.{u3, u1} S M _inst_4 _inst_2 _inst_6 (Submodule.restrictScalars.{u3, u2, u1} S R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toSemiring.{u3} S _inst_4) _inst_6 _inst_3 _inst_5 _inst_7 P)) (Submodule.Quotient.module'.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 S (Ring.toSemiring.{u3} S _inst_4) _inst_5 _inst_6 _inst_7 P) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_4))) (RingHomInvPair.ids.{u3} S (Ring.toSemiring.{u3} S _inst_4)) (RingHomInvPair.ids.{u3} S (Ring.toSemiring.{u3} S _inst_4)) (Submodule.Quotient.restrictScalarsEquiv.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6 _inst_7 P)) (Submodule.Quotient.mk.{u2, u1} R M _inst_1 _inst_2 _inst_3 P x)) (Submodule.Quotient.mk.{u2, u1} R M _inst_1 _inst_2 _inst_3 P x)
Case conversion may be inaccurate. Consider using '#align submodule.quotient.restrict_scalars_equiv_symm_mk Submodule.Quotient.restrictScalarsEquiv_symm_mkₓ'. -/
@[simp]
theorem restrictScalarsEquiv_symm_mk [Ring S] [SMul S R] [Module S M] [IsScalarTower S R M]
@@ -497,7 +497,7 @@ variable {M₂ : Type _} [AddCommGroup M₂] [Module R M₂]
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {M₂ : Type.{u3}} [_inst_4 : AddCommGroup.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4)] {{f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5}} {{g : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5}}, (forall (x : M), Eq.{succ u3} M₂ (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 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(HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) -> M₂) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5) => (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) -> M₂) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) g (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x))) -> (Eq.{max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5) f g)
but is expected to have type
- forall {R : Type.{u3}} {M : Type.{u2}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {M₂ : Type.{u1}} [_inst_4 : AddCommGroup.{u1} M₂] [_inst_5 : Module.{u3, u1} R M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4)] (f : LinearMap.{u3, u3, u2, u1} 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))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4) (Submodule.Quotient.module.{u3, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5) (g : LinearMap.{u3, u3, u2, u1} 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))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4) (Submodule.Quotient.module.{u3, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5), (forall (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) => M₂) (Submodule.Quotient.mk.{u3, u2} R M _inst_1 _inst_2 _inst_3 p x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} 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))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4) (Submodule.Quotient.module.{u3, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (fun (_x : HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4) (Submodule.Quotient.module.{u3, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) f (Submodule.Quotient.mk.{u3, u2} R M _inst_1 _inst_2 _inst_3 p x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} 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))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4) (Submodule.Quotient.module.{u3, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (fun (_x : HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4) (Submodule.Quotient.module.{u3, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) g (Submodule.Quotient.mk.{u3, u2} R M _inst_1 _inst_2 _inst_3 p x))) -> (Eq.{max (succ u2) (succ u1)} (LinearMap.{u3, u3, u2, u1} 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))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4) (Submodule.Quotient.module.{u3, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5) f g)
+ forall {R : Type.{u3}} {M : Type.{u2}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {M₂ : Type.{u1}} [_inst_4 : AddCommGroup.{u1} M₂] [_inst_5 : Module.{u3, u1} R M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4)] (f : LinearMap.{u3, u3, u2, u1} 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))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4) (Submodule.Quotient.module.{u3, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5) (g : LinearMap.{u3, u3, u2, u1} 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))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4) (Submodule.Quotient.module.{u3, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5), (forall (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) => M₂) (Submodule.Quotient.mk.{u3, u2} R M _inst_1 _inst_2 _inst_3 p x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} 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))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4) (Submodule.Quotient.module.{u3, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (fun (_x : HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4) (Submodule.Quotient.module.{u3, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) f (Submodule.Quotient.mk.{u3, u2} R M _inst_1 _inst_2 _inst_3 p x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} 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))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4) (Submodule.Quotient.module.{u3, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (fun (_x : HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4) (Submodule.Quotient.module.{u3, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) g (Submodule.Quotient.mk.{u3, u2} R M _inst_1 _inst_2 _inst_3 p x))) -> (Eq.{max (succ u2) (succ u1)} (LinearMap.{u3, u3, u2, u1} 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))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4) (Submodule.Quotient.module.{u3, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5) f g)
Case conversion may be inaccurate. Consider using '#align submodule.quot_hom_ext Submodule.quot_hom_extₓ'. -/
theorem quot_hom_ext ⦃f g : M ⧸ p →ₗ[R] M₂⦄ (h : ∀ x, f (Quotient.mk x) = g (Quotient.mk x)) :
f = g :=
@@ -517,7 +517,7 @@ def mkQ : M →ₗ[R] M ⧸ p where
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (x : M), Eq.{succ u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) => M -> (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p)) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) x) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x)
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (x : M), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) x) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) x) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x)
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (x : M), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) x) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) x) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x)
Case conversion may be inaccurate. Consider using '#align submodule.mkq_apply Submodule.mkQ_applyₓ'. -/
@[simp]
theorem mkQ_apply (x : M) : p.mkQ x = Quotient.mk x :=
@@ -528,7 +528,7 @@ theorem mkQ_apply (x : M) : p.mkQ x = Quotient.mk x :=
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (A : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), Function.Surjective.{succ u2, succ u2} M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) A) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) A) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) A) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 A)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 A)) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) A) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) A) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 A)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 A)) => M -> (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) A)) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) A) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) A) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 A)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 A) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 A))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (A : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3), Function.Surjective.{succ u1, succ u1} M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) A) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} 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))) M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) A) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) A) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 A)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 A)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) A) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) A) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) A) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 A)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 A) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.mkQ.{u2, u1} R M _inst_1 _inst_2 _inst_3 A))
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (A : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3), Function.Surjective.{succ u1, succ u1} M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) A) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} 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))) M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) A) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) A) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 A)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 A)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) A) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) A) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) A) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 A)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 A) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.mkQ.{u2, u1} R M _inst_1 _inst_2 _inst_3 A))
Case conversion may be inaccurate. Consider using '#align submodule.mkq_surjective Submodule.mkQ_surjectiveₓ'. -/
theorem mkQ_surjective (A : Submodule R M) : Function.Surjective A.mkQ := by
rintro ⟨x⟩ <;> exact ⟨x, rfl⟩
@@ -570,7 +570,7 @@ def liftQ (f : M →ₛₗ[τ₁₂] M₂) (h : p ≤ f.ker) : M ⧸ p →ₛₗ
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) {h : LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)} (x : M), Eq.{succ u4} M₂ (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) (fun (_x : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) => (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) -> M₂) (LinearMap.hasCoeToFun.{u1, u3, u2, u4} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) (Submodule.liftQ.{u1, u2, u3, u4} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x)) (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f x)
but is expected to have type
- forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) {h : LE.le.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (LinearMap.ker.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)} (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) => M₂) (Submodule.Quotient.mk.{u4, u2} R M _inst_1 _inst_2 _inst_3 p x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) 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M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) (Submodule.liftQ.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h) (Submodule.Quotient.mk.{u4, u2} R M _inst_1 _inst_2 _inst_3 p x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f x)
+ forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) {h : LE.le.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (LinearMap.ker.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)} (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) => M₂) (Submodule.Quotient.mk.{u4, u2} R M _inst_1 _inst_2 _inst_3 p x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (fun (_x : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) (Submodule.liftQ.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h) (Submodule.Quotient.mk.{u4, u2} R M _inst_1 _inst_2 _inst_3 p x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f x)
Case conversion may be inaccurate. Consider using '#align submodule.liftq_apply Submodule.liftQ_applyₓ'. -/
@[simp]
theorem liftQ_apply (f : M →ₛₗ[τ₁₂] M₂) {h} (x : M) : p.liftQ f h (Quotient.mk x) = f x :=
@@ -591,7 +591,7 @@ theorem liftQ_mkQ (f : M →ₛₗ[τ₁₂] M₂) (h) : (p.liftQ f h).comp p.mk
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (x : M) (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6), (Eq.{succ u4} M₂ (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f x) (OfNat.ofNat.{u4} M₂ 0 (OfNat.mk.{u4} M₂ 0 (Zero.zero.{u4} M₂ (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (SubNegMonoid.toAddMonoid.{u4} M₂ (AddGroup.toSubNegMonoid.{u4} M₂ (AddCommGroup.toAddGroup.{u4} M₂ _inst_5))))))))) -> (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x)))) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))) _inst_6)
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (x : M) (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6), (Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) x) (FunLike.coe.{max (succ u2) (succ u4), succ u2, succ u4} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f x) (OfNat.ofNat.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) x) 0 (Zero.toOfNat0.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) x) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) x) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) x) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) x) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) x) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) x) _inst_5)))))))) -> (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x)))) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) _inst_6)
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (x : M) (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6), (Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) x) (FunLike.coe.{max (succ u2) (succ u4), succ u2, succ u4} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f x) (OfNat.ofNat.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) x) 0 (Zero.toOfNat0.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) x) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) x) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) x) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) x) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) x) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) x) _inst_5)))))))) -> (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x)))) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) _inst_6)
Case conversion may be inaccurate. Consider using '#align submodule.liftq_span_singleton Submodule.liftQSpanSingletonₓ'. -/
/-- Special case of `liftq` when `p` is the span of `x`. In this case, the condition on `f` simply
becomes vanishing at `x`.-/
@@ -603,7 +603,7 @@ def liftQSpanSingleton (x : M) (f : M →ₛₗ[τ₁₂] M₂) (h : f x = 0) :
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (x : M) (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (h : Eq.{succ u4} M₂ (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} 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(AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x)))) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))) _inst_6) => (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))) -> M₂) (LinearMap.hasCoeToFun.{u1, u3, u2, u4} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M 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_inst_1 _inst_2 _inst_3 R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ x f h) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x)) y)) (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f y)
but is expected to have type
- forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (x : M) (f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (h : Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ 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(Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) (fun (_x : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x)))) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) _inst_6 τ₁₂) (Submodule.liftQSpanSingleton.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ x f h) (Submodule.Quotient.mk.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x)) y)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f y)
+ forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (x : M) (f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (h : Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) x) (NegZeroClass.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) x) (SubNegZeroMonoid.toNegZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) x) (SubtractionMonoid.toSubNegZeroMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) x) (SubtractionCommMonoid.toSubtractionMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) x) (AddCommGroup.toDivisionAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) x) _inst_5)))))))) (y : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) => M₂) (Submodule.Quotient.mk.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x)) y)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x)))) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) _inst_6) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) (fun (_x : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x)))) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) _inst_6 τ₁₂) (Submodule.liftQSpanSingleton.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ x f h) (Submodule.Quotient.mk.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x)) y)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f y)
Case conversion may be inaccurate. Consider using '#align submodule.liftq_span_singleton_apply Submodule.liftQSpanSingleton_applyₓ'. -/
@[simp]
theorem liftQSpanSingleton_apply (x : M) (f : M →ₛₗ[τ₁₂] M₂) (h : f x = 0) (y : M) :
@@ -688,7 +688,7 @@ def mapQ (f : M →ₛₗ[τ₁₂] M₂) (h : p ≤ comap f q) : M ⧸ p →ₛ
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (q : Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) {h : LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f q)} (x : M), Eq.{succ u4} (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) 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but is expected to have type
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(Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q) τ₁₂) (Submodule.mapQ.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ q f h) (Submodule.Quotient.mk.{u4, u2} R M _inst_1 _inst_2 _inst_3 p x)) (Submodule.Quotient.mk.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f x))
+ forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (q : Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) {h : LE.le.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (Submodule.comap.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f q)} (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) => HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.mk.{u4, u2} R M _inst_1 _inst_2 _inst_3 p x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (fun (_x : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) => HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q) τ₁₂) (Submodule.mapQ.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ q f h) (Submodule.Quotient.mk.{u4, u2} R M _inst_1 _inst_2 _inst_3 p x)) (Submodule.Quotient.mk.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f x))
Case conversion may be inaccurate. Consider using '#align submodule.mapq_apply Submodule.mapQ_applyₓ'. -/
@[simp]
theorem mapQ_apply (f : M →ₛₗ[τ₁₂] M₂) {h} (x : M) :
@@ -869,7 +869,7 @@ theorem comapMkQOrderEmbedding_eq (p' : Submodule R (M ⧸ p)) :
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} [_inst_7 : RingHomSurjective.{u1, u3} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂] {f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6} {s : Set.{u4} M₂}, (Set.Nonempty.{u4} M₂ s) -> (HasSubset.Subset.{u4} (Set.{u4} M₂) (Set.hasSubset.{u4} M₂) s ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Set.{u4} M₂) (HasLiftT.mk.{succ u4, succ u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Set.{u4} M₂) (CoeTCₓ.coe.{succ u4, succ u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Set.{u4} M₂) (SetLike.Set.hasCoeT.{u4, u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) M₂ (Submodule.setLike.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6)))) (LinearMap.range.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) _inst_7 f))) -> (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Set.preimage.{u2, u4} M M₂ (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f) s)) (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f (Submodule.span.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6 s)))
but is expected to have type
- forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} [_inst_7 : RingHomSurjective.{u4, u3} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂] {f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6} {s : Set.{u1} M₂}, (Set.Nonempty.{u1} M₂ s) -> (HasSubset.Subset.{u1} (Set.{u1} M₂) (Set.instHasSubsetSet.{u1} M₂) s (SetLike.coe.{u1, u1} (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) M₂ (Submodule.setLike.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (LinearMap.range.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) _inst_7 f))) -> (Eq.{succ u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Set.preimage.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f) s)) (Submodule.comap.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f (Submodule.span.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6 s)))
+ forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} [_inst_7 : RingHomSurjective.{u4, u3} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂] {f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6} {s : Set.{u1} M₂}, (Set.Nonempty.{u1} M₂ s) -> (HasSubset.Subset.{u1} (Set.{u1} M₂) (Set.instHasSubsetSet.{u1} M₂) s (SetLike.coe.{u1, u1} (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) M₂ (Submodule.setLike.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (LinearMap.range.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) _inst_7 f))) -> (Eq.{succ u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Set.preimage.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f) s)) (Submodule.comap.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f (Submodule.span.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6 s)))
Case conversion may be inaccurate. Consider using '#align submodule.span_preimage_eq Submodule.span_preimage_eqₓ'. -/
theorem span_preimage_eq [RingHomSurjective τ₁₂] {f : M →ₛₗ[τ₁₂] M₂} {s : Set M₂} (h₀ : s.Nonempty)
(h₁ : s ⊆ range f) : span R (f ⁻¹' s) = (span R₂ s).comap f :=
@@ -1035,7 +1035,7 @@ def quotEquivOfEqBot (hp : p = ⊥) : (M ⧸ p) ≃ₗ[R] M :=
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (hp : Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p (Bot.bot.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasBot.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) (x : M), Eq.{succ u2} M (coeFn.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Submodule.quotEquivOfEqBot._proof_1.{u1} R _inst_1) (Submodule.quotEquivOfEqBot._proof_2.{u1} R _inst_1) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_3) (fun (_x : LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Submodule.quotEquivOfEqBot._proof_1.{u1} R _inst_1) (Submodule.quotEquivOfEqBot._proof_2.{u1} R _inst_1) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_3) => (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) -> M) (LinearEquiv.hasCoeToFun.{u1, u1, u2, u2} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Submodule.quotEquivOfEqBot._proof_1.{u1} R _inst_1) (Submodule.quotEquivOfEqBot._proof_2.{u1} R _inst_1)) (Submodule.quotEquivOfEqBot.{u1, u2} R M _inst_1 _inst_2 _inst_3 p hp) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x)) x
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (hp : Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p (Bot.bot.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instBotSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) (x : M), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) => M) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_3) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (fun (_x : HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) => M) _x) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_3) R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M (SMulZeroClass.toSMul.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddMonoid.toZero.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommMonoid.toAddMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)))) (DistribSMul.toSMulZeroClass.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddMonoid.toAddZeroClass.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommMonoid.toAddMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)))) (DistribMulAction.toDistribSMul.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p))) (Module.toDistribMulAction.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p))))) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2))) (DistribSMul.toSMulZeroClass.{u1, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)) (Module.toDistribMulAction.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_3) R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p))) (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)) (Module.toDistribMulAction.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Module.toDistribMulAction.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_3) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_3 (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, u2, u2} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_3) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, u2} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (Submodule.quotEquivOfEqBot.{u1, u2} R M _inst_1 _inst_2 _inst_3 p hp) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x)) x
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (hp : Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p (Bot.bot.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instBotSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) (x : M), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) => M) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_3) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (fun (_x : HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) => M) _x) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_3) R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M (SMulZeroClass.toSMul.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddMonoid.toZero.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommMonoid.toAddMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)))) (DistribSMul.toSMulZeroClass.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddMonoid.toAddZeroClass.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommMonoid.toAddMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)))) (DistribMulAction.toDistribSMul.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p))) (Module.toDistribMulAction.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p))))) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2))) (DistribSMul.toSMulZeroClass.{u1, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)) (Module.toDistribMulAction.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_3) R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p))) (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)) (Module.toDistribMulAction.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Module.toDistribMulAction.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_3) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_3 (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, u2, u2} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_3) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, u2} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (Submodule.quotEquivOfEqBot.{u1, u2} R M _inst_1 _inst_2 _inst_3 p hp) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x)) x
Case conversion may be inaccurate. Consider using '#align submodule.quot_equiv_of_eq_bot_apply_mk Submodule.quotEquivOfEqBot_apply_mkₓ'. -/
@[simp]
theorem quotEquivOfEqBot_apply_mk (hp : p = ⊥) (x : M) :
@@ -1047,7 +1047,7 @@ theorem quotEquivOfEqBot_apply_mk (hp : p = ⊥) (x : M) :
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (hp : Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p (Bot.bot.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasBot.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) (x : M), Eq.{succ u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (coeFn.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Submodule.quotEquivOfEqBot._proof_2.{u1} R _inst_1) (Submodule.quotEquivOfEqBot._proof_1.{u1} R _inst_1) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (fun (_x : LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Submodule.quotEquivOfEqBot._proof_2.{u1} R _inst_1) (Submodule.quotEquivOfEqBot._proof_1.{u1} R _inst_1) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) => M -> (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p)) (LinearEquiv.hasCoeToFun.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Submodule.quotEquivOfEqBot._proof_2.{u1} R _inst_1) (Submodule.quotEquivOfEqBot._proof_1.{u1} R _inst_1)) (LinearEquiv.symm.{u1, u1, u2, u2} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Submodule.quotEquivOfEqBot._proof_1.{u1} R _inst_1) (Submodule.quotEquivOfEqBot._proof_2.{u1} R _inst_1) (Submodule.quotEquivOfEqBot.{u1, u2} R M _inst_1 _inst_2 _inst_3 p hp)) x) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x)
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (hp : Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p (Bot.bot.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instBotSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) (x : M), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M) => HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) x) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M) => HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) _x) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2))) (DistribSMul.toSMulZeroClass.{u1, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)) (Module.toDistribMulAction.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (SMulZeroClass.toSMul.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddMonoid.toZero.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommMonoid.toAddMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)))) (DistribSMul.toSMulZeroClass.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddMonoid.toAddZeroClass.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommMonoid.toAddMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)))) (DistribMulAction.toDistribSMul.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p))) (Module.toDistribMulAction.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)) (AddCommMonoid.toAddMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p))) (Module.toDistribMulAction.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Module.toDistribMulAction.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.quotEquivOfEqBot.{u1, u2} R M _inst_1 _inst_2 _inst_3 p hp)) x) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x)
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (hp : Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p (Bot.bot.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instBotSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) (x : M), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : M) => HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) x) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : M) => HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) _x) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2))) (DistribSMul.toSMulZeroClass.{u1, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)) (Module.toDistribMulAction.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (SMulZeroClass.toSMul.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddMonoid.toZero.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommMonoid.toAddMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)))) (DistribSMul.toSMulZeroClass.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddMonoid.toAddZeroClass.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommMonoid.toAddMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)))) (DistribMulAction.toDistribSMul.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p))) (Module.toDistribMulAction.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)) (AddCommMonoid.toAddMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p))) (Module.toDistribMulAction.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Module.toDistribMulAction.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.quotEquivOfEqBot.{u1, u2} R M _inst_1 _inst_2 _inst_3 p hp)) x) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x)
Case conversion may be inaccurate. Consider using '#align submodule.quot_equiv_of_eq_bot_symm_apply Submodule.quotEquivOfEqBot_symm_applyₓ'. -/
@[simp]
theorem quotEquivOfEqBot_symm_apply (hp : p = ⊥) (x : M) :
@@ -1088,7 +1088,7 @@ def quotEquivOfEq (h : p = p') : (M ⧸ p) ≃ₗ[R] M ⧸ p' :=
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (p' : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (h : Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p p') (x : M), Eq.{succ u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (coeFn.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Submodule.quotEquivOfEq._proof_1.{u1} R _inst_1) (Submodule.quotEquivOfEq._proof_2.{u1} R _inst_1) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p')) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p')) (fun (_x : LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Submodule.quotEquivOfEq._proof_1.{u1} R _inst_1) (Submodule.quotEquivOfEq._proof_2.{u1} R _inst_1) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p')) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p')) => (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) -> (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p')) (LinearEquiv.hasCoeToFun.{u1, u1, u2, u2} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p')) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p') (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Submodule.quotEquivOfEq._proof_1.{u1} R _inst_1) (Submodule.quotEquivOfEq._proof_2.{u1} R _inst_1)) (Submodule.quotEquivOfEq.{u1, u2} R M _inst_1 _inst_2 _inst_3 p p' h) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x)) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p' x)
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (p' : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (h : Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p p') (x : M), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) => HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) 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_inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Module.toDistribMulAction.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p')) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p')) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p')) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p')) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p')) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p') (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, u2, u2} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p')) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p')) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p')) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p') (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, u2} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p')) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p') (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (Submodule.quotEquivOfEq.{u1, u2} R M _inst_1 _inst_2 _inst_3 p p' h) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x)) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p' x)
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (p' : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (h : Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p p') (x : M), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) => HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p')) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p')) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (fun (_x : 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_inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) 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_inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Module.toDistribMulAction.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p')) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p')) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p')) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p')) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p')) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p') (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, u2, u2} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p')) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p')) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p')) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p') (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, u2} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p') (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p')) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p') (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (Submodule.quotEquivOfEq.{u1, u2} R M _inst_1 _inst_2 _inst_3 p p' h) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x)) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p' x)
Case conversion may be inaccurate. Consider using '#align submodule.quot_equiv_of_eq_mk Submodule.quotEquivOfEq_mkₓ'. -/
@[simp]
theorem quotEquivOfEq_mk (h : p = p') (x : M) :
mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4
@@ -857,7 +857,7 @@ def Submodule.comapMkQOrderEmbedding : Submodule R (M ⧸ p) ↪o Submodule R M
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (p' : Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)), Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.setLike.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p))))) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (fun (_x : RelEmbedding.{u2, u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LE.le.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M 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(Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) => (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 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(Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.setLike.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)))))) (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) (Submodule.comapMkQOrderEmbedding.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) p') (Submodule.comap.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) p')
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (p : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (p' : Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)), Eq.{succ u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) => Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) p') (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.completeLattice.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)))))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))))) (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (fun (_x : Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) => Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) _x) (RelHomClass.toFunLike.{u1, u1, u1} 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(Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.completeLattice.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)))))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))))) 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x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => LE.le.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Submodule.comapMkQOrderEmbedding.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) p') (Submodule.comap.{u2, u2, u1, u1, u1} R R M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} 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))) M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.mkQ.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) p')
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (p : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (p' : Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)), Eq.{succ u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) => Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) p') (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.completeLattice.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)))))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))))) (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (fun (_x : Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) => Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) 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_inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.completeLattice.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)))))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => LE.le.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Submodule.comapMkQOrderEmbedding.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) p') (Submodule.comap.{u2, u2, u1, u1, u1} R R M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} 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))) M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.mkQ.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) p')
Case conversion may be inaccurate. Consider using '#align submodule.comap_mkq_embedding_eq Submodule.comapMkQOrderEmbedding_eqₓ'. -/
@[simp]
theorem comapMkQOrderEmbedding_eq (p' : Submodule R (M ⧸ p)) :
mathlib commit https://github.com/leanprover-community/mathlib/commit/c89fe2d59ae06402c3f55f978016d1ada444f57e
@@ -497,7 +497,7 @@ variable {M₂ : Type _} [AddCommGroup M₂] [Module R M₂]
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {M₂ : Type.{u3}} [_inst_4 : AddCommGroup.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4)] {{f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5}} {{g : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5}}, (forall (x : M), Eq.{succ u3} M₂ (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 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(HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) -> M₂) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5) => (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) -> M₂) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) g (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x))) -> (Eq.{max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5) f g)
but is expected to have type
- forall {R : Type.{u3}} {M : Type.{u2}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {M₂ : Type.{u1}} [_inst_4 : AddCommGroup.{u1} M₂] [_inst_5 : Module.{u3, u1} R M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4)] (f : LinearMap.{u3, u3, u2, u1} 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))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4) (Submodule.Quotient.module.{u3, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5) (g : LinearMap.{u3, u3, u2, u1} 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))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4) (Submodule.Quotient.module.{u3, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5), (forall (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) => M₂) (Submodule.Quotient.mk.{u3, u2} R M _inst_1 _inst_2 _inst_3 p x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} 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))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4) (Submodule.Quotient.module.{u3, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (fun (_x : HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4) (Submodule.Quotient.module.{u3, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) f (Submodule.Quotient.mk.{u3, u2} R M _inst_1 _inst_2 _inst_3 p x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} 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))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4) (Submodule.Quotient.module.{u3, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (fun (_x : HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4) (Submodule.Quotient.module.{u3, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) g (Submodule.Quotient.mk.{u3, u2} R M _inst_1 _inst_2 _inst_3 p x))) -> (Eq.{max (succ u2) (succ u1)} (LinearMap.{u3, u3, u2, u1} 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))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4) (Submodule.Quotient.module.{u3, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5) f g)
+ forall {R : Type.{u3}} {M : Type.{u2}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {M₂ : Type.{u1}} [_inst_4 : AddCommGroup.{u1} M₂] [_inst_5 : Module.{u3, u1} R M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4)] (f : LinearMap.{u3, u3, u2, u1} 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))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4) (Submodule.Quotient.module.{u3, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5) (g : LinearMap.{u3, u3, u2, u1} 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))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4) (Submodule.Quotient.module.{u3, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5), (forall (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) => M₂) (Submodule.Quotient.mk.{u3, u2} R M _inst_1 _inst_2 _inst_3 p x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} 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))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4) (Submodule.Quotient.module.{u3, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (fun (_x : HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4) (Submodule.Quotient.module.{u3, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) f (Submodule.Quotient.mk.{u3, u2} R M _inst_1 _inst_2 _inst_3 p x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} 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))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4) (Submodule.Quotient.module.{u3, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (fun (_x : HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4) (Submodule.Quotient.module.{u3, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) g (Submodule.Quotient.mk.{u3, u2} R M _inst_1 _inst_2 _inst_3 p x))) -> (Eq.{max (succ u2) (succ u1)} (LinearMap.{u3, u3, u2, u1} 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))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4) (Submodule.Quotient.module.{u3, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5) f g)
Case conversion may be inaccurate. Consider using '#align submodule.quot_hom_ext Submodule.quot_hom_extₓ'. -/
theorem quot_hom_ext ⦃f g : M ⧸ p →ₗ[R] M₂⦄ (h : ∀ x, f (Quotient.mk x) = g (Quotient.mk x)) :
f = g :=
@@ -517,7 +517,7 @@ def mkQ : M →ₗ[R] M ⧸ p where
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (x : M), Eq.{succ u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) => M -> (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p)) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) x) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x)
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (x : M), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) x) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) x) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x)
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (x : M), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) x) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) x) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x)
Case conversion may be inaccurate. Consider using '#align submodule.mkq_apply Submodule.mkQ_applyₓ'. -/
@[simp]
theorem mkQ_apply (x : M) : p.mkQ x = Quotient.mk x :=
@@ -528,7 +528,7 @@ theorem mkQ_apply (x : M) : p.mkQ x = Quotient.mk x :=
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (A : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), Function.Surjective.{succ u2, succ u2} M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) A) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) A) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) A) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 A)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 A)) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) A) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) A) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 A)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 A)) => M -> (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) A)) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) A) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) A) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 A)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 A) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 A))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (A : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3), Function.Surjective.{succ u1, succ u1} M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) A) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} 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))) M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) A) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) A) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 A)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 A)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) A) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) A) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) A) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 A)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 A) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.mkQ.{u2, u1} R M _inst_1 _inst_2 _inst_3 A))
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (A : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3), Function.Surjective.{succ u1, succ u1} M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) A) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} 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))) M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) A) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) A) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 A)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 A)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) A) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) A) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) A) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 A)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 A) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.mkQ.{u2, u1} R M _inst_1 _inst_2 _inst_3 A))
Case conversion may be inaccurate. Consider using '#align submodule.mkq_surjective Submodule.mkQ_surjectiveₓ'. -/
theorem mkQ_surjective (A : Submodule R M) : Function.Surjective A.mkQ := by
rintro ⟨x⟩ <;> exact ⟨x, rfl⟩
@@ -557,7 +557,7 @@ theorem linearMap_qext ⦃f g : M ⧸ p →ₛₗ[τ₁₂] M₂⦄ (h : f.comp
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6), (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)) -> (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6)
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6), (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)) -> (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6)
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6), (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)) -> (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6)
Case conversion may be inaccurate. Consider using '#align submodule.liftq Submodule.liftQₓ'. -/
/-- The map from the quotient of `M` by a submodule `p` to `M₂` induced by a linear map `f : M → M₂`
vanishing on `p`, as a linear map. -/
@@ -570,7 +570,7 @@ def liftQ (f : M →ₛₗ[τ₁₂] M₂) (h : p ≤ f.ker) : M ⧸ p →ₛₗ
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) {h : LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)} (x : M), Eq.{succ u4} M₂ (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) (fun (_x : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) => (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) -> M₂) (LinearMap.hasCoeToFun.{u1, u3, u2, u4} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) (Submodule.liftQ.{u1, u2, u3, u4} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x)) (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f x)
but is expected to have type
- forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) {h : LE.le.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (LinearMap.ker.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)} (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) => M₂) (Submodule.Quotient.mk.{u4, u2} R M _inst_1 _inst_2 _inst_3 p x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (fun (_x : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) (Submodule.liftQ.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h) (Submodule.Quotient.mk.{u4, u2} R M _inst_1 _inst_2 _inst_3 p x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f x)
+ forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) {h : LE.le.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (LinearMap.ker.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)} (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) => M₂) (Submodule.Quotient.mk.{u4, u2} R M _inst_1 _inst_2 _inst_3 p x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (fun (_x : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) (Submodule.liftQ.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h) (Submodule.Quotient.mk.{u4, u2} R M _inst_1 _inst_2 _inst_3 p x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f x)
Case conversion may be inaccurate. Consider using '#align submodule.liftq_apply Submodule.liftQ_applyₓ'. -/
@[simp]
theorem liftQ_apply (f : M →ₛₗ[τ₁₂] M₂) {h} (x : M) : p.liftQ f h (Quotient.mk x) = f x :=
@@ -581,7 +581,7 @@ theorem liftQ_apply (f : M →ₛₗ[τ₁₂] M₂) {h} (x : M) : p.liftQ f h (
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (h : LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)), Eq.{max (succ u2) (succ u4)} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.comp.{u1, u1, u3, u2, u2, u4} R R R₂ M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) τ₁₂ τ₁₂ (RingHomCompTriple.ids.{u1, u3} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂) (Submodule.liftQ.{u1, u2, u3, u4} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) f
but is expected to have type
- forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (h : LE.le.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (LinearMap.ker.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)), Eq.{max (succ u2) (succ u1)} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.comp.{u4, u4, u3, u2, u2, u1} R R R₂ M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) τ₁₂ τ₁₂ (RingHomCompTriple.ids.{u4, u3} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂) (Submodule.liftQ.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h) (Submodule.mkQ.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) f
+ forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (h : LE.le.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (LinearMap.ker.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)), Eq.{max (succ u2) (succ u1)} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.comp.{u4, u4, u3, u2, u2, u1} R R R₂ M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) τ₁₂ τ₁₂ (RingHomCompTriple.ids.{u4, u3} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂) (Submodule.liftQ.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h) (Submodule.mkQ.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) f
Case conversion may be inaccurate. Consider using '#align submodule.liftq_mkq Submodule.liftQ_mkQₓ'. -/
@[simp]
theorem liftQ_mkQ (f : M →ₛₗ[τ₁₂] M₂) (h) : (p.liftQ f h).comp p.mkQ = f := by ext <;> rfl
@@ -591,7 +591,7 @@ theorem liftQ_mkQ (f : M →ₛₗ[τ₁₂] M₂) (h) : (p.liftQ f h).comp p.mk
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (x : M) (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6), (Eq.{succ u4} M₂ (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f x) (OfNat.ofNat.{u4} M₂ 0 (OfNat.mk.{u4} M₂ 0 (Zero.zero.{u4} M₂ (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (SubNegMonoid.toAddMonoid.{u4} M₂ (AddGroup.toSubNegMonoid.{u4} M₂ (AddCommGroup.toAddGroup.{u4} M₂ _inst_5))))))))) -> (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x)))) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))) _inst_6)
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (x : M) (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6), (Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) x) (FunLike.coe.{max (succ u2) (succ u4), succ u2, succ u4} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f x) (OfNat.ofNat.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) x) 0 (Zero.toOfNat0.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) x) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) x) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) x) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) x) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) x) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) x) _inst_5)))))))) -> (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x)))) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) _inst_6)
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (x : M) (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6), (Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) x) (FunLike.coe.{max (succ u2) (succ u4), succ u2, succ u4} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f x) (OfNat.ofNat.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) x) 0 (Zero.toOfNat0.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) x) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) x) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) x) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) x) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) x) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) x) _inst_5)))))))) -> (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x)))) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) _inst_6)
Case conversion may be inaccurate. Consider using '#align submodule.liftq_span_singleton Submodule.liftQSpanSingletonₓ'. -/
/-- Special case of `liftq` when `p` is the span of `x`. In this case, the condition on `f` simply
becomes vanishing at `x`.-/
@@ -603,7 +603,7 @@ def liftQSpanSingleton (x : M) (f : M →ₛₗ[τ₁₂] M₂) (h : f x = 0) :
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (x : M) (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (h : Eq.{succ u4} M₂ (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} 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(AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f y)
but is expected to have type
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u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x)) y)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 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(Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) (fun (_x : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, 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(Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x)))) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) _inst_6 τ₁₂) (Submodule.liftQSpanSingleton.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ x f h) (Submodule.Quotient.mk.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x)) y)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f y)
+ forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (x : M) (f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (h : Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) x) (NegZeroClass.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) x) (SubNegZeroMonoid.toNegZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) x) (SubtractionMonoid.toSubNegZeroMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) x) (SubtractionCommMonoid.toSubtractionMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) x) (AddCommGroup.toDivisionAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) x) _inst_5)))))))) (y : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) => M₂) (Submodule.Quotient.mk.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x)) y)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x)))) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) _inst_6) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) (fun (_x : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x)))) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) _inst_6 τ₁₂) (Submodule.liftQSpanSingleton.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ x f h) (Submodule.Quotient.mk.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x)) y)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f y)
Case conversion may be inaccurate. Consider using '#align submodule.liftq_span_singleton_apply Submodule.liftQSpanSingleton_applyₓ'. -/
@[simp]
theorem liftQSpanSingleton_apply (x : M) (f : M →ₛₗ[τ₁₂] M₂) (h : f x = 0) (y : M) :
@@ -615,28 +615,24 @@ theorem liftQSpanSingleton_apply (x : M) (f : M →ₛₗ[τ₁₂] M₂) (h : f
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), Eq.{succ u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.range.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Top.top.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.hasTop.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)))
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), Eq.{succ u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.range.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Top.top.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.instTopSubmodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)))
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), Eq.{succ u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.range.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Top.top.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.instTopSubmodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)))
Case conversion may be inaccurate. Consider using '#align submodule.range_mkq Submodule.range_mkQₓ'. -/
@[simp]
theorem range_mkQ : p.mkQ.range = ⊤ :=
eq_top_iff'.2 <| by rintro ⟨x⟩ <;> exact ⟨x, rfl⟩
#align submodule.range_mkq Submodule.range_mkQ
-/- warning: submodule.ker_mkq -> Submodule.ker_mkQ is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align submodule.ker_mkq Submodule.ker_mkQₓ'. -/
+#print Submodule.ker_mkQ /-
@[simp]
theorem ker_mkQ : p.mkQ.ker = p := by ext <;> simp
#align submodule.ker_mkq Submodule.ker_mkQ
+-/
/- warning: submodule.le_comap_mkq -> Submodule.le_comap_mkQ is a dubious translation:
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but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (p : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (p' : Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)), LE.le.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) p (Submodule.comap.{u2, u2, u1, u1, u1} R R M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} 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))) M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.mkQ.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) p')
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (p : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (p' : Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)), LE.le.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) p (Submodule.comap.{u2, u2, u1, u1, u1} R R M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} 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))) M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.mkQ.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) p')
Case conversion may be inaccurate. Consider using '#align submodule.le_comap_mkq Submodule.le_comap_mkQₓ'. -/
theorem le_comap_mkQ (p' : Submodule R (M ⧸ p)) : p ≤ comap p.mkQ p' := by
simpa using (comap_mono bot_le : p.mkq.ker ≤ comap p.mkq p')
@@ -646,7 +642,7 @@ theorem le_comap_mkQ (p' : Submodule R (M ⧸ p)) : p ≤ comap p.mkQ p' := by
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), Eq.{succ u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.map.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) p) (Bot.bot.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.hasBot.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)))
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), Eq.{succ u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.map.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) p) (Bot.bot.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.instBotSubmodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)))
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), Eq.{succ u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.map.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) p) (Bot.bot.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.instBotSubmodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)))
Case conversion may be inaccurate. Consider using '#align submodule.mkq_map_self Submodule.mkQ_map_selfₓ'. -/
@[simp]
theorem mkQ_map_self : map p.mkQ p = ⊥ := by
@@ -657,7 +653,7 @@ theorem mkQ_map_self : map p.mkQ p = ⊥ := by
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (p' : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.comap.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.map.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) p')) (Sup.sup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p p')
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (p' : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.comap.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.map.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) p')) (Sup.sup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p p')
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (p' : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.comap.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.map.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) p')) (Sup.sup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p p')
Case conversion may be inaccurate. Consider using '#align submodule.comap_map_mkq Submodule.comap_map_mkQₓ'. -/
@[simp]
theorem comap_map_mkQ : comap p.mkQ (map p.mkQ p') = p ⊔ p' := by simp [comap_map_eq, sup_comm]
@@ -667,7 +663,7 @@ theorem comap_map_mkQ : comap p.mkQ (map p.mkQ p') = p ⊔ p' := by simp [comap_
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (p' : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), Iff (Eq.{succ u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.map.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) p') (Top.top.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.hasTop.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)))) (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Sup.sup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p p') (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (p' : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), Iff (Eq.{succ u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.map.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) p') (Top.top.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.instTopSubmodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)))) (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Sup.sup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p p') (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (p' : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), Iff (Eq.{succ u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.map.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) p') (Top.top.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.instTopSubmodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)))) (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Sup.sup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p p') (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))
Case conversion may be inaccurate. Consider using '#align submodule.map_mkq_eq_top Submodule.map_mkQ_eq_topₓ'. -/
@[simp]
theorem map_mkQ_eq_top : map p.mkQ p' = ⊤ ↔ p ⊔ p' = ⊤ := by
@@ -680,7 +676,7 @@ variable (q : Submodule R₂ M₂)
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (q : Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6), (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f q)) -> (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q))
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (q : Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6), (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f q)) -> (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q))
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (q : Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6), (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f q)) -> (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q))
Case conversion may be inaccurate. Consider using '#align submodule.mapq Submodule.mapQₓ'. -/
/-- The map from the quotient of `M` by submodule `p` to the quotient of `M₂` by submodule `q` along
`f : M → M₂` is linear. -/
@@ -692,7 +688,7 @@ def mapQ (f : M →ₛₗ[τ₁₂] M₂) (h : p ≤ comap f q) : M ⧸ p →ₛ
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (q : Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) {h : LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f q)} (x : M), Eq.{succ u4} (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) 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but is expected to have type
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(Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q) τ₁₂) (Submodule.mapQ.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ q f h) (Submodule.Quotient.mk.{u4, u2} R M _inst_1 _inst_2 _inst_3 p x)) (Submodule.Quotient.mk.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f x))
+ forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (q : Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) {h : LE.le.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (Submodule.comap.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f q)} (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) => HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.mk.{u4, u2} R M _inst_1 _inst_2 _inst_3 p x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (fun (_x : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) => HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q) τ₁₂) (Submodule.mapQ.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ q f h) (Submodule.Quotient.mk.{u4, u2} R M _inst_1 _inst_2 _inst_3 p x)) (Submodule.Quotient.mk.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f x))
Case conversion may be inaccurate. Consider using '#align submodule.mapq_apply Submodule.mapQ_applyₓ'. -/
@[simp]
theorem mapQ_apply (f : M →ₛₗ[τ₁₂] M₂) {h} (x : M) :
@@ -704,7 +700,7 @@ theorem mapQ_apply (f : M →ₛₗ[τ₁₂] M₂) {h} (x : M) :
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (q : Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) {h : LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f q)}, Eq.{max (succ u2) (succ u4)} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) _inst_3 (Submodule.Quotient.module.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (LinearMap.comp.{u1, u1, u3, u2, u2, u4} R R R₂ M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) τ₁₂ τ₁₂ (RingHomCompTriple.ids.{u1, u3} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂) (Submodule.mapQ.{u1, u2, u3, u4} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ q f h) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.comp.{u1, u3, u3, u2, u4, u4} R R₂ R₂ M M₂ (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u4} (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) _inst_3 _inst_6 (Submodule.Quotient.module.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q) τ₁₂ (RingHom.id.{u3} R₂ (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))) τ₁₂ (RingHomCompTriple.right_ids.{u1, u3} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂) (Submodule.mkQ.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q) f)
but is expected to have type
- forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (q : Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) {h : LE.le.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (Submodule.comap.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f q)}, Eq.{max (succ u2) (succ u1)} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) _inst_3 (Submodule.Quotient.module.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (LinearMap.comp.{u4, u4, u3, u2, u2, u1} R R R₂ M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) _inst_3 (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) τ₁₂ τ₁₂ (RingHomCompTriple.ids.{u4, u3} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂) (Submodule.mapQ.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ q f h) (Submodule.mkQ.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.comp.{u4, u3, u3, u2, u1, u1} R R₂ R₂ M M₂ (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) _inst_3 _inst_6 (Submodule.Quotient.module.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q) τ₁₂ (RingHom.id.{u3} R₂ (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))) τ₁₂ (RingHomCompTriple.right_ids.{u4, u3} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂) (Submodule.mkQ.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q) f)
+ forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (q : Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) {h : LE.le.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (Submodule.comap.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f q)}, Eq.{max (succ u2) (succ u1)} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) _inst_3 (Submodule.Quotient.module.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (LinearMap.comp.{u4, u4, u3, u2, u2, u1} R R R₂ M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) _inst_3 (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) τ₁₂ τ₁₂ (RingHomCompTriple.ids.{u4, u3} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂) (Submodule.mapQ.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ q f h) (Submodule.mkQ.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.comp.{u4, u3, u3, u2, u1, u1} R R₂ R₂ M M₂ (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) _inst_3 _inst_6 (Submodule.Quotient.module.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q) τ₁₂ (RingHom.id.{u3} R₂ (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))) τ₁₂ (RingHomCompTriple.right_ids.{u4, u3} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂) (Submodule.mkQ.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q) f)
Case conversion may be inaccurate. Consider using '#align submodule.mapq_mkq Submodule.mapQ_mkQₓ'. -/
theorem mapQ_mkQ (f : M →ₛₗ[τ₁₂] M₂) {h} : (mapQ p q f h).comp p.mkQ = q.mkQ.comp f := by
ext x <;> rfl
@@ -714,7 +710,7 @@ theorem mapQ_mkQ (f : M →ₛₗ[τ₁₂] M₂) {h} : (mapQ p q f h).comp p.mk
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (q : Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (h : optParam.{0} (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) (OfNat.ofNat.{max u2 u4} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) 0 (OfNat.mk.{max u2 u4} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) 0 (Zero.zero.{max u2 u4} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.hasZero.{u1, u3, u2, 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_inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) (OfNat.ofNat.{max u2 u4} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) 0 (OfNat.mk.{max u2 u4} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M 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(AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (LinearMap.hasZero.{u1, u3, u2, u4} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q) τ₁₂))))
but is expected to have type
- forall {R : Type.{u3}} {M : Type.{u4}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u4} M] [_inst_3 : Module.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2)] (p : Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) {R₂ : Type.{u2}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u2} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u2, u1} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u3, u2} R R₂ (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R₂ (Ring.toSemiring.{u2} R₂ _inst_4))} (q : Submodule.{u2, u1} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (h : optParam.{0} (LE.le.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Preorder.toLE.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Submodule.completeLattice.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3))))) p (Submodule.comap.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u3, u2, u4, u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) (OfNat.ofNat.{max u4 u1} (LinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) 0 (Zero.toOfNat0.{max u4 u1} (LinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instZeroLinearMap.{u3, u2, u4, u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂))) q)) (of_eq_true (LE.le.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Preorder.toLE.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Submodule.completeLattice.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3))))) p (Submodule.comap.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u3, u2, u4, u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) (OfNat.ofNat.{max u4 u1} (LinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) 0 (Zero.toOfNat0.{max u4 u1} (LinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instZeroLinearMap.{u3, u2, u4, u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂))) q)) (Eq.trans.{1} Prop (LE.le.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Preorder.toLE.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Submodule.completeLattice.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3))))) p (Submodule.comap.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u3, u2, u4, u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) (OfNat.ofNat.{max u4 u1} (LinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) 0 (Zero.toOfNat0.{max u4 u1} (LinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instZeroLinearMap.{u3, u2, u4, u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂))) q)) (LE.le.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Preorder.toLE.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Submodule.completeLattice.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3))))) p (Top.top.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3))) True (congrArg.{succ u4, 1} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) Prop (Submodule.comap.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u3, u2, u4, u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) (OfNat.ofNat.{max u4 u1} (LinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) 0 (Zero.toOfNat0.{max u4 u1} (LinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instZeroLinearMap.{u3, u2, u4, u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂))) q) (Top.top.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3)) (LE.le.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Preorder.toLE.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M 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(Submodule.hasQuotient.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.Quotient.module.{u3, u4} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.mapQ.{u3, u4, u2, u1} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ q (OfNat.ofNat.{max u4 u1} (LinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) 0 (Zero.toOfNat0.{max u4 u1} (LinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instZeroLinearMap.{u3, u2, u4, u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂))) h) (OfNat.ofNat.{max u4 u1} (LinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u4} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u2, u1} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (AddCommGroup.toAddCommMonoid.{u4} (HasQuotient.Quotient.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u4} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u4} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u2, u1} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.Quotient.module.{u3, u4} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) 0 (Zero.toOfNat0.{max u4 u1} (LinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u4} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u2, u1} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (AddCommGroup.toAddCommMonoid.{u4} (HasQuotient.Quotient.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u4} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u4} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u2, u1} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.Quotient.module.{u3, u4} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (LinearMap.instZeroLinearMap.{u3, u2, u4, u1} R R₂ (HasQuotient.Quotient.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u4} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u2, u1} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} (HasQuotient.Quotient.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u4} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u4} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u2, u1} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.Quotient.module.{u3, u4} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q) τ₁₂)))
+ forall {R : Type.{u3}} {M : Type.{u4}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u4} M] [_inst_3 : Module.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2)] (p : Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) {R₂ : Type.{u2}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u2} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u2, u1} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u3, u2} R R₂ (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R₂ (Ring.toSemiring.{u2} R₂ _inst_4))} (q : Submodule.{u2, u1} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (h : optParam.{0} (LE.le.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Preorder.toLE.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Submodule.completeLattice.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3))))) p (Submodule.comap.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u3, u2, u4, u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) (OfNat.ofNat.{max u4 u1} (LinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) 0 (Zero.toOfNat0.{max u4 u1} (LinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instZeroLinearMap.{u3, u2, u4, u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ 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(AddCommGroup.toAddCommMonoid.{u4} (HasQuotient.Quotient.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u4} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u4} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u2, u1} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.Quotient.module.{u3, u4} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (LinearMap.instZeroLinearMap.{u3, u2, u4, u1} R R₂ (HasQuotient.Quotient.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) 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(Submodule.Quotient.module.{u3, u4} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q) τ₁₂)))
Case conversion may be inaccurate. Consider using '#align submodule.mapq_zero Submodule.mapQ_zeroₓ'. -/
@[simp]
theorem mapQ_zero (h : p ≤ q.comap (0 : M →ₛₗ[τ₁₂] M₂) := (by simp)) :
@@ -727,7 +723,7 @@ theorem mapQ_zero (h : p ≤ q.comap (0 : M →ₛₗ[τ₁₂] M₂) := (by sim
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} {R₃ : Type.{u5}} {M₃ : Type.{u6}} [_inst_7 : Ring.{u5} R₃] [_inst_8 : AddCommGroup.{u6} M₃] [_inst_9 : Module.{u5, u6} R₃ M₃ (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8)] (p₂ : Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (p₃ : Submodule.{u5, u6} R₃ M₃ (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_9) {τ₂₃ : RingHom.{u3, u5} R₂ R₃ (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4)) (NonAssocRing.toNonAssocSemiring.{u5} R₃ (Ring.toNonAssocRing.{u5} R₃ _inst_7))} {τ₁₃ : RingHom.{u1, u5} R R₃ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u5} R₃ (Ring.toNonAssocRing.{u5} R₃ _inst_7))} [_inst_10 : RingHomCompTriple.{u1, u3, u5} R R₂ R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) τ₁₂ τ₂₃ τ₁₃] (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (g : LinearMap.{u3, u5, u4, u6} R₂ R₃ (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_6 _inst_9) (hf : LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f p₂)) (hg : LE.le.{u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Preorder.toHasLe.{u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (PartialOrder.toPreorder.{u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (SetLike.partialOrder.{u4, u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) M₂ (Submodule.setLike.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6)))) p₂ (Submodule.comap.{u3, u5, u4, u6, max u4 u6} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_6 _inst_9 τ₂₃ (LinearMap.{u3, u5, u4, u6} R₂ R₃ (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_6 _inst_9) (LinearMap.semilinearMapClass.{u3, u5, u4, u6} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_6 _inst_9 τ₂₃) g p₃)) (h : optParam.{0} (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f (Submodule.comap.{u3, u5, u4, u6, max u4 u6} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_6 _inst_9 τ₂₃ (LinearMap.{u3, u5, u4, u6} R₂ R₃ (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_6 _inst_9) (LinearMap.semilinearMapClass.{u3, u5, u4, u6} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_6 _inst_9 τ₂₃) g p₃))) (LE.le.trans.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) p (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) 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(AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f (Submodule.comap.{u3, u5, u4, u6, max u4 u6} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_6 _inst_9 τ₂₃ (LinearMap.{u3, u5, u4, u6} R₂ R₃ (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_6 _inst_9) (LinearMap.semilinearMapClass.{u3, u5, u4, u6} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_6 _inst_9 τ₂₃) g p₃)) hf (Submodule.comap_mono.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f p₂ (Submodule.comap.{u3, u5, u4, u6, max u4 u6} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_6 _inst_9 τ₂₃ (LinearMap.{u3, u5, u4, u6} R₂ R₃ (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_6 _inst_9) (LinearMap.semilinearMapClass.{u3, u5, u4, u6} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_6 _inst_9 τ₂₃) g p₃) hg))), Eq.{max (succ u2) (succ u6)} (LinearMap.{u1, u5, u2, u6} R R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u5} R₃ _inst_7) τ₁₃ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u6, u6} M₃ (Submodule.{u5, u6} R₃ M₃ (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_9) (Submodule.hasQuotient.{u5, u6} R₃ M₃ _inst_7 _inst_8 _inst_9) p₃) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u6} (HasQuotient.Quotient.{u6, u6} M₃ (Submodule.{u5, u6} R₃ M₃ (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_9) (Submodule.hasQuotient.{u5, u6} R₃ M₃ _inst_7 _inst_8 _inst_9) p₃) (Submodule.Quotient.addCommGroup.{u5, u6} R₃ M₃ _inst_7 _inst_8 _inst_9 p₃)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u5, u6} R₃ M₃ _inst_7 _inst_8 _inst_9 p₃)) (Submodule.mapQ.{u1, u2, u5, u6} R M _inst_1 _inst_2 _inst_3 p R₃ M₃ _inst_7 _inst_8 _inst_9 τ₁₃ p₃ (LinearMap.comp.{u1, u3, u5, u2, u4, u6} R R₂ R₃ M M₂ M₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_3 _inst_6 _inst_9 τ₁₂ τ₂₃ τ₁₃ _inst_10 g f) h) (LinearMap.comp.{u1, u3, u5, u2, u4, u6} R R₂ R₃ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) p₂) (HasQuotient.Quotient.{u6, u6} M₃ (Submodule.{u5, u6} R₃ M₃ (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_9) (Submodule.hasQuotient.{u5, u6} R₃ M₃ _inst_7 _inst_8 _inst_9) p₃) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) p₂) (Submodule.Quotient.addCommGroup.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 p₂)) (AddCommGroup.toAddCommMonoid.{u6} (HasQuotient.Quotient.{u6, u6} M₃ (Submodule.{u5, u6} R₃ M₃ (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_9) (Submodule.hasQuotient.{u5, u6} R₃ M₃ _inst_7 _inst_8 _inst_9) p₃) (Submodule.Quotient.addCommGroup.{u5, u6} R₃ M₃ _inst_7 _inst_8 _inst_9 p₃)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 p₂) (Submodule.Quotient.module.{u5, u6} R₃ M₃ _inst_7 _inst_8 _inst_9 p₃) τ₁₂ τ₂₃ τ₁₃ _inst_10 (Submodule.mapQ.{u3, u4, u5, u6} R₂ M₂ _inst_4 _inst_5 _inst_6 p₂ R₃ M₃ _inst_7 _inst_8 _inst_9 τ₂₃ p₃ g hg) (Submodule.mapQ.{u1, u2, u3, u4} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ p₂ f hf))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (p : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) {R₂ : Type.{u4}} {M₂ : Type.{u3}} [_inst_4 : Ring.{u4} R₂] [_inst_5 : AddCommGroup.{u3} M₂] [_inst_6 : Module.{u4, u3} R₂ M₂ (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5)] {τ₁₂ : RingHom.{u2, u4} R R₂ (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} R₂ (Ring.toSemiring.{u4} R₂ _inst_4))} {R₃ : Type.{u6}} {M₃ : Type.{u5}} [_inst_7 : Ring.{u6} R₃] [_inst_8 : AddCommGroup.{u5} M₃] [_inst_9 : Module.{u6, u5} R₃ M₃ (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8)] (p₂ : Submodule.{u4, u3} R₂ M₂ (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) (p₃ : Submodule.{u6, u5} R₃ M₃ (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_9) {τ₂₃ : RingHom.{u4, u6} R₂ R₃ (Semiring.toNonAssocSemiring.{u4} R₂ (Ring.toSemiring.{u4} R₂ _inst_4)) (Semiring.toNonAssocSemiring.{u6} R₃ (Ring.toSemiring.{u6} R₃ _inst_7))} {τ₁₃ : RingHom.{u2, u6} R R₃ (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u6} R₃ (Ring.toSemiring.{u6} R₃ _inst_7))} [_inst_10 : RingHomCompTriple.{u2, u4, u6} R R₂ R₃ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) τ₁₂ τ₂₃ τ₁₃] (f : LinearMap.{u2, u4, u1, u3} R R₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6) (g : LinearMap.{u4, u6, u3, u5} R₂ R₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9) (hf : LE.le.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) p (Submodule.comap.{u2, u4, u1, u3, max u1 u3} R R₂ M M₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u2, u4, u1, u3} R R₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u2, u4, u1, u3} R R₂ M M₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f p₂)) (hg : LE.le.{u3} (Submodule.{u4, u3} R₂ M₂ (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) (Preorder.toLE.{u3} (Submodule.{u4, u3} R₂ M₂ (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) (PartialOrder.toPreorder.{u3} (Submodule.{u4, u3} R₂ M₂ (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u4, u3} R₂ M₂ (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u4, u3} R₂ M₂ (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) (Submodule.completeLattice.{u4, u3} R₂ M₂ (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6))))) p₂ (Submodule.comap.{u4, u6, u3, u5, max u3 u5} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9 τ₂₃ (LinearMap.{u4, u6, u3, u5} R₂ R₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9) (LinearMap.instSemilinearMapClassLinearMap.{u4, u6, u3, u5} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9 τ₂₃) g p₃)) (h : optParam.{0} (LE.le.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) p (Submodule.comap.{u2, u4, u1, u3, max u1 u3} R R₂ M M₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u2, u4, u1, u3} R R₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u2, u4, u1, u3} R R₂ M M₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f (Submodule.comap.{u4, u6, u3, u5, max u3 u5} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9 τ₂₃ (LinearMap.{u4, u6, u3, u5} R₂ R₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9) (LinearMap.instSemilinearMapClassLinearMap.{u4, u6, u3, u5} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9 τ₂₃) g p₃))) (LE.le.trans.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) p (Submodule.comap.{u2, u4, u1, u3, max u1 u3} R R₂ M M₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u2, u4, u1, u3} R R₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u2, u4, u1, u3} R R₂ M M₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f p₂) (Submodule.comap.{u2, u4, u1, u3, max u1 u3} R R₂ M M₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u2, u4, u1, u3} R R₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u2, u4, u1, u3} R R₂ M M₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f (Submodule.comap.{u4, u6, u3, u5, max u3 u5} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9 τ₂₃ (LinearMap.{u4, u6, u3, u5} R₂ R₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9) (LinearMap.instSemilinearMapClassLinearMap.{u4, u6, u3, u5} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9 τ₂₃) g p₃)) hf (Submodule.comap_mono.{max u1 u3, u2, u1, u3, u4} R R₂ M M₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u2, u4, u1, u3} R R₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u2, u4, u1, u3} R R₂ M M₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f p₂ (Submodule.comap.{u4, u6, u3, u5, max u3 u5} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9 τ₂₃ (LinearMap.{u4, u6, u3, u5} R₂ R₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9) (LinearMap.instSemilinearMapClassLinearMap.{u4, u6, u3, u5} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9 τ₂₃) g p₃) hg))), Eq.{max (succ u1) (succ u5)} (LinearMap.{u2, u6, u1, u5} R R₃ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u6} R₃ _inst_7) τ₁₃ (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u5, u5} M₃ (Submodule.{u6, u5} R₃ M₃ (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_9) (Submodule.hasQuotient.{u6, u5} R₃ M₃ _inst_7 _inst_8 _inst_9) p₃) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u5} (HasQuotient.Quotient.{u5, u5} M₃ (Submodule.{u6, u5} R₃ M₃ (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_9) (Submodule.hasQuotient.{u6, u5} R₃ M₃ _inst_7 _inst_8 _inst_9) p₃) (Submodule.Quotient.addCommGroup.{u6, u5} R₃ M₃ _inst_7 _inst_8 _inst_9 p₃)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u6, u5} R₃ M₃ _inst_7 _inst_8 _inst_9 p₃)) (Submodule.mapQ.{u2, u1, u6, u5} R M _inst_1 _inst_2 _inst_3 p R₃ M₃ _inst_7 _inst_8 _inst_9 τ₁₃ p₃ (LinearMap.comp.{u2, u4, u6, u1, u3, u5} R R₂ R₃ M M₂ M₃ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_3 _inst_6 _inst_9 τ₁₂ τ₂₃ τ₁₃ _inst_10 g f) h) (LinearMap.comp.{u2, u4, u6, u1, u3, u5} R R₂ R₃ (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u3, u3} M₂ (Submodule.{u4, u3} R₂ M₂ (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u4, u3} R₂ M₂ _inst_4 _inst_5 _inst_6) p₂) (HasQuotient.Quotient.{u5, u5} M₃ (Submodule.{u6, u5} R₃ M₃ (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_9) (Submodule.hasQuotient.{u6, u5} R₃ M₃ _inst_7 _inst_8 _inst_9) p₃) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u3} (HasQuotient.Quotient.{u3, u3} M₂ (Submodule.{u4, u3} R₂ M₂ (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u4, u3} R₂ M₂ _inst_4 _inst_5 _inst_6) p₂) (Submodule.Quotient.addCommGroup.{u4, u3} R₂ M₂ _inst_4 _inst_5 _inst_6 p₂)) (AddCommGroup.toAddCommMonoid.{u5} (HasQuotient.Quotient.{u5, u5} M₃ (Submodule.{u6, u5} R₃ M₃ (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_9) (Submodule.hasQuotient.{u6, u5} R₃ M₃ _inst_7 _inst_8 _inst_9) p₃) (Submodule.Quotient.addCommGroup.{u6, u5} R₃ M₃ _inst_7 _inst_8 _inst_9 p₃)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u4, u3} R₂ M₂ _inst_4 _inst_5 _inst_6 p₂) (Submodule.Quotient.module.{u6, u5} R₃ M₃ _inst_7 _inst_8 _inst_9 p₃) τ₁₂ τ₂₃ τ₁₃ _inst_10 (Submodule.mapQ.{u4, u3, u6, u5} R₂ M₂ _inst_4 _inst_5 _inst_6 p₂ R₃ M₃ _inst_7 _inst_8 _inst_9 τ₂₃ p₃ g hg) (Submodule.mapQ.{u2, u1, u4, u3} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ p₂ f hf))
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (p : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) {R₂ : Type.{u4}} {M₂ : Type.{u3}} [_inst_4 : Ring.{u4} R₂] [_inst_5 : AddCommGroup.{u3} M₂] [_inst_6 : Module.{u4, u3} R₂ M₂ (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5)] {τ₁₂ : RingHom.{u2, u4} R R₂ (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} R₂ (Ring.toSemiring.{u4} R₂ _inst_4))} {R₃ : Type.{u6}} {M₃ : Type.{u5}} [_inst_7 : Ring.{u6} R₃] [_inst_8 : AddCommGroup.{u5} M₃] [_inst_9 : Module.{u6, u5} R₃ M₃ (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8)] (p₂ : Submodule.{u4, u3} R₂ M₂ (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) (p₃ : Submodule.{u6, u5} R₃ M₃ (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_9) {τ₂₃ : RingHom.{u4, u6} R₂ R₃ (Semiring.toNonAssocSemiring.{u4} R₂ (Ring.toSemiring.{u4} R₂ _inst_4)) (Semiring.toNonAssocSemiring.{u6} R₃ (Ring.toSemiring.{u6} R₃ _inst_7))} {τ₁₃ : RingHom.{u2, u6} R R₃ (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u6} R₃ (Ring.toSemiring.{u6} R₃ _inst_7))} [_inst_10 : RingHomCompTriple.{u2, u4, u6} R R₂ R₃ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) τ₁₂ τ₂₃ τ₁₃] (f : LinearMap.{u2, u4, u1, u3} R R₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6) (g : LinearMap.{u4, u6, u3, u5} R₂ R₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9) (hf : LE.le.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) p (Submodule.comap.{u2, u4, u1, u3, max u1 u3} R R₂ M M₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u2, u4, u1, u3} R R₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u2, u4, u1, u3} R R₂ M M₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f p₂)) (hg : LE.le.{u3} (Submodule.{u4, u3} R₂ M₂ (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) (Preorder.toLE.{u3} (Submodule.{u4, u3} R₂ M₂ (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) (PartialOrder.toPreorder.{u3} (Submodule.{u4, u3} R₂ M₂ (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u4, u3} R₂ M₂ (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u4, u3} R₂ M₂ (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) (Submodule.completeLattice.{u4, u3} R₂ M₂ (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6))))) p₂ (Submodule.comap.{u4, u6, u3, u5, max u3 u5} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9 τ₂₃ (LinearMap.{u4, u6, u3, u5} R₂ R₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9) (LinearMap.semilinearMapClass.{u4, u6, u3, u5} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9 τ₂₃) g p₃)) (h : optParam.{0} (LE.le.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) p (Submodule.comap.{u2, u4, u1, u3, max u1 u3} R R₂ M M₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u2, u4, u1, u3} R R₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u2, u4, u1, u3} R R₂ M M₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f (Submodule.comap.{u4, u6, u3, u5, max u3 u5} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9 τ₂₃ (LinearMap.{u4, u6, u3, u5} R₂ R₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9) (LinearMap.semilinearMapClass.{u4, u6, u3, u5} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9 τ₂₃) g p₃))) (LE.le.trans.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) p (Submodule.comap.{u2, u4, u1, u3, max u1 u3} R R₂ M M₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u2, u4, u1, u3} R R₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u2, u4, u1, u3} R R₂ M M₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f p₂) (Submodule.comap.{u2, u4, u1, u3, max u1 u3} R R₂ M M₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u2, u4, u1, u3} R R₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u2, u4, u1, u3} R R₂ M M₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f (Submodule.comap.{u4, u6, u3, u5, max u3 u5} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9 τ₂₃ (LinearMap.{u4, u6, u3, u5} R₂ R₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9) (LinearMap.semilinearMapClass.{u4, u6, u3, u5} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9 τ₂₃) g p₃)) hf (Submodule.comap_mono.{max u1 u3, u2, u1, u3, u4} R R₂ M M₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u2, u4, u1, u3} R R₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u2, u4, u1, u3} R R₂ M M₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f p₂ (Submodule.comap.{u4, u6, u3, u5, max u3 u5} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9 τ₂₃ (LinearMap.{u4, u6, u3, u5} R₂ R₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9) (LinearMap.semilinearMapClass.{u4, u6, u3, u5} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9 τ₂₃) g p₃) hg))), Eq.{max (succ u1) (succ u5)} (LinearMap.{u2, u6, u1, u5} R R₃ (Ring.toSemiring.{u2} R 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(Submodule.hasQuotient.{u6, u5} R₃ M₃ _inst_7 _inst_8 _inst_9) p₃) (Submodule.Quotient.addCommGroup.{u6, u5} R₃ M₃ _inst_7 _inst_8 _inst_9 p₃)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u6, u5} R₃ M₃ _inst_7 _inst_8 _inst_9 p₃)) (Submodule.mapQ.{u2, u1, u6, u5} R M _inst_1 _inst_2 _inst_3 p R₃ M₃ _inst_7 _inst_8 _inst_9 τ₁₃ p₃ (LinearMap.comp.{u2, u4, u6, u1, u3, u5} R R₂ R₃ M M₂ M₃ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_3 _inst_6 _inst_9 τ₁₂ τ₂₃ τ₁₃ _inst_10 g f) h) (LinearMap.comp.{u2, u4, u6, u1, u3, u5} R R₂ R₃ (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u3, u3} M₂ (Submodule.{u4, u3} R₂ M₂ (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u4, u3} R₂ M₂ _inst_4 _inst_5 _inst_6) p₂) (HasQuotient.Quotient.{u5, u5} M₃ (Submodule.{u6, u5} R₃ M₃ (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_9) (Submodule.hasQuotient.{u6, u5} R₃ M₃ _inst_7 _inst_8 _inst_9) p₃) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u3} (HasQuotient.Quotient.{u3, u3} M₂ (Submodule.{u4, u3} R₂ M₂ (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u4, u3} R₂ M₂ _inst_4 _inst_5 _inst_6) p₂) (Submodule.Quotient.addCommGroup.{u4, u3} R₂ M₂ _inst_4 _inst_5 _inst_6 p₂)) (AddCommGroup.toAddCommMonoid.{u5} (HasQuotient.Quotient.{u5, u5} M₃ (Submodule.{u6, u5} R₃ M₃ (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_9) (Submodule.hasQuotient.{u6, u5} R₃ M₃ _inst_7 _inst_8 _inst_9) p₃) (Submodule.Quotient.addCommGroup.{u6, u5} R₃ M₃ _inst_7 _inst_8 _inst_9 p₃)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u4, u3} R₂ M₂ _inst_4 _inst_5 _inst_6 p₂) (Submodule.Quotient.module.{u6, u5} R₃ M₃ _inst_7 _inst_8 _inst_9 p₃) τ₁₂ τ₂₃ τ₁₃ _inst_10 (Submodule.mapQ.{u4, u3, u6, u5} R₂ M₂ _inst_4 _inst_5 _inst_6 p₂ R₃ M₃ _inst_7 _inst_8 _inst_9 τ₂₃ p₃ g hg) (Submodule.mapQ.{u2, u1, u4, u3} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ p₂ f hf))
Case conversion may be inaccurate. Consider using '#align submodule.mapq_comp Submodule.mapQ_compₓ'. -/
/-- Given submodules `p ⊆ M`, `p₂ ⊆ M₂`, `p₃ ⊆ M₃` and maps `f : M → M₂`, `g : M₂ → M₃` inducing
`mapq f : M ⧸ p → M₂ ⧸ p₂` and `mapq g : M₂ ⧸ p₂ → M₃ ⧸ p₃` then
@@ -746,7 +742,7 @@ theorem mapQ_comp {R₃ M₃ : Type _} [Ring R₃] [AddCommGroup M₃] [Module R
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (h : optParam.{0} (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p)) (Eq.mpr.{0} (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R 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(Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) p))), Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.mapQ.{u1, u2, u1, u2} R M _inst_1 _inst_2 _inst_3 p R M _inst_1 _inst_2 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) p (LinearMap.id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) h) (LinearMap.id.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p))
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (h : optParam.{0} (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R 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+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (h : optParam.{0} (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (Submodule.comap.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p)) (Eq.mpr.{0} (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (Submodule.comap.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p)) (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p p) (id.{0} (Eq.{1} Prop (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (Submodule.comap.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p)) (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p p)) (Eq.ndrec.{0, succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.comap.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p) (fun (_a : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => Eq.{1} Prop (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (Submodule.comap.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p)) (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p _a)) (Eq.refl.{1} Prop (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (Submodule.comap.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p))) p (Submodule.comap_id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 p))) (le_refl.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p))), Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.mapQ.{u1, u2, u1, u2} R M _inst_1 _inst_2 _inst_3 p R M _inst_1 _inst_2 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) p (LinearMap.id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) h) (LinearMap.id.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p))
Case conversion may be inaccurate. Consider using '#align submodule.mapq_id Submodule.mapQ_idₓ'. -/
@[simp]
theorem mapQ_id
@@ -763,7 +759,7 @@ theorem mapQ_id
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3} (h : LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f p)) (k : Nat) (h' : optParam.{0} (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (HPow.hPow.{u2, 0, u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) Nat (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (instHPow.{u2, 0} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) Nat (Monoid.Pow.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.monoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) f k) p)) (Submodule.le_comap_pow_of_le_comap.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 p f h k)), Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.mapQ.{u1, u2, u1, u2} R M _inst_1 _inst_2 _inst_3 p R M _inst_1 _inst_2 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) p (HPow.hPow.{u2, 0, u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) Nat (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (instHPow.{u2, 0} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) Nat (Monoid.Pow.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.monoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) f k) h') (HPow.hPow.{u2, 0, u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) Nat (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (instHPow.{u2, 0} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) Nat (Monoid.Pow.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Module.End.monoid.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)))) (Submodule.mapQ.{u1, u2, u1, u2} R M _inst_1 _inst_2 _inst_3 p R M _inst_1 _inst_2 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) p f h) k)
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (p : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) {f : LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3} (h : LE.le.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) p (Submodule.comap.{u2, u2, u1, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f p)) (k : Nat) (h' : optParam.{0} (LE.le.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) p (Submodule.comap.{u2, u2, u1, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (HPow.hPow.{u1, 0, u1} (LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) Nat (LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (instHPow.{u1, 0} (LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) Nat (Monoid.Pow.{u1} (LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.monoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))) f k) p)) (Submodule.le_comap_pow_of_le_comap.{u1, u2} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 p f h k)), Eq.{succ u1} (LinearMap.{u2, u2, u1, u1} 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))) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.mapQ.{u2, u1, u2, u1} R M _inst_1 _inst_2 _inst_3 p R M _inst_1 _inst_2 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) p (HPow.hPow.{u1, 0, u1} (LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) Nat (LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (instHPow.{u1, 0} (LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) Nat (Monoid.Pow.{u1} (LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.monoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))) f k) h') (HPow.hPow.{u1, 0, u1} (LinearMap.{u2, u2, u1, u1} 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))) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) Nat (LinearMap.{u2, u2, u1, u1} 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))) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (instHPow.{u1, 0} (LinearMap.{u2, u2, u1, u1} 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))) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) Nat (Monoid.Pow.{u1} (LinearMap.{u2, u2, u1, u1} 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))) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Module.End.monoid.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)))) (Submodule.mapQ.{u2, u1, u2, u1} R M _inst_1 _inst_2 _inst_3 p R M _inst_1 _inst_2 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) p f h) k)
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (p : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) {f : LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3} (h : LE.le.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) p (Submodule.comap.{u2, u2, u1, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f p)) (k : Nat) (h' : optParam.{0} (LE.le.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) p (Submodule.comap.{u2, u2, u1, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (HPow.hPow.{u1, 0, u1} (LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) Nat (LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (instHPow.{u1, 0} (LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) Nat (Monoid.Pow.{u1} (LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.monoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))) f k) p)) (Submodule.le_comap_pow_of_le_comap.{u1, u2} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 p f h k)), Eq.{succ u1} (LinearMap.{u2, u2, u1, u1} 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))) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.mapQ.{u2, u1, u2, u1} R M _inst_1 _inst_2 _inst_3 p R M _inst_1 _inst_2 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) p (HPow.hPow.{u1, 0, u1} (LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) Nat (LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (instHPow.{u1, 0} (LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) Nat (Monoid.Pow.{u1} (LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.monoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))) f k) h') (HPow.hPow.{u1, 0, u1} (LinearMap.{u2, u2, u1, u1} 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))) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) Nat (LinearMap.{u2, u2, u1, u1} 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))) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (instHPow.{u1, 0} (LinearMap.{u2, u2, u1, u1} 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))) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) Nat (Monoid.Pow.{u1} (LinearMap.{u2, u2, u1, u1} 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))) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Module.End.monoid.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)))) (Submodule.mapQ.{u2, u1, u2, u1} R M _inst_1 _inst_2 _inst_3 p R M _inst_1 _inst_2 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) p f h) k)
Case conversion may be inaccurate. Consider using '#align submodule.mapq_pow Submodule.mapQ_powₓ'. -/
theorem mapQ_pow {f : M →ₗ[R] M} (h : p ≤ p.comap f) (k : ℕ)
(h' : p ≤ p.comap (f ^ k) := p.le_comap_pow_of_le_comap h k) :
@@ -779,7 +775,7 @@ theorem mapQ_pow {f : M →ₗ[R] M} (h : p ≤ p.comap f) (k : ℕ)
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (q : Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (h : LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)), Eq.{succ u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) (Submodule.liftQ.{u1, u2, u3, u4} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h) q) (Submodule.map.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f q))
but is expected to have type
- forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (q : Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (h : LE.le.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (LinearMap.ker.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)), Eq.{succ u2} (Submodule.{u4, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.comap.{u4, u3, u2, u1, max u2 u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) (Submodule.liftQ.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h) q) (Submodule.map.{u4, u4, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (RingHomSurjective.ids.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u2, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.instSemilinearMapClassLinearMap.{u4, u4, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) (Submodule.mkQ.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.comap.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f q))
+ forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (q : Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (h : LE.le.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (LinearMap.ker.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)), Eq.{succ u2} (Submodule.{u4, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.comap.{u4, u3, u2, u1, max u2 u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) (Submodule.liftQ.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h) q) (Submodule.map.{u4, u4, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (RingHomSurjective.ids.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u2, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.semilinearMapClass.{u4, u4, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) (Submodule.mkQ.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.comap.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f q))
Case conversion may be inaccurate. Consider using '#align submodule.comap_liftq Submodule.comap_liftQₓ'. -/
theorem comap_liftQ (f : M →ₛₗ[τ₁₂] M₂) (h) : q.comap (p.liftQ f h) = (q.comap f).map (mkQ p) :=
le_antisymm (by rintro ⟨x⟩ hx <;> exact ⟨_, hx, rfl⟩)
@@ -790,7 +786,7 @@ theorem comap_liftQ (f : M →ₛₗ[τ₁₂] M₂) (h) : q.comap (p.liftQ f h)
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} [_inst_7 : RingHomSurjective.{u1, u3} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂] (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (h : LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)) (q : Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)), Eq.{succ u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.map.{u1, u3, u2, u4, max u2 u4} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂ _inst_7 (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) (Submodule.liftQ.{u1, u2, u3, u4} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h) q) (Submodule.map.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ _inst_7 (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f (Submodule.comap.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) q))
but is expected to have type
- forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} [_inst_7 : RingHomSurjective.{u4, u3} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (h : LE.le.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (LinearMap.ker.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)) (q : Submodule.{u4, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)), Eq.{succ u1} (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) (Submodule.liftQ.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h) q) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f (Submodule.comap.{u4, u4, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (LinearMap.{u4, u4, u2, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.instSemilinearMapClassLinearMap.{u4, u4, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) (Submodule.mkQ.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) q))
+ forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} [_inst_7 : RingHomSurjective.{u4, u3} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (h : LE.le.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (LinearMap.ker.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)) (q : Submodule.{u4, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)), Eq.{succ u1} (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) (Submodule.liftQ.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h) q) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f (Submodule.comap.{u4, u4, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (LinearMap.{u4, u4, u2, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.semilinearMapClass.{u4, u4, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) (Submodule.mkQ.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) q))
Case conversion may be inaccurate. Consider using '#align submodule.map_liftq Submodule.map_liftQₓ'. -/
theorem map_liftQ [RingHomSurjective τ₁₂] (f : M →ₛₗ[τ₁₂] M₂) (h) (q : Submodule R (M ⧸ p)) :
q.map (p.liftQ f h) = (q.comap p.mkQ).map f :=
@@ -802,7 +798,7 @@ theorem map_liftQ [RingHomSurjective τ₁₂] (f : M →ₛₗ[τ₁₂] M₂)
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (h : LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)), Eq.{succ u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) (Submodule.liftQ.{u1, u2, u3, u4} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h)) (Submodule.map.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f))
but is expected to have type
- forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (h : LE.le.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (LinearMap.ker.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)), Eq.{succ u2} (Submodule.{u4, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.ker.{u4, u3, u2, u1, max u2 u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) (Submodule.liftQ.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h)) (Submodule.map.{u4, u4, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (RingHomSurjective.ids.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u2, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.instSemilinearMapClassLinearMap.{u4, u4, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) (Submodule.mkQ.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) (LinearMap.ker.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f))
+ forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (h : LE.le.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (LinearMap.ker.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)), Eq.{succ u2} (Submodule.{u4, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.ker.{u4, u3, u2, u1, max u2 u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) (Submodule.liftQ.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h)) (Submodule.map.{u4, u4, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (RingHomSurjective.ids.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u2, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.semilinearMapClass.{u4, u4, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) (Submodule.mkQ.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) (LinearMap.ker.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f))
Case conversion may be inaccurate. Consider using '#align submodule.ker_liftq Submodule.ker_liftQₓ'. -/
theorem ker_liftQ (f : M →ₛₗ[τ₁₂] M₂) (h) : ker (p.liftQ f h) = (ker f).map (mkQ p) :=
comap_liftQ _ _ _ _
@@ -812,7 +808,7 @@ theorem ker_liftQ (f : M →ₛₗ[τ₁₂] M₂) (h) : ker (p.liftQ f h) = (ke
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} [_inst_7 : RingHomSurjective.{u1, u3} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂] (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (h : LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)), Eq.{succ u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (LinearMap.range.{u1, u3, u2, u4, max u2 u4} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) _inst_7 (Submodule.liftQ.{u1, u2, u3, u4} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h)) (LinearMap.range.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) _inst_7 f)
but is expected to have type
- forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} [_inst_7 : RingHomSurjective.{u4, u3} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (h : LE.le.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (LinearMap.ker.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)), Eq.{succ u1} (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (LinearMap.range.{u4, u3, u2, u1, max u2 u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) _inst_7 (Submodule.liftQ.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h)) (LinearMap.range.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) _inst_7 f)
+ forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} [_inst_7 : RingHomSurjective.{u4, u3} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (h : LE.le.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (LinearMap.ker.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)), Eq.{succ u1} (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (LinearMap.range.{u4, u3, u2, u1, max u2 u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) _inst_7 (Submodule.liftQ.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h)) (LinearMap.range.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) _inst_7 f)
Case conversion may be inaccurate. Consider using '#align submodule.range_liftq Submodule.range_liftQₓ'. -/
theorem range_liftQ [RingHomSurjective τ₁₂] (f : M →ₛₗ[τ₁₂] M₂) (h) :
range (p.liftQ f h) = range f := by simpa only [range_eq_map] using map_liftq _ _ _ _
@@ -822,7 +818,7 @@ theorem range_liftQ [RingHomSurjective τ₁₂] (f : M →ₛₗ[τ₁₂] M₂
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (h : LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)), (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f) p) -> (Eq.{succ u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) (Submodule.liftQ.{u1, u2, u3, u4} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h)) (Bot.bot.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.hasBot.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p))))
but is expected to have type
- forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (h : LE.le.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (LinearMap.ker.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)), (LE.le.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (LinearMap.ker.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f) p) -> (Eq.{succ u2} (Submodule.{u4, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.ker.{u4, u3, u2, u1, max u2 u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) (Submodule.liftQ.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h)) (Bot.bot.{u2} (Submodule.{u4, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.instBotSubmodule.{u4, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p))))
+ forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (h : LE.le.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (LinearMap.ker.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)), (LE.le.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (LinearMap.ker.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f) p) -> (Eq.{succ u2} (Submodule.{u4, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.ker.{u4, u3, u2, u1, max u2 u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) (Submodule.liftQ.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h)) (Bot.bot.{u2} (Submodule.{u4, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.instBotSubmodule.{u4, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p))))
Case conversion may be inaccurate. Consider using '#align submodule.ker_liftq_eq_bot Submodule.ker_liftQ_eq_botₓ'. -/
theorem ker_liftQ_eq_bot (f : M →ₛₗ[τ₁₂] M₂) (h) (h' : ker f ≤ p) : ker (p.liftQ f h) = ⊥ := by
rw [ker_liftq, le_antisymm h h', mkq_map_self]
@@ -861,7 +857,7 @@ def Submodule.comapMkQOrderEmbedding : Submodule R (M ⧸ p) ↪o Submodule R M
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (p' : Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)), Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.setLike.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p))))) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) 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_inst_2 _inst_3 p) p')
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (p : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (p' : Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)), Eq.{succ u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) => Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) p') (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.completeLattice.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)))))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))))) (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (fun (_x : Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) => Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.completeLattice.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)))))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))))) 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x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => LE.le.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Submodule.comapMkQOrderEmbedding.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) p') (Submodule.comap.{u2, u2, u1, u1, u1} R R M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} 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))) M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.mkQ.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) p')
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (p : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (p' : Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)), Eq.{succ u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) => Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) p') (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.completeLattice.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)))))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))))) (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (fun (_x : Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) => Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) 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_inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.completeLattice.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)))))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => LE.le.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Submodule.comapMkQOrderEmbedding.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) p') (Submodule.comap.{u2, u2, u1, u1, u1} R R M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} 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))) M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.mkQ.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) p')
Case conversion may be inaccurate. Consider using '#align submodule.comap_mkq_embedding_eq Submodule.comapMkQOrderEmbedding_eqₓ'. -/
@[simp]
theorem comapMkQOrderEmbedding_eq (p' : Submodule R (M ⧸ p)) :
@@ -873,7 +869,7 @@ theorem comapMkQOrderEmbedding_eq (p' : Submodule R (M ⧸ p)) :
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} [_inst_7 : RingHomSurjective.{u1, u3} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂] {f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6} {s : Set.{u4} M₂}, (Set.Nonempty.{u4} M₂ s) -> (HasSubset.Subset.{u4} (Set.{u4} M₂) (Set.hasSubset.{u4} M₂) s ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Set.{u4} M₂) (HasLiftT.mk.{succ u4, succ u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Set.{u4} M₂) (CoeTCₓ.coe.{succ u4, succ u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Set.{u4} M₂) (SetLike.Set.hasCoeT.{u4, u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) M₂ (Submodule.setLike.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6)))) (LinearMap.range.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) _inst_7 f))) -> (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Set.preimage.{u2, u4} M M₂ (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f) s)) (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f (Submodule.span.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6 s)))
but is expected to have type
- forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} [_inst_7 : RingHomSurjective.{u4, u3} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂] {f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6} {s : Set.{u1} M₂}, (Set.Nonempty.{u1} M₂ s) -> (HasSubset.Subset.{u1} (Set.{u1} M₂) (Set.instHasSubsetSet.{u1} M₂) s (SetLike.coe.{u1, u1} (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) M₂ (Submodule.setLike.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (LinearMap.range.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) _inst_7 f))) -> (Eq.{succ u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Set.preimage.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f) s)) (Submodule.comap.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f (Submodule.span.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6 s)))
+ forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} [_inst_7 : RingHomSurjective.{u4, u3} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂] {f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6} {s : Set.{u1} M₂}, (Set.Nonempty.{u1} M₂ s) -> (HasSubset.Subset.{u1} (Set.{u1} M₂) (Set.instHasSubsetSet.{u1} M₂) s (SetLike.coe.{u1, u1} (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) M₂ (Submodule.setLike.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (LinearMap.range.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) _inst_7 f))) -> (Eq.{succ u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Set.preimage.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f) s)) (Submodule.comap.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f (Submodule.span.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6 s)))
Case conversion may be inaccurate. Consider using '#align submodule.span_preimage_eq Submodule.span_preimage_eqₓ'. -/
theorem span_preimage_eq [RingHomSurjective τ₁₂] {f : M →ₛₗ[τ₁₂] M₂} {s : Set M₂} (h₀ : s.Nonempty)
(h₁ : s ⊆ range f) : span R (f ⁻¹' s) = (span R₂ s).comap f :=
@@ -979,7 +975,7 @@ variable [RingHomCompTriple τ₁₂ τ₂₃ τ₁₃] [RingHomSurjective τ₁
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u3} R₂] [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_7 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_8 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_2))} [_inst_11 : RingHomSurjective.{u1, u3} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂] (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8), Eq.{max (succ u2) (succ u4)} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M 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(AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) _inst_4 (AddCommGroup.toAddCommMonoid.{u4} (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_8) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_2 _inst_5 _inst_8) (LinearMap.range.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) 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(AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f))) (LinearMap.hasZero.{u1, u3, u2, u4} R R₂ M (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_8) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_2 _inst_5 _inst_8) (LinearMap.range.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u4} (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_8) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_2 _inst_5 _inst_8) (LinearMap.range.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (Submodule.Quotient.addCommGroup.{u3, u4} R₂ M₂ _inst_2 _inst_5 _inst_8 (LinearMap.range.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f))) _inst_7 (Submodule.Quotient.module.{u3, u4} R₂ M₂ _inst_2 _inst_5 _inst_8 (LinearMap.range.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) τ₁₂))))
but is expected to have type
- forall {R : Type.{u4}} {M : Type.{u2}} {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_1 : Ring.{u4} R] [_inst_2 : Ring.{u3} R₂] [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_7 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) _inst_4] [_inst_8 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_2))} [_inst_11 : RingHomSurjective.{u4, u3} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8), Eq.{max (succ u2) (succ u1)} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_8) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_2 _inst_5 _inst_8) (LinearMap.range.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) 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_inst_7 _inst_8 τ₁₂) _inst_11 f))) (LinearMap.comp.{u4, u3, u3, u2, u1, u1} R R₂ R₂ M M₂ (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_8) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_2 _inst_5 _inst_8) (LinearMap.range.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u3} R₂ 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(Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_8) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_2 _inst_5 _inst_8) (LinearMap.range.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (Submodule.Quotient.addCommGroup.{u3, u1} R₂ M₂ _inst_2 _inst_5 _inst_8 (LinearMap.range.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f))) _inst_7 (Submodule.Quotient.module.{u3, u1} R₂ M₂ _inst_2 _inst_5 _inst_8 (LinearMap.range.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f))) (LinearMap.instZeroLinearMap.{u4, u3, u2, u1} R R₂ M (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_8) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_2 _inst_5 _inst_8) (LinearMap.range.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_8) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_2 _inst_5 _inst_8) (LinearMap.range.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (Submodule.Quotient.addCommGroup.{u3, u1} R₂ M₂ _inst_2 _inst_5 _inst_8 (LinearMap.range.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f))) _inst_7 (Submodule.Quotient.module.{u3, u1} R₂ M₂ _inst_2 _inst_5 _inst_8 (LinearMap.range.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) τ₁₂)))
+ forall {R : Type.{u4}} {M : Type.{u2}} {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_1 : Ring.{u4} R] [_inst_2 : Ring.{u3} R₂] [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_7 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) _inst_4] [_inst_8 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_2))} [_inst_11 : RingHomSurjective.{u4, u3} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8), Eq.{max (succ u2) (succ u1)} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_8) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_2 _inst_5 _inst_8) (LinearMap.range.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_8) 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Case conversion may be inaccurate. Consider using '#align linear_map.range_mkq_comp LinearMap.range_mkQ_compₓ'. -/
theorem range_mkQ_comp (f : M →ₛₗ[τ₁₂] M₂) : f.range.mkQ.comp f = 0 :=
LinearMap.ext fun x => by simp
@@ -989,7 +985,7 @@ theorem range_mkQ_comp (f : M →ₛₗ[τ₁₂] M₂) : f.range.mkQ.comp f = 0
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} {R₂ : Type.{u3}} {M₂ : Type.{u4}} {R₃ : Type.{u5}} {M₃ : Type.{u6}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u3} R₂] [_inst_3 : Ring.{u5} R₃] [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : AddCommMonoid.{u6} M₃] [_inst_7 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_8 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] [_inst_9 : Module.{u5, u6} R₃ M₃ (Ring.toSemiring.{u5} R₃ _inst_3) _inst_6] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_2))} {τ₂₃ : RingHom.{u3, u5} R₂ R₃ (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u5} R₃ (Ring.toNonAssocRing.{u5} R₃ _inst_3))} [_inst_11 : RingHomSurjective.{u1, u3} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂] {f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8} {g : LinearMap.{u3, u5, u4, u6} R₂ R₃ (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u5} R₃ _inst_3) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6 _inst_8 _inst_9}, Iff (LE.le.{u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_8) (Preorder.toHasLe.{u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_8) (PartialOrder.toPreorder.{u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_8) (SetLike.partialOrder.{u4, u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_8) M₂ 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_inst_7 _inst_8 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u3} R₂ _inst_2) (Submodule.addCommMonoid.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_8 (LinearMap.ker.{u3, u5, u4, u6, max u4 u6} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u5} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃ (LinearMap.{u3, u5, u4, u6} R₂ R₃ (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u5} R₃ _inst_3) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6 _inst_8 _inst_9) (LinearMap.semilinearMapClass.{u3, u5, u4, u6} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u5} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃) g)) (AddCommGroup.toAddCommMonoid.{u4} (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_8) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_2 _inst_5 _inst_8) (LinearMap.range.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (Submodule.Quotient.addCommGroup.{u3, u4} R₂ M₂ _inst_2 _inst_5 _inst_8 (LinearMap.range.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f))) (Submodule.module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_8 (LinearMap.ker.{u3, u5, u4, u6, max u4 u6} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u5} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃ (LinearMap.{u3, u5, u4, u6} R₂ R₃ (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u5} R₃ _inst_3) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6 _inst_8 _inst_9) (LinearMap.semilinearMapClass.{u3, u5, u4, u6} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u5} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃) g)) (Submodule.Quotient.module.{u3, u4} R₂ M₂ _inst_2 _inst_5 _inst_8 (LinearMap.range.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (RingHom.id.{u3} R₂ (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_2))))))))
but is expected to have type
- forall {R : Type.{u6}} {M : Type.{u4}} {R₂ : Type.{u5}} {M₂ : Type.{u3}} {R₃ : Type.{u2}} {M₃ : Type.{u1}} [_inst_1 : Ring.{u6} R] [_inst_2 : Ring.{u5} R₂] [_inst_3 : Ring.{u2} R₃] [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : AddCommGroup.{u3} M₂] [_inst_6 : AddCommMonoid.{u1} M₃] [_inst_7 : Module.{u6, u4} R M (Ring.toSemiring.{u6} R _inst_1) _inst_4] [_inst_8 : Module.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5)] [_inst_9 : Module.{u2, u1} R₃ M₃ (Ring.toSemiring.{u2} R₃ _inst_3) _inst_6] {τ₁₂ : RingHom.{u6, u5} R R₂ (Semiring.toNonAssocSemiring.{u6} R (Ring.toSemiring.{u6} R _inst_1)) (Semiring.toNonAssocSemiring.{u5} R₂ (Ring.toSemiring.{u5} R₂ _inst_2))} {τ₂₃ : RingHom.{u5, u2} R₂ R₃ (Semiring.toNonAssocSemiring.{u5} R₂ (Ring.toSemiring.{u5} R₂ _inst_2)) (Semiring.toNonAssocSemiring.{u2} R₃ (Ring.toSemiring.{u2} R₃ _inst_3))} [_inst_11 : RingHomSurjective.{u6, u5} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) τ₁₂] {f : LinearMap.{u6, u5, u4, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8} {g : LinearMap.{u5, u2, u3, u1} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9}, Iff (LE.le.{u3} (Submodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) (Preorder.toLE.{u3} (Submodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) (PartialOrder.toPreorder.{u3} (Submodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) 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R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u6, u5, u4, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u6, u5, u4, u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u5} R₂ _inst_2) (Submodule.addCommMonoid.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8 (LinearMap.ker.{u5, u2, u3, u1, max u3 u1} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃ (LinearMap.{u5, u2, u3, u1} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9) (LinearMap.instSemilinearMapClassLinearMap.{u5, u2, u3, u1} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃) g)) (AddCommGroup.toAddCommMonoid.{u3} (HasQuotient.Quotient.{u3, u3} M₂ (Submodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) (Submodule.hasQuotient.{u5, u3} R₂ M₂ _inst_2 _inst_5 _inst_8) (LinearMap.range.{u6, u5, u4, u3, max u4 u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u6, u5, u4, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u6, u5, u4, u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (Submodule.Quotient.addCommGroup.{u5, u3} R₂ M₂ _inst_2 _inst_5 _inst_8 (LinearMap.range.{u6, u5, u4, u3, max u4 u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u6, u5, u4, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u6, u5, u4, u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f))) (Submodule.module.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8 (LinearMap.ker.{u5, u2, u3, u1, max u3 u1} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃ (LinearMap.{u5, u2, u3, u1} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9) (LinearMap.instSemilinearMapClassLinearMap.{u5, u2, u3, u1} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃) g)) (Submodule.Quotient.module.{u5, u3} R₂ M₂ _inst_2 _inst_5 _inst_8 (LinearMap.range.{u6, u5, u4, u3, max u4 u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u6, u5, u4, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u6, u5, u4, u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (RingHom.id.{u5} R₂ (Semiring.toNonAssocSemiring.{u5} R₂ (Ring.toSemiring.{u5} R₂ _inst_2)))))))
+ forall {R : Type.{u6}} {M : Type.{u4}} {R₂ : Type.{u5}} {M₂ : Type.{u3}} {R₃ : Type.{u2}} {M₃ : Type.{u1}} [_inst_1 : Ring.{u6} R] [_inst_2 : Ring.{u5} R₂] [_inst_3 : Ring.{u2} R₃] [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : AddCommGroup.{u3} M₂] [_inst_6 : AddCommMonoid.{u1} M₃] [_inst_7 : Module.{u6, u4} R M (Ring.toSemiring.{u6} R _inst_1) _inst_4] [_inst_8 : Module.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5)] [_inst_9 : Module.{u2, u1} R₃ M₃ (Ring.toSemiring.{u2} R₃ _inst_3) _inst_6] {τ₁₂ : RingHom.{u6, u5} R R₂ (Semiring.toNonAssocSemiring.{u6} R (Ring.toSemiring.{u6} R _inst_1)) (Semiring.toNonAssocSemiring.{u5} R₂ (Ring.toSemiring.{u5} R₂ _inst_2))} {τ₂₃ : RingHom.{u5, u2} R₂ R₃ (Semiring.toNonAssocSemiring.{u5} R₂ (Ring.toSemiring.{u5} R₂ _inst_2)) (Semiring.toNonAssocSemiring.{u2} R₃ (Ring.toSemiring.{u2} R₃ _inst_3))} [_inst_11 : RingHomSurjective.{u6, u5} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) τ₁₂] {f : LinearMap.{u6, u5, u4, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8} {g : LinearMap.{u5, u2, u3, u1} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9}, Iff (LE.le.{u3} (Submodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) (Preorder.toLE.{u3} (Submodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) (PartialOrder.toPreorder.{u3} (Submodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) (Submodule.completeLattice.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8))))) (LinearMap.ker.{u5, u2, u3, u1, max u3 u1} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃ (LinearMap.{u5, u2, u3, u1} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9) (LinearMap.semilinearMapClass.{u5, u2, u3, u1} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃) g) (LinearMap.range.{u6, u5, u4, u3, max u4 u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u6, u5, u4, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.semilinearMapClass.{u6, u5, u4, u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (Eq.{succ u3} (LinearMap.{u5, u5, u3, u3} R₂ R₂ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u5} R₂ _inst_2) (RingHom.id.{u5} R₂ (Semiring.toNonAssocSemiring.{u5} R₂ (Ring.toSemiring.{u5} R₂ _inst_2))) (Subtype.{succ u3} M₂ (fun (x : M₂) => Membership.mem.{u3, u3} M₂ (Submodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) (SetLike.instMembership.{u3, u3} (Submodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) M₂ (Submodule.setLike.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8)) x (LinearMap.ker.{u5, u2, u3, u1, max u3 u1} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃ (LinearMap.{u5, u2, u3, u1} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9) (LinearMap.semilinearMapClass.{u5, u2, u3, u1} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃) g))) (HasQuotient.Quotient.{u3, u3} M₂ (Submodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) (Submodule.hasQuotient.{u5, u3} R₂ M₂ _inst_2 _inst_5 _inst_8) (LinearMap.range.{u6, u5, u4, u3, max u4 u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u6, u5, u4, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.semilinearMapClass.{u6, u5, u4, u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (Submodule.addCommMonoid.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8 (LinearMap.ker.{u5, u2, u3, u1, max u3 u1} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃ (LinearMap.{u5, u2, u3, u1} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) 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(AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃) g)) (Submodule.Quotient.module.{u5, u3} R₂ M₂ _inst_2 _inst_5 _inst_8 (LinearMap.range.{u6, u5, u4, u3, max u4 u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u6, u5, u4, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.semilinearMapClass.{u6, u5, u4, u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (RingHom.id.{u5} R₂ (Semiring.toNonAssocSemiring.{u5} R₂ (Ring.toSemiring.{u5} R₂ _inst_2)))))))
Case conversion may be inaccurate. Consider using '#align linear_map.ker_le_range_iff LinearMap.ker_le_range_iffₓ'. -/
theorem ker_le_range_iff {f : M →ₛₗ[τ₁₂] M₂} {g : M₂ →ₛₗ[τ₂₃] M₃} :
g.ker ≤ f.range ↔ f.range.mkQ.comp g.ker.Subtype = 0 := by
@@ -1000,7 +996,7 @@ theorem ker_le_range_iff {f : M →ₛₗ[τ₁₂] M₂} {g : M₂ →ₛₗ[τ
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u3} R₂] [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_7 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_8 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_2))} [_inst_11 : RingHomSurjective.{u1, u3} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂] {f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8}, (forall (u : LinearMap.{u3, u3, u4, u4} R₂ R₂ (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u3} R₂ _inst_2) (RingHom.id.{u3} R₂ 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_inst_2 _inst_5 _inst_8 (LinearMap.range.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f))) u v)) -> (Eq.{succ u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_8) (LinearMap.range.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f) (Top.top.{u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_8) (Submodule.hasTop.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_8)))
but is expected to have type
- forall {R : Type.{u4}} {M : Type.{u2}} {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_1 : Ring.{u4} R] [_inst_2 : Ring.{u3} R₂] [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_7 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) _inst_4] [_inst_8 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_2))} [_inst_11 : RingHomSurjective.{u4, u3} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂] {f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8}, (forall (u : LinearMap.{u3, u3, u1, u1} R₂ R₂ (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u3} R₂ _inst_2) (RingHom.id.{u3} R₂ 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R₂ (Ring.toSemiring.{u3} R₂ _inst_2))) τ₁₂ (RingHomCompTriple.right_ids.{u4, u3} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂) u f) (LinearMap.comp.{u4, u3, u3, u2, u1, u1} R R₂ R₂ M M₂ (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_8) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_2 _inst_5 _inst_8) (LinearMap.range.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_8) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_2 _inst_5 _inst_8) (LinearMap.range.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (Submodule.Quotient.addCommGroup.{u3, u1} R₂ M₂ _inst_2 _inst_5 _inst_8 (LinearMap.range.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f))) _inst_7 _inst_8 (Submodule.Quotient.module.{u3, u1} R₂ M₂ _inst_2 _inst_5 _inst_8 (LinearMap.range.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) τ₁₂ (RingHom.id.{u3} R₂ (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_2))) τ₁₂ (RingHomCompTriple.right_ids.{u4, u3} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂) v f)) -> (Eq.{succ u1} (LinearMap.{u3, u3, u1, u1} R₂ R₂ (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u3} R₂ _inst_2) (RingHom.id.{u3} R₂ (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_2))) M₂ (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_8) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_2 _inst_5 _inst_8) (LinearMap.range.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_8) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_2 _inst_5 _inst_8) (LinearMap.range.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (Submodule.Quotient.addCommGroup.{u3, u1} R₂ M₂ _inst_2 _inst_5 _inst_8 (LinearMap.range.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f))) _inst_8 (Submodule.Quotient.module.{u3, u1} R₂ M₂ _inst_2 _inst_5 _inst_8 (LinearMap.range.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f))) u v)) -> (Eq.{succ u1} (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_8) (LinearMap.range.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f) (Top.top.{u1} (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_8) (Submodule.instTopSubmodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_8)))
+ forall {R : Type.{u4}} {M : Type.{u2}} {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_1 : Ring.{u4} R] [_inst_2 : Ring.{u3} R₂] [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_7 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) _inst_4] [_inst_8 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_2))} [_inst_11 : RingHomSurjective.{u4, u3} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂] {f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8}, (forall (u : LinearMap.{u3, u3, u1, u1} R₂ R₂ (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u3} R₂ _inst_2) (RingHom.id.{u3} R₂ (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_2))) M₂ (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_8) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_2 _inst_5 _inst_8) (LinearMap.range.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_8) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_2 _inst_5 _inst_8) (LinearMap.range.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (Submodule.Quotient.addCommGroup.{u3, u1} R₂ M₂ _inst_2 _inst_5 _inst_8 (LinearMap.range.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f))) _inst_8 (Submodule.Quotient.module.{u3, u1} R₂ M₂ _inst_2 _inst_5 _inst_8 (LinearMap.range.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R 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τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_8) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_2 _inst_5 _inst_8) (LinearMap.range.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (Submodule.Quotient.addCommGroup.{u3, u1} R₂ M₂ _inst_2 _inst_5 _inst_8 (LinearMap.range.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f))) _inst_8 (Submodule.Quotient.module.{u3, u1} R₂ M₂ _inst_2 _inst_5 _inst_8 (LinearMap.range.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f))) u v)) -> (Eq.{succ u1} (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_8) (LinearMap.range.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f) (Top.top.{u1} (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_8) (Submodule.instTopSubmodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_8)))
Case conversion may be inaccurate. Consider using '#align linear_map.range_eq_top_of_cancel LinearMap.range_eq_top_of_cancelₓ'. -/
/-- An epimorphism is surjective. -/
theorem range_eq_top_of_cancel {f : M →ₛₗ[τ₁₂] M₂}
@@ -1104,7 +1100,7 @@ theorem quotEquivOfEq_mk (h : p = p') (x : M) :
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (P : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Q : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (hf : Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.map.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 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_inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.refl.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) P) Q), Eq.{succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Submodule.Quotient.equiv._proof_10.{u1} R _inst_1) (Submodule.Quotient.equiv._proof_11.{u1} R _inst_1) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) Q) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 P)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.refl.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (LinearMap.id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearEquiv.refl_toLinearMap.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) P P (rfl.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) P)) (Submodule.map_id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 P)) Q Q (rfl.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Q)) hf)))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (P : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Q : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (hf : Eq.{succ u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.map.{u2, u2, u1, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (LinearEquiv.refl.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) P) Q), Eq.{succ u1} (LinearEquiv.{u2, u2, u1, u1} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) Q) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 P)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) Q) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 Q)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 P) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 Q)) (Submodule.Quotient.equiv.{u2, u1, u1} R M _inst_1 _inst_2 _inst_3 M _inst_2 _inst_3 P Q (LinearEquiv.refl.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) hf) (Submodule.quotEquivOfEq.{u2, u1} R M _inst_1 _inst_2 _inst_3 P Q (Eq.mp.{0} (Eq.{succ u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.map.{u2, u2, u1, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearMap.id.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) P) Q) (Eq.{succ u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) P Q) (congrFun.{succ u1, 1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (a._@.Init.Prelude._hyg.170 : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Prop) (Eq.{succ u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.map.{u2, u2, u1, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearMap.id.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) P)) (Eq.{succ u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) P) (congrArg.{succ u1, succ u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) ((Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) -> Prop) (Submodule.map.{u2, u2, u1, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearMap.id.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) P) P (Eq.{succ u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) (Submodule.map_id.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 P)) Q) hf))
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (P : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Q : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (hf : Eq.{succ u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.map.{u2, u2, u1, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (LinearEquiv.refl.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) P) Q), Eq.{succ u1} (LinearEquiv.{u2, u2, u1, u1} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) Q) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) P) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 P)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) Q) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 Q)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 P) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 Q)) (Submodule.Quotient.equiv.{u2, u1, u1} R M _inst_1 _inst_2 _inst_3 M _inst_2 _inst_3 P Q (LinearEquiv.refl.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) hf) (Submodule.quotEquivOfEq.{u2, u1} R M _inst_1 _inst_2 _inst_3 P Q (Eq.mp.{0} (Eq.{succ u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.map.{u2, u2, u1, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearMap.id.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) P) Q) (Eq.{succ u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) P Q) (congrFun.{succ u1, 1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (a._@.Init.Prelude._hyg.170 : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Prop) (Eq.{succ u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.map.{u2, u2, u1, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearMap.id.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) P)) (Eq.{succ u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) P) (congrArg.{succ u1, succ u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) ((Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) -> Prop) (Submodule.map.{u2, u2, u1, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearMap.id.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) P) P (Eq.{succ u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) (Submodule.map_id.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 P)) Q) hf))
Case conversion may be inaccurate. Consider using '#align submodule.quotient.equiv_refl Submodule.Quotient.equiv_reflₓ'. -/
@[simp]
theorem Quotient.equiv_refl (P : Submodule R M) (Q : Submodule R M)
mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
@@ -394,7 +394,7 @@ theorem mk_surjective : Function.Surjective (@mk _ _ _ _ _ p) :=
/- warning: submodule.quotient.nontrivial_of_lt_top -> Submodule.Quotient.nontrivial_of_lt_top is a dubious translation:
lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), (LT.lt.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLT.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) -> (Nontrivial.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p))
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), (LT.lt.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLt.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) -> (Nontrivial.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p))
but is expected to have type
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), (LT.lt.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLT.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) -> (Nontrivial.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p))
Case conversion may be inaccurate. Consider using '#align submodule.quotient.nontrivial_of_lt_top Submodule.Quotient.nontrivial_of_lt_topₓ'. -/
@@ -555,7 +555,7 @@ theorem linearMap_qext ⦃f g : M ⧸ p →ₛₗ[τ₁₂] M₂⦄ (h : f.comp
/- warning: submodule.liftq -> Submodule.liftQ is a dubious translation:
lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6), (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)) -> (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6)
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6), (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)) -> (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6)
but is expected to have type
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6), (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)) -> (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6)
Case conversion may be inaccurate. Consider using '#align submodule.liftq Submodule.liftQₓ'. -/
@@ -568,7 +568,7 @@ def liftQ (f : M →ₛₗ[τ₁₂] M₂) (h : p ≤ f.ker) : M ⧸ p →ₛₗ
/- warning: submodule.liftq_apply -> Submodule.liftQ_apply is a dubious translation:
lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) {h : LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)} (x : M), Eq.{succ u4} M₂ (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) (fun (_x : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) => (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) -> M₂) (LinearMap.hasCoeToFun.{u1, u3, u2, u4} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) (Submodule.liftQ.{u1, u2, u3, u4} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x)) (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f x)
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) {h : LE.le.{u2} (Submodule.{u1, u2} R M 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but is expected to have type
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Case conversion may be inaccurate. Consider using '#align submodule.liftq_apply Submodule.liftQ_applyₓ'. -/
@@ -579,7 +579,7 @@ theorem liftQ_apply (f : M →ₛₗ[τ₁₂] M₂) {h} (x : M) : p.liftQ f h (
/- warning: submodule.liftq_mkq -> Submodule.liftQ_mkQ is a dubious translation:
lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (h : LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)), Eq.{max (succ u2) (succ u4)} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.comp.{u1, u1, u3, u2, u2, u4} R R R₂ M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) τ₁₂ τ₁₂ (RingHomCompTriple.ids.{u1, u3} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂) (Submodule.liftQ.{u1, u2, u3, u4} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) f
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (h : LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)), Eq.{max (succ u2) (succ u4)} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.comp.{u1, u1, u3, u2, u2, u4} R R R₂ M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) τ₁₂ τ₁₂ (RingHomCompTriple.ids.{u1, u3} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂) (Submodule.liftQ.{u1, u2, u3, u4} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) f
but is expected to have type
forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (h : LE.le.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (LinearMap.ker.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)), Eq.{max (succ u2) (succ u1)} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.comp.{u4, u4, u3, u2, u2, u1} R R R₂ M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) τ₁₂ τ₁₂ (RingHomCompTriple.ids.{u4, u3} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂) (Submodule.liftQ.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h) (Submodule.mkQ.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) f
Case conversion may be inaccurate. Consider using '#align submodule.liftq_mkq Submodule.liftQ_mkQₓ'. -/
@@ -634,7 +634,7 @@ theorem ker_mkQ : p.mkQ.ker = p := by ext <;> simp
/- warning: submodule.le_comap_mkq -> Submodule.le_comap_mkQ is a dubious translation:
lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (p' : Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)), LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) p')
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (p' : Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)), LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) p')
but is expected to have type
forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (p : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (p' : Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)), LE.le.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) p (Submodule.comap.{u2, u2, u1, u1, u1} R R M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} 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))) M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.mkQ.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) p')
Case conversion may be inaccurate. Consider using '#align submodule.le_comap_mkq Submodule.le_comap_mkQₓ'. -/
@@ -678,7 +678,7 @@ variable (q : Submodule R₂ M₂)
/- warning: submodule.mapq -> Submodule.mapQ is a dubious translation:
lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (q : Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6), (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f q)) -> (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q))
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (q : Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6), (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f q)) -> (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q))
but is expected to have type
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (q : Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6), (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f q)) -> (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q))
Case conversion may be inaccurate. Consider using '#align submodule.mapq Submodule.mapQₓ'. -/
@@ -690,7 +690,7 @@ def mapQ (f : M →ₛₗ[τ₁₂] M₂) (h : p ≤ comap f q) : M ⧸ p →ₛ
/- warning: submodule.mapq_apply -> Submodule.mapQ_apply is a dubious translation:
lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (q : Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) {h : LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f q)} (x : M), Eq.{succ u4} (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) 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+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (q : Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) 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(Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f x))
but is expected to have type
forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (q : Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) {h : LE.le.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (Submodule.comap.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f q)} (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) => HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.mk.{u4, u2} R M _inst_1 _inst_2 _inst_3 p x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (fun (_x : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) => HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q) τ₁₂) (Submodule.mapQ.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ q f h) (Submodule.Quotient.mk.{u4, u2} R M _inst_1 _inst_2 _inst_3 p x)) (Submodule.Quotient.mk.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f x))
Case conversion may be inaccurate. Consider using '#align submodule.mapq_apply Submodule.mapQ_applyₓ'. -/
@@ -702,7 +702,7 @@ theorem mapQ_apply (f : M →ₛₗ[τ₁₂] M₂) {h} (x : M) :
/- warning: submodule.mapq_mkq -> Submodule.mapQ_mkQ is a dubious translation:
lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (q : Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) {h : LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f q)}, Eq.{max (succ u2) (succ u4)} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) _inst_3 (Submodule.Quotient.module.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (LinearMap.comp.{u1, u1, u3, u2, u2, u4} R R R₂ M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) τ₁₂ τ₁₂ (RingHomCompTriple.ids.{u1, u3} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂) (Submodule.mapQ.{u1, u2, u3, u4} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ q f h) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.comp.{u1, u3, u3, u2, u4, u4} R R₂ R₂ M M₂ (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u4} (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) _inst_3 _inst_6 (Submodule.Quotient.module.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q) τ₁₂ (RingHom.id.{u3} R₂ (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))) τ₁₂ (RingHomCompTriple.right_ids.{u1, u3} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂) (Submodule.mkQ.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q) f)
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (q : Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) {h : LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f q)}, Eq.{max (succ u2) (succ u4)} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) _inst_3 (Submodule.Quotient.module.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (LinearMap.comp.{u1, u1, u3, u2, u2, u4} R R R₂ M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) τ₁₂ τ₁₂ (RingHomCompTriple.ids.{u1, u3} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂) (Submodule.mapQ.{u1, u2, u3, u4} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ q f h) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.comp.{u1, u3, u3, u2, u4, u4} R R₂ R₂ M M₂ (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u4} (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) _inst_3 _inst_6 (Submodule.Quotient.module.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q) τ₁₂ (RingHom.id.{u3} R₂ (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))) τ₁₂ (RingHomCompTriple.right_ids.{u1, u3} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂) (Submodule.mkQ.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q) f)
but is expected to have type
forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (q : Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) {h : LE.le.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (Submodule.comap.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f q)}, Eq.{max (succ u2) (succ u1)} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) _inst_3 (Submodule.Quotient.module.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (LinearMap.comp.{u4, u4, u3, u2, u2, u1} R R R₂ M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) _inst_3 (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) τ₁₂ τ₁₂ (RingHomCompTriple.ids.{u4, u3} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂) (Submodule.mapQ.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ q f h) (Submodule.mkQ.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.comp.{u4, u3, u3, u2, u1, u1} R R₂ R₂ M M₂ (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) _inst_3 _inst_6 (Submodule.Quotient.module.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q) τ₁₂ (RingHom.id.{u3} R₂ (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))) τ₁₂ (RingHomCompTriple.right_ids.{u4, u3} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂) (Submodule.mkQ.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q) f)
Case conversion may be inaccurate. Consider using '#align submodule.mapq_mkq Submodule.mapQ_mkQₓ'. -/
@@ -712,7 +712,7 @@ theorem mapQ_mkQ (f : M →ₛₗ[τ₁₂] M₂) {h} : (mapQ p q f h).comp p.mk
/- warning: submodule.mapq_zero -> Submodule.mapQ_zero is a dubious translation:
lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (q : Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (h : optParam.{0} (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) (OfNat.ofNat.{max u2 u4} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) 0 (OfNat.mk.{max u2 u4} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) 0 (Zero.zero.{max u2 u4} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.hasZero.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂)))) q)) (Eq.mpr.{0} (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) (OfNat.ofNat.{max u2 u4} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) 0 (OfNat.mk.{max u2 u4} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) 0 (Zero.zero.{max u2 u4} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.hasZero.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂)))) q)) True (id_tag Tactic.IdTag.simp (Eq.{1} Prop (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) (OfNat.ofNat.{max u2 u4} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) 0 (OfNat.mk.{max u2 u4} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) 0 (Zero.zero.{max u2 u4} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.hasZero.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂)))) q)) True) (Eq.trans.{1} Prop (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ 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_inst_3)))) p (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) True ((fun [self : LE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)] (ᾰ : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ᾰ_1 : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (e_2 : Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ᾰ ᾰ_1) (ᾰ_2 : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ᾰ_3 : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) 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(Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p p (rfl.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p) (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) (OfNat.ofNat.{max u2 u4} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) 0 (OfNat.mk.{max u2 u4} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) 0 (Zero.zero.{max u2 u4} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.hasZero.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂)))) q) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (Submodule.comap_zero.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ q)) (propext (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OrderTop.toHasTop.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (Submodule.orderTop.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) True ((fun {α : Type.{u2}} [_inst_1 : LE.{u2} α] [_inst_2 : OrderTop.{u2} α _inst_1] {a : α} => iff_true_intro (LE.le.{u2} α _inst_1 a (Top.top.{u2} α (OrderTop.toHasTop.{u2} α _inst_1 _inst_2))) (le_top.{u2} α _inst_1 _inst_2 a)) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (Submodule.orderTop.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p)))) trivial)), Eq.{max (succ u2) (succ u4)} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.mapQ.{u1, u2, u3, u4} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ q (OfNat.ofNat.{max u2 u4} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) 0 (OfNat.mk.{max u2 u4} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) 0 (Zero.zero.{max u2 u4} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.hasZero.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂)))) h) (OfNat.ofNat.{max u2 u4} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) 0 (OfNat.mk.{max u2 u4} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) 0 (Zero.zero.{max u2 u4} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (LinearMap.hasZero.{u1, u3, u2, u4} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q) τ₁₂))))
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (q : Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (h : optParam.{0} (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) (OfNat.ofNat.{max u2 u4} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) 0 (OfNat.mk.{max u2 u4} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) 0 (Zero.zero.{max u2 u4} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.hasZero.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂)))) q)) (Eq.mpr.{0} (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) (OfNat.ofNat.{max u2 u4} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) 0 (OfNat.mk.{max u2 u4} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) 0 (Zero.zero.{max u2 u4} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.hasZero.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂)))) q)) True (id_tag Tactic.IdTag.simp (Eq.{1} Prop (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) 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(LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) 0 (OfNat.mk.{max u2 u4} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) 0 (Zero.zero.{max u2 u4} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.hasZero.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂)))) q)) True) (Eq.trans.{1} Prop (LE.le.{u2} (Submodule.{u1, u2} R M 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_inst_3)))) p (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) True ((fun [self : LE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)] (ᾰ : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ᾰ_1 : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (e_2 : Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ᾰ ᾰ_1) (ᾰ_2 : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ᾰ_3 : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) (OfNat.ofNat.{max u2 u4} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) 0 (OfNat.mk.{max u2 u4} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) 0 (Zero.zero.{max u2 u4} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ 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R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (Submodule.orderTop.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p)))) trivial)), Eq.{max (succ u2) (succ u4)} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ 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(AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (LinearMap.hasZero.{u1, u3, u2, u4} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q) τ₁₂))))
but is expected to have type
forall {R : Type.{u3}} {M : Type.{u4}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u4} M] [_inst_3 : Module.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2)] (p : Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) {R₂ : Type.{u2}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u2} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u2, u1} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u3, u2} R R₂ (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R₂ (Ring.toSemiring.{u2} R₂ _inst_4))} (q : Submodule.{u2, u1} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (h : optParam.{0} (LE.le.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Preorder.toLE.{u4} (Submodule.{u3, 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(Submodule.hasQuotient.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.Quotient.module.{u3, u4} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.mapQ.{u3, u4, u2, u1} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ q (OfNat.ofNat.{max u4 u1} (LinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) 0 (Zero.toOfNat0.{max u4 u1} (LinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instZeroLinearMap.{u3, u2, u4, u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂))) h) (OfNat.ofNat.{max u4 u1} (LinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u4} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u2, u1} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (AddCommGroup.toAddCommMonoid.{u4} (HasQuotient.Quotient.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u4} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u4} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u2, u1} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.Quotient.module.{u3, u4} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) 0 (Zero.toOfNat0.{max u4 u1} (LinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u4} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u2, u1} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (AddCommGroup.toAddCommMonoid.{u4} (HasQuotient.Quotient.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u4} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u4} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u2, u1} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.Quotient.module.{u3, u4} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (LinearMap.instZeroLinearMap.{u3, u2, u4, u1} R R₂ (HasQuotient.Quotient.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u4} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u2, u1} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} (HasQuotient.Quotient.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u4} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u4} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u2, u1} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.Quotient.module.{u3, u4} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q) τ₁₂)))
Case conversion may be inaccurate. Consider using '#align submodule.mapq_zero Submodule.mapQ_zeroₓ'. -/
@@ -725,7 +725,7 @@ theorem mapQ_zero (h : p ≤ q.comap (0 : M →ₛₗ[τ₁₂] M₂) := (by sim
/- warning: submodule.mapq_comp -> Submodule.mapQ_comp is a dubious translation:
lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} {R₃ : Type.{u5}} {M₃ : Type.{u6}} [_inst_7 : Ring.{u5} R₃] [_inst_8 : AddCommGroup.{u6} M₃] [_inst_9 : Module.{u5, u6} R₃ M₃ (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8)] (p₂ : Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (p₃ : Submodule.{u5, u6} R₃ M₃ (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_9) {τ₂₃ : RingHom.{u3, u5} R₂ R₃ (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4)) (NonAssocRing.toNonAssocSemiring.{u5} R₃ (Ring.toNonAssocRing.{u5} R₃ _inst_7))} {τ₁₃ : RingHom.{u1, u5} R R₃ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u5} R₃ (Ring.toNonAssocRing.{u5} R₃ _inst_7))} [_inst_10 : RingHomCompTriple.{u1, u3, u5} R R₂ R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) τ₁₂ τ₂₃ τ₁₃] (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (g : LinearMap.{u3, u5, u4, u6} R₂ R₃ (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_6 _inst_9) (hf : LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f p₂)) (hg : LE.le.{u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Preorder.toLE.{u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (PartialOrder.toPreorder.{u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (SetLike.partialOrder.{u4, u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) M₂ (Submodule.setLike.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6)))) p₂ (Submodule.comap.{u3, u5, u4, u6, max u4 u6} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_6 _inst_9 τ₂₃ (LinearMap.{u3, u5, u4, u6} R₂ R₃ (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_6 _inst_9) (LinearMap.semilinearMapClass.{u3, u5, u4, u6} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_6 _inst_9 τ₂₃) g p₃)) (h : optParam.{0} (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f (Submodule.comap.{u3, u5, u4, u6, max u4 u6} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_6 _inst_9 τ₂₃ (LinearMap.{u3, u5, u4, u6} R₂ R₃ (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_6 _inst_9) (LinearMap.semilinearMapClass.{u3, u5, u4, u6} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_6 _inst_9 τ₂₃) g p₃))) (LE.le.trans.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) p (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f p₂) (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f (Submodule.comap.{u3, u5, u4, u6, max u4 u6} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_6 _inst_9 τ₂₃ (LinearMap.{u3, u5, u4, u6} R₂ R₃ (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_6 _inst_9) (LinearMap.semilinearMapClass.{u3, u5, u4, u6} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_6 _inst_9 τ₂₃) g p₃)) hf (Submodule.comap_mono.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f p₂ (Submodule.comap.{u3, u5, u4, u6, max u4 u6} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_6 _inst_9 τ₂₃ (LinearMap.{u3, u5, u4, u6} R₂ R₃ (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_6 _inst_9) (LinearMap.semilinearMapClass.{u3, u5, u4, u6} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_6 _inst_9 τ₂₃) g p₃) hg))), Eq.{max (succ u2) (succ u6)} (LinearMap.{u1, u5, u2, u6} R R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u5} R₃ _inst_7) τ₁₃ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u6, u6} M₃ (Submodule.{u5, u6} R₃ M₃ (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_9) (Submodule.hasQuotient.{u5, u6} R₃ M₃ _inst_7 _inst_8 _inst_9) p₃) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u6} (HasQuotient.Quotient.{u6, u6} M₃ (Submodule.{u5, u6} R₃ M₃ (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_9) (Submodule.hasQuotient.{u5, u6} R₃ M₃ _inst_7 _inst_8 _inst_9) p₃) (Submodule.Quotient.addCommGroup.{u5, u6} R₃ M₃ _inst_7 _inst_8 _inst_9 p₃)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u5, u6} R₃ M₃ _inst_7 _inst_8 _inst_9 p₃)) (Submodule.mapQ.{u1, u2, u5, u6} R M _inst_1 _inst_2 _inst_3 p R₃ M₃ _inst_7 _inst_8 _inst_9 τ₁₃ p₃ (LinearMap.comp.{u1, u3, u5, u2, u4, u6} R R₂ R₃ M M₂ M₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_3 _inst_6 _inst_9 τ₁₂ τ₂₃ τ₁₃ _inst_10 g f) h) (LinearMap.comp.{u1, u3, u5, u2, u4, u6} R R₂ R₃ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) p₂) (HasQuotient.Quotient.{u6, u6} M₃ (Submodule.{u5, u6} R₃ M₃ (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_9) (Submodule.hasQuotient.{u5, u6} R₃ M₃ _inst_7 _inst_8 _inst_9) p₃) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) p₂) (Submodule.Quotient.addCommGroup.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 p₂)) (AddCommGroup.toAddCommMonoid.{u6} (HasQuotient.Quotient.{u6, u6} M₃ (Submodule.{u5, u6} R₃ M₃ (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_9) (Submodule.hasQuotient.{u5, u6} R₃ M₃ _inst_7 _inst_8 _inst_9) p₃) (Submodule.Quotient.addCommGroup.{u5, u6} R₃ M₃ _inst_7 _inst_8 _inst_9 p₃)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 p₂) (Submodule.Quotient.module.{u5, u6} R₃ M₃ _inst_7 _inst_8 _inst_9 p₃) τ₁₂ τ₂₃ τ₁₃ _inst_10 (Submodule.mapQ.{u3, u4, u5, u6} R₂ M₂ _inst_4 _inst_5 _inst_6 p₂ R₃ M₃ _inst_7 _inst_8 _inst_9 τ₂₃ p₃ g hg) (Submodule.mapQ.{u1, u2, u3, u4} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ p₂ f hf))
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} {R₃ : Type.{u5}} {M₃ : Type.{u6}} [_inst_7 : Ring.{u5} R₃] [_inst_8 : AddCommGroup.{u6} M₃] [_inst_9 : Module.{u5, u6} R₃ M₃ (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8)] (p₂ : Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (p₃ : Submodule.{u5, u6} R₃ M₃ (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_9) {τ₂₃ : RingHom.{u3, u5} R₂ R₃ (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4)) (NonAssocRing.toNonAssocSemiring.{u5} R₃ (Ring.toNonAssocRing.{u5} R₃ _inst_7))} {τ₁₃ : RingHom.{u1, u5} R R₃ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u5} R₃ (Ring.toNonAssocRing.{u5} R₃ _inst_7))} [_inst_10 : RingHomCompTriple.{u1, u3, u5} R R₂ R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) τ₁₂ τ₂₃ τ₁₃] (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (g : LinearMap.{u3, u5, u4, u6} R₂ R₃ (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_6 _inst_9) (hf : LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f p₂)) (hg : LE.le.{u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Preorder.toHasLe.{u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (PartialOrder.toPreorder.{u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (SetLike.partialOrder.{u4, u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) M₂ (Submodule.setLike.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6)))) p₂ (Submodule.comap.{u3, u5, u4, u6, max u4 u6} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_6 _inst_9 τ₂₃ (LinearMap.{u3, u5, u4, u6} R₂ R₃ (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_6 _inst_9) (LinearMap.semilinearMapClass.{u3, u5, u4, u6} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_6 _inst_9 τ₂₃) g p₃)) (h : optParam.{0} (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f (Submodule.comap.{u3, u5, u4, u6, max u4 u6} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_6 _inst_9 τ₂₃ (LinearMap.{u3, u5, u4, u6} R₂ R₃ (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_6 _inst_9) (LinearMap.semilinearMapClass.{u3, u5, u4, u6} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_6 _inst_9 τ₂₃) g p₃))) (LE.le.trans.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) p (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f p₂) (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f (Submodule.comap.{u3, u5, u4, u6, max u4 u6} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_6 _inst_9 τ₂₃ (LinearMap.{u3, u5, u4, u6} R₂ R₃ (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_6 _inst_9) (LinearMap.semilinearMapClass.{u3, u5, u4, u6} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_6 _inst_9 τ₂₃) g p₃)) hf (Submodule.comap_mono.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f p₂ (Submodule.comap.{u3, u5, u4, u6, max u4 u6} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_6 _inst_9 τ₂₃ (LinearMap.{u3, u5, u4, u6} R₂ R₃ (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_6 _inst_9) (LinearMap.semilinearMapClass.{u3, u5, u4, u6} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_6 _inst_9 τ₂₃) g p₃) hg))), Eq.{max (succ u2) (succ u6)} (LinearMap.{u1, u5, u2, u6} R R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u5} R₃ _inst_7) τ₁₃ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u6, u6} M₃ (Submodule.{u5, u6} R₃ M₃ (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_9) (Submodule.hasQuotient.{u5, u6} R₃ M₃ _inst_7 _inst_8 _inst_9) p₃) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u6} (HasQuotient.Quotient.{u6, u6} M₃ (Submodule.{u5, u6} R₃ M₃ (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_9) (Submodule.hasQuotient.{u5, u6} R₃ M₃ _inst_7 _inst_8 _inst_9) p₃) (Submodule.Quotient.addCommGroup.{u5, u6} R₃ M₃ _inst_7 _inst_8 _inst_9 p₃)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u5, u6} R₃ M₃ _inst_7 _inst_8 _inst_9 p₃)) (Submodule.mapQ.{u1, u2, u5, u6} R M _inst_1 _inst_2 _inst_3 p R₃ M₃ _inst_7 _inst_8 _inst_9 τ₁₃ p₃ (LinearMap.comp.{u1, u3, u5, u2, u4, u6} R R₂ R₃ M M₂ M₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_3 _inst_6 _inst_9 τ₁₂ τ₂₃ τ₁₃ _inst_10 g f) h) (LinearMap.comp.{u1, u3, u5, u2, u4, u6} R R₂ R₃ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) p₂) (HasQuotient.Quotient.{u6, u6} M₃ (Submodule.{u5, u6} R₃ M₃ (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_9) (Submodule.hasQuotient.{u5, u6} R₃ M₃ _inst_7 _inst_8 _inst_9) p₃) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) p₂) (Submodule.Quotient.addCommGroup.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 p₂)) (AddCommGroup.toAddCommMonoid.{u6} (HasQuotient.Quotient.{u6, u6} M₃ (Submodule.{u5, u6} R₃ M₃ (Ring.toSemiring.{u5} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_8) _inst_9) (Submodule.hasQuotient.{u5, u6} R₃ M₃ _inst_7 _inst_8 _inst_9) p₃) (Submodule.Quotient.addCommGroup.{u5, u6} R₃ M₃ _inst_7 _inst_8 _inst_9 p₃)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 p₂) (Submodule.Quotient.module.{u5, u6} R₃ M₃ _inst_7 _inst_8 _inst_9 p₃) τ₁₂ τ₂₃ τ₁₃ _inst_10 (Submodule.mapQ.{u3, u4, u5, u6} R₂ M₂ _inst_4 _inst_5 _inst_6 p₂ R₃ M₃ _inst_7 _inst_8 _inst_9 τ₂₃ p₃ g hg) (Submodule.mapQ.{u1, u2, u3, u4} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ p₂ f hf))
but is expected to have type
forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (p : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) {R₂ : Type.{u4}} {M₂ : Type.{u3}} [_inst_4 : Ring.{u4} R₂] [_inst_5 : AddCommGroup.{u3} M₂] [_inst_6 : Module.{u4, u3} R₂ M₂ (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5)] {τ₁₂ : RingHom.{u2, u4} R R₂ (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} R₂ (Ring.toSemiring.{u4} R₂ _inst_4))} {R₃ : Type.{u6}} {M₃ : Type.{u5}} [_inst_7 : Ring.{u6} R₃] [_inst_8 : AddCommGroup.{u5} M₃] [_inst_9 : Module.{u6, u5} R₃ M₃ (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8)] (p₂ : Submodule.{u4, u3} R₂ M₂ (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) (p₃ : Submodule.{u6, u5} R₃ M₃ (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_9) {τ₂₃ : RingHom.{u4, u6} R₂ R₃ (Semiring.toNonAssocSemiring.{u4} R₂ (Ring.toSemiring.{u4} R₂ _inst_4)) (Semiring.toNonAssocSemiring.{u6} R₃ (Ring.toSemiring.{u6} R₃ _inst_7))} {τ₁₃ : RingHom.{u2, u6} R R₃ (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u6} R₃ (Ring.toSemiring.{u6} R₃ _inst_7))} [_inst_10 : RingHomCompTriple.{u2, u4, u6} R R₂ R₃ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) τ₁₂ τ₂₃ τ₁₃] (f : LinearMap.{u2, u4, u1, u3} R R₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6) (g : LinearMap.{u4, u6, u3, u5} R₂ R₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9) (hf : LE.le.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) p (Submodule.comap.{u2, u4, u1, u3, max u1 u3} R R₂ M M₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u2, u4, u1, u3} R R₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u2, u4, u1, u3} R R₂ M M₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f p₂)) (hg : LE.le.{u3} (Submodule.{u4, u3} R₂ M₂ (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) (Preorder.toLE.{u3} (Submodule.{u4, u3} R₂ M₂ (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) (PartialOrder.toPreorder.{u3} (Submodule.{u4, u3} R₂ M₂ (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u4, u3} R₂ M₂ (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u4, u3} R₂ M₂ (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) (Submodule.completeLattice.{u4, u3} R₂ M₂ (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6))))) p₂ (Submodule.comap.{u4, u6, u3, u5, max u3 u5} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9 τ₂₃ (LinearMap.{u4, u6, u3, u5} R₂ R₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9) (LinearMap.instSemilinearMapClassLinearMap.{u4, u6, u3, u5} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9 τ₂₃) g p₃)) (h : optParam.{0} (LE.le.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) p (Submodule.comap.{u2, u4, u1, u3, max u1 u3} R R₂ M M₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u2, u4, u1, u3} R R₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u2, u4, u1, u3} R R₂ M M₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f (Submodule.comap.{u4, u6, u3, u5, max u3 u5} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9 τ₂₃ (LinearMap.{u4, u6, u3, u5} R₂ R₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9) (LinearMap.instSemilinearMapClassLinearMap.{u4, u6, u3, u5} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9 τ₂₃) g p₃))) (LE.le.trans.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) p (Submodule.comap.{u2, u4, u1, u3, max u1 u3} R R₂ M M₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u2, u4, u1, u3} R R₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u2, u4, u1, u3} R R₂ M M₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f p₂) (Submodule.comap.{u2, u4, u1, u3, max u1 u3} R R₂ M M₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u2, u4, u1, u3} R R₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u2, u4, u1, u3} R R₂ M M₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f (Submodule.comap.{u4, u6, u3, u5, max u3 u5} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9 τ₂₃ (LinearMap.{u4, u6, u3, u5} R₂ R₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9) (LinearMap.instSemilinearMapClassLinearMap.{u4, u6, u3, u5} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9 τ₂₃) g p₃)) hf (Submodule.comap_mono.{max u1 u3, u2, u1, u3, u4} R R₂ M M₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u2, u4, u1, u3} R R₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u2, u4, u1, u3} R R₂ M M₂ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f p₂ (Submodule.comap.{u4, u6, u3, u5, max u3 u5} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9 τ₂₃ (LinearMap.{u4, u6, u3, u5} R₂ R₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9) (LinearMap.instSemilinearMapClassLinearMap.{u4, u6, u3, u5} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_6 _inst_9 τ₂₃) g p₃) hg))), Eq.{max (succ u1) (succ u5)} (LinearMap.{u2, u6, u1, u5} R R₃ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u6} R₃ _inst_7) τ₁₃ (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u5, u5} M₃ (Submodule.{u6, u5} R₃ M₃ (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_9) (Submodule.hasQuotient.{u6, u5} R₃ M₃ _inst_7 _inst_8 _inst_9) p₃) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u5} (HasQuotient.Quotient.{u5, u5} M₃ (Submodule.{u6, u5} R₃ M₃ (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_9) (Submodule.hasQuotient.{u6, u5} R₃ M₃ _inst_7 _inst_8 _inst_9) p₃) (Submodule.Quotient.addCommGroup.{u6, u5} R₃ M₃ _inst_7 _inst_8 _inst_9 p₃)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u6, u5} R₃ M₃ _inst_7 _inst_8 _inst_9 p₃)) (Submodule.mapQ.{u2, u1, u6, u5} R M _inst_1 _inst_2 _inst_3 p R₃ M₃ _inst_7 _inst_8 _inst_9 τ₁₃ p₃ (LinearMap.comp.{u2, u4, u6, u1, u3, u5} R R₂ R₃ M M₂ M₃ (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_3 _inst_6 _inst_9 τ₁₂ τ₂₃ τ₁₃ _inst_10 g f) h) (LinearMap.comp.{u2, u4, u6, u1, u3, u5} R R₂ R₃ (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u3, u3} M₂ (Submodule.{u4, u3} R₂ M₂ (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u4, u3} R₂ M₂ _inst_4 _inst_5 _inst_6) p₂) (HasQuotient.Quotient.{u5, u5} M₃ (Submodule.{u6, u5} R₃ M₃ (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_9) (Submodule.hasQuotient.{u6, u5} R₃ M₃ _inst_7 _inst_8 _inst_9) p₃) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} R₂ _inst_4) (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u3} (HasQuotient.Quotient.{u3, u3} M₂ (Submodule.{u4, u3} R₂ M₂ (Ring.toSemiring.{u4} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u4, u3} R₂ M₂ _inst_4 _inst_5 _inst_6) p₂) (Submodule.Quotient.addCommGroup.{u4, u3} R₂ M₂ _inst_4 _inst_5 _inst_6 p₂)) (AddCommGroup.toAddCommMonoid.{u5} (HasQuotient.Quotient.{u5, u5} M₃ (Submodule.{u6, u5} R₃ M₃ (Ring.toSemiring.{u6} R₃ _inst_7) (AddCommGroup.toAddCommMonoid.{u5} M₃ _inst_8) _inst_9) (Submodule.hasQuotient.{u6, u5} R₃ M₃ _inst_7 _inst_8 _inst_9) p₃) (Submodule.Quotient.addCommGroup.{u6, u5} R₃ M₃ _inst_7 _inst_8 _inst_9 p₃)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u4, u3} R₂ M₂ _inst_4 _inst_5 _inst_6 p₂) (Submodule.Quotient.module.{u6, u5} R₃ M₃ _inst_7 _inst_8 _inst_9 p₃) τ₁₂ τ₂₃ τ₁₃ _inst_10 (Submodule.mapQ.{u4, u3, u6, u5} R₂ M₂ _inst_4 _inst_5 _inst_6 p₂ R₃ M₃ _inst_7 _inst_8 _inst_9 τ₂₃ p₃ g hg) (Submodule.mapQ.{u2, u1, u4, u3} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ p₂ f hf))
Case conversion may be inaccurate. Consider using '#align submodule.mapq_comp Submodule.mapQ_compₓ'. -/
@@ -744,7 +744,7 @@ theorem mapQ_comp {R₃ M₃ : Type _} [Ring R₃] [AddCommGroup M₃] [Module R
/- warning: submodule.mapq_id -> Submodule.mapQ_id is a dubious translation:
lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (h : optParam.{0} (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p)) (Eq.mpr.{0} (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p)) (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p p) (id_tag Tactic.IdTag.rw (Eq.{1} Prop (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p)) (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p p)) (Eq.ndrec.{0, succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.comap.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p) (fun (_a : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => Eq.{1} Prop (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p)) (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p _a)) (rfl.{1} Prop (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p))) p (Submodule.comap_id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 p))) (le_refl.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) p))), Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.mapQ.{u1, u2, u1, u2} R M _inst_1 _inst_2 _inst_3 p R M _inst_1 _inst_2 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) p (LinearMap.id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) h) (LinearMap.id.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p))
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (h : optParam.{0} (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p)) (Eq.mpr.{0} (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p)) (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p p) (id_tag Tactic.IdTag.rw (Eq.{1} Prop (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p)) (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p p)) (Eq.ndrec.{0, succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.comap.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p) (fun (_a : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => Eq.{1} Prop (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p)) (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p _a)) (rfl.{1} Prop (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p))) p (Submodule.comap_id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 p))) (le_refl.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) p))), Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.mapQ.{u1, u2, u1, u2} R M _inst_1 _inst_2 _inst_3 p R M _inst_1 _inst_2 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) p (LinearMap.id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) h) (LinearMap.id.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p))
but is expected to have type
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (h : optParam.{0} (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (Submodule.comap.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p)) (Eq.mpr.{0} (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) 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(Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M 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(Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p) (fun (_a : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => Eq.{1} Prop (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M 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R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p)) (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) 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(Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 p))) (le_refl.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p))), Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.mapQ.{u1, u2, u1, u2} R M _inst_1 _inst_2 _inst_3 p R M _inst_1 _inst_2 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) p (LinearMap.id.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) h) (LinearMap.id.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p))
Case conversion may be inaccurate. Consider using '#align submodule.mapq_id Submodule.mapQ_idₓ'. -/
@@ -761,7 +761,7 @@ theorem mapQ_id
/- warning: submodule.mapq_pow -> Submodule.mapQ_pow is a dubious translation:
lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3} (h : LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f p)) (k : Nat) (h' : optParam.{0} (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (HPow.hPow.{u2, 0, u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) Nat (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (instHPow.{u2, 0} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) Nat (Monoid.Pow.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.monoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) f k) p)) (Submodule.le_comap_pow_of_le_comap.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 p f h k)), Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.mapQ.{u1, u2, u1, u2} R M _inst_1 _inst_2 _inst_3 p R M _inst_1 _inst_2 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) p (HPow.hPow.{u2, 0, u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) Nat (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (instHPow.{u2, 0} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) Nat (Monoid.Pow.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.monoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) f k) h') (HPow.hPow.{u2, 0, u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) Nat (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (instHPow.{u2, 0} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) Nat (Monoid.Pow.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Module.End.monoid.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)))) (Submodule.mapQ.{u1, u2, u1, u2} R M _inst_1 _inst_2 _inst_3 p R M _inst_1 _inst_2 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) p f h) k)
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3} (h : LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f p)) (k : Nat) (h' : optParam.{0} (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (HPow.hPow.{u2, 0, u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) Nat (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (instHPow.{u2, 0} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) Nat (Monoid.Pow.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.monoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) f k) p)) (Submodule.le_comap_pow_of_le_comap.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 p f h k)), Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.mapQ.{u1, u2, u1, u2} R M _inst_1 _inst_2 _inst_3 p R M _inst_1 _inst_2 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) p (HPow.hPow.{u2, 0, u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) Nat (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (instHPow.{u2, 0} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) Nat (Monoid.Pow.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.monoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) f k) h') (HPow.hPow.{u2, 0, u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) Nat (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (instHPow.{u2, 0} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) Nat (Monoid.Pow.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Module.End.monoid.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)))) (Submodule.mapQ.{u1, u2, u1, u2} R M _inst_1 _inst_2 _inst_3 p R M _inst_1 _inst_2 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) p f h) k)
but is expected to have type
forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (p : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) {f : LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3} (h : LE.le.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) p (Submodule.comap.{u2, u2, u1, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f p)) (k : Nat) (h' : optParam.{0} (LE.le.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) p (Submodule.comap.{u2, u2, u1, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (HPow.hPow.{u1, 0, u1} (LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) Nat (LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (instHPow.{u1, 0} (LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) Nat (Monoid.Pow.{u1} (LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.monoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))) f k) p)) (Submodule.le_comap_pow_of_le_comap.{u1, u2} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 p f h k)), Eq.{succ u1} (LinearMap.{u2, u2, u1, u1} 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))) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.mapQ.{u2, u1, u2, u1} R M _inst_1 _inst_2 _inst_3 p R M _inst_1 _inst_2 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) p (HPow.hPow.{u1, 0, u1} (LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) Nat (LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (instHPow.{u1, 0} (LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) Nat (Monoid.Pow.{u1} (LinearMap.{u2, u2, u1, u1} 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))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.monoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))) f k) h') (HPow.hPow.{u1, 0, u1} (LinearMap.{u2, u2, u1, u1} 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))) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) Nat (LinearMap.{u2, u2, u1, u1} 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))) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (instHPow.{u1, 0} (LinearMap.{u2, u2, u1, u1} 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))) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) Nat (Monoid.Pow.{u1} (LinearMap.{u2, u2, u1, u1} 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))) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Module.End.monoid.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)))) (Submodule.mapQ.{u2, u1, u2, u1} R M _inst_1 _inst_2 _inst_3 p R M _inst_1 _inst_2 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) p f h) k)
Case conversion may be inaccurate. Consider using '#align submodule.mapq_pow Submodule.mapQ_powₓ'. -/
@@ -777,7 +777,7 @@ theorem mapQ_pow {f : M →ₗ[R] M} (h : p ≤ p.comap f) (k : ℕ)
/- warning: submodule.comap_liftq -> Submodule.comap_liftQ is a dubious translation:
lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (q : Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (h : LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)), Eq.{succ u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) (Submodule.liftQ.{u1, u2, u3, u4} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h) q) (Submodule.map.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f q))
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (q : Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (h : LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)), Eq.{succ u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) (Submodule.liftQ.{u1, u2, u3, u4} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h) q) (Submodule.map.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f q))
but is expected to have type
forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (q : Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (h : LE.le.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (LinearMap.ker.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)), Eq.{succ u2} (Submodule.{u4, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.comap.{u4, u3, u2, u1, max u2 u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) (Submodule.liftQ.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h) q) (Submodule.map.{u4, u4, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (RingHomSurjective.ids.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u2, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.instSemilinearMapClassLinearMap.{u4, u4, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) (Submodule.mkQ.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.comap.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f q))
Case conversion may be inaccurate. Consider using '#align submodule.comap_liftq Submodule.comap_liftQₓ'. -/
@@ -788,7 +788,7 @@ theorem comap_liftQ (f : M →ₛₗ[τ₁₂] M₂) (h) : q.comap (p.liftQ f h)
/- warning: submodule.map_liftq -> Submodule.map_liftQ is a dubious translation:
lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} [_inst_7 : RingHomSurjective.{u1, u3} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂] (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (h : LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)) (q : Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)), Eq.{succ u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.map.{u1, u3, u2, u4, max u2 u4} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂ _inst_7 (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) (Submodule.liftQ.{u1, u2, u3, u4} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h) q) (Submodule.map.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ _inst_7 (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f (Submodule.comap.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) q))
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} [_inst_7 : RingHomSurjective.{u1, u3} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂] (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (h : LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)) (q : Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)), Eq.{succ u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.map.{u1, u3, u2, u4, max u2 u4} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂ _inst_7 (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) (Submodule.liftQ.{u1, u2, u3, u4} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h) q) (Submodule.map.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ _inst_7 (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f (Submodule.comap.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) q))
but is expected to have type
forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} [_inst_7 : RingHomSurjective.{u4, u3} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (h : LE.le.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (LinearMap.ker.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)) (q : Submodule.{u4, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)), Eq.{succ u1} (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) (Submodule.liftQ.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h) q) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f (Submodule.comap.{u4, u4, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (LinearMap.{u4, u4, u2, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.instSemilinearMapClassLinearMap.{u4, u4, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) (Submodule.mkQ.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) q))
Case conversion may be inaccurate. Consider using '#align submodule.map_liftq Submodule.map_liftQₓ'. -/
@@ -800,7 +800,7 @@ theorem map_liftQ [RingHomSurjective τ₁₂] (f : M →ₛₗ[τ₁₂] M₂)
/- warning: submodule.ker_liftq -> Submodule.ker_liftQ is a dubious translation:
lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (h : LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)), Eq.{succ u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) (Submodule.liftQ.{u1, u2, u3, u4} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h)) (Submodule.map.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f))
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (h : LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)), Eq.{succ u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) (Submodule.liftQ.{u1, u2, u3, u4} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h)) (Submodule.map.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f))
but is expected to have type
forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (h : LE.le.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (LinearMap.ker.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)), Eq.{succ u2} (Submodule.{u4, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.ker.{u4, u3, u2, u1, max u2 u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) (Submodule.liftQ.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h)) (Submodule.map.{u4, u4, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (RingHomSurjective.ids.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u2, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.instSemilinearMapClassLinearMap.{u4, u4, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) (Submodule.mkQ.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) (LinearMap.ker.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f))
Case conversion may be inaccurate. Consider using '#align submodule.ker_liftq Submodule.ker_liftQₓ'. -/
@@ -810,7 +810,7 @@ theorem ker_liftQ (f : M →ₛₗ[τ₁₂] M₂) (h) : ker (p.liftQ f h) = (ke
/- warning: submodule.range_liftq -> Submodule.range_liftQ is a dubious translation:
lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} [_inst_7 : RingHomSurjective.{u1, u3} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂] (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (h : LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)), Eq.{succ u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (LinearMap.range.{u1, u3, u2, u4, max u2 u4} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) _inst_7 (Submodule.liftQ.{u1, u2, u3, u4} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h)) (LinearMap.range.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) _inst_7 f)
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} [_inst_7 : RingHomSurjective.{u1, u3} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂] (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (h : LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)), Eq.{succ u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (LinearMap.range.{u1, u3, u2, u4, max u2 u4} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) _inst_7 (Submodule.liftQ.{u1, u2, u3, u4} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h)) (LinearMap.range.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) _inst_7 f)
but is expected to have type
forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} [_inst_7 : RingHomSurjective.{u4, u3} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (h : LE.le.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (LinearMap.ker.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)), Eq.{succ u1} (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (LinearMap.range.{u4, u3, u2, u1, max u2 u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) _inst_7 (Submodule.liftQ.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h)) (LinearMap.range.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) _inst_7 f)
Case conversion may be inaccurate. Consider using '#align submodule.range_liftq Submodule.range_liftQₓ'. -/
@@ -820,7 +820,7 @@ theorem range_liftQ [RingHomSurjective τ₁₂] (f : M →ₛₗ[τ₁₂] M₂
/- warning: submodule.ker_liftq_eq_bot -> Submodule.ker_liftQ_eq_bot is a dubious translation:
lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (h : LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)), (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f) p) -> (Eq.{succ u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) (Submodule.liftQ.{u1, u2, u3, u4} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h)) (Bot.bot.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.hasBot.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p))))
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (h : LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)), (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f) p) -> (Eq.{succ u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) (Submodule.liftQ.{u1, u2, u3, u4} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h)) (Bot.bot.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.hasBot.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p))))
but is expected to have type
forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (h : LE.le.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (LinearMap.ker.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)), (LE.le.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (LinearMap.ker.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f) p) -> (Eq.{succ u2} (Submodule.{u4, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.ker.{u4, u3, u2, u1, max u2 u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) (Submodule.liftQ.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h)) (Bot.bot.{u2} (Submodule.{u4, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.instBotSubmodule.{u4, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p))))
Case conversion may be inaccurate. Consider using '#align submodule.ker_liftq_eq_bot Submodule.ker_liftQ_eq_botₓ'. -/
@@ -830,7 +830,7 @@ theorem ker_liftQ_eq_bot (f : M →ₛₗ[τ₁₂] M₂) (h) (h' : ker f ≤ p)
/- warning: submodule.comap_mkq.rel_iso -> Submodule.comapMkQRelIso is a dubious translation:
lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), OrderIso.{u2, u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Subtype.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (p' : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p p')) (Preorder.toLE.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.setLike.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p))))) (Subtype.hasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (fun (p' : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p p'))
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), OrderIso.{u2, u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Subtype.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (p' : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p p')) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.setLike.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p))))) (Subtype.hasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (fun (p' : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p p'))
but is expected to have type
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), OrderIso.{u2, u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Subtype.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (p' : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p p')) (Preorder.toLE.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.completeLattice.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)))))) (Subtype.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (fun (p' : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p p'))
Case conversion may be inaccurate. Consider using '#align submodule.comap_mkq.rel_iso Submodule.comapMkQRelIsoₓ'. -/
@@ -847,7 +847,7 @@ def Submodule.comapMkQRelIso : Submodule R (M ⧸ p) ≃o { p' : Submodule R M /
/- warning: submodule.comap_mkq.order_embedding -> Submodule.comapMkQOrderEmbedding is a dubious translation:
lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), OrderEmbedding.{u2, u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.setLike.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p))))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), OrderEmbedding.{u2, u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.setLike.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p))))) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))
but is expected to have type
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), OrderEmbedding.{u2, u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.completeLattice.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)))))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))
Case conversion may be inaccurate. Consider using '#align submodule.comap_mkq.order_embedding Submodule.comapMkQOrderEmbeddingₓ'. -/
@@ -859,7 +859,7 @@ def Submodule.comapMkQOrderEmbedding : Submodule R (M ⧸ p) ↪o Submodule R M
/- warning: submodule.comap_mkq_embedding_eq -> Submodule.comapMkQOrderEmbedding_eq is a dubious translation:
lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (p' : Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)), Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.setLike.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p))))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (fun (_x : RelEmbedding.{u2, u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LE.le.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.setLike.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)))))) (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) => (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) -> (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (RelEmbedding.hasCoeToFun.{u2, u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LE.le.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.setLike.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)))))) (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) (Submodule.comapMkQOrderEmbedding.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) p') (Submodule.comap.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) p')
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (p' : Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)), Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.setLike.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p))))) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (fun (_x : RelEmbedding.{u2, u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LE.le.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M 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_inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) p')
but is expected to have type
forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (p : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (p' : Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)), Eq.{succ u1} ((fun 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(Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} 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))) M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.mkQ.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) p')
Case conversion may be inaccurate. Consider using '#align submodule.comap_mkq_embedding_eq Submodule.comapMkQOrderEmbedding_eqₓ'. -/
@@ -987,7 +987,7 @@ theorem range_mkQ_comp (f : M →ₛₗ[τ₁₂] M₂) : f.range.mkQ.comp f = 0
/- warning: linear_map.ker_le_range_iff -> LinearMap.ker_le_range_iff is a dubious translation:
lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} {R₂ : Type.{u3}} {M₂ : Type.{u4}} {R₃ : Type.{u5}} {M₃ : Type.{u6}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u3} R₂] [_inst_3 : Ring.{u5} R₃] [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : AddCommMonoid.{u6} M₃] [_inst_7 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_8 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] [_inst_9 : Module.{u5, u6} R₃ M₃ (Ring.toSemiring.{u5} R₃ _inst_3) _inst_6] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_2))} {τ₂₃ : RingHom.{u3, u5} R₂ R₃ (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u5} R₃ (Ring.toNonAssocRing.{u5} R₃ _inst_3))} [_inst_11 : RingHomSurjective.{u1, u3} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂] {f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8} {g : LinearMap.{u3, u5, u4, u6} R₂ R₃ (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u5} R₃ _inst_3) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6 _inst_8 _inst_9}, Iff (LE.le.{u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_8) (Preorder.toLE.{u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_8) (PartialOrder.toPreorder.{u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_8) (SetLike.partialOrder.{u4, u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_8) M₂ (Submodule.setLike.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_8)))) (LinearMap.ker.{u3, u5, u4, u6, max u4 u6} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u5} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃ (LinearMap.{u3, u5, u4, u6} R₂ R₃ (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u5} R₃ _inst_3) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6 _inst_8 _inst_9) (LinearMap.semilinearMapClass.{u3, u5, u4, u6} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u5} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃) g) (LinearMap.range.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (Eq.{succ u4} (LinearMap.{u3, u3, u4, u4} R₂ R₂ (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u3} R₂ _inst_2) (RingHom.id.{u3} R₂ (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_2))) (coeSort.{succ u4, succ (succ u4)} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_8) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_8) M₂ (Submodule.setLike.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_8)) (LinearMap.ker.{u3, u5, u4, u6, max u4 u6} R₂ R₃ 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(Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (Submodule.addCommMonoid.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_8 (LinearMap.ker.{u3, u5, u4, u6, max u4 u6} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u5} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃ (LinearMap.{u3, u5, u4, u6} R₂ R₃ (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u5} R₃ _inst_3) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6 _inst_8 _inst_9) (LinearMap.semilinearMapClass.{u3, u5, u4, u6} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u5} R₃ _inst_3) 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(AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃) g)) M₂ (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_8) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_2 _inst_5 _inst_8) (LinearMap.range.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u3} R₂ _inst_2) 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_inst_5) _inst_6 _inst_8 _inst_9 τ₂₃ (LinearMap.{u3, u5, u4, u6} R₂ R₃ (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u5} R₃ _inst_3) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6 _inst_8 _inst_9) (LinearMap.semilinearMapClass.{u3, u5, u4, u6} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u5} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃) g)) (Submodule.Quotient.module.{u3, u4} R₂ M₂ _inst_2 _inst_5 _inst_8 (LinearMap.range.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (RingHom.id.{u3} R₂ (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_2))))))))
+ forall {R : Type.{u1}} {M : Type.{u2}} {R₂ : Type.{u3}} {M₂ : Type.{u4}} {R₃ : Type.{u5}} {M₃ : Type.{u6}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u3} R₂] [_inst_3 : Ring.{u5} R₃] [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : AddCommMonoid.{u6} M₃] [_inst_7 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_8 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] [_inst_9 : Module.{u5, u6} R₃ M₃ (Ring.toSemiring.{u5} R₃ _inst_3) _inst_6] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_2))} {τ₂₃ : RingHom.{u3, u5} R₂ R₃ (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u5} R₃ (Ring.toNonAssocRing.{u5} R₃ _inst_3))} [_inst_11 : RingHomSurjective.{u1, u3} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂] {f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8} {g : LinearMap.{u3, u5, u4, u6} R₂ R₃ (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u5} R₃ _inst_3) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6 _inst_8 _inst_9}, Iff (LE.le.{u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_8) (Preorder.toHasLe.{u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_8) (PartialOrder.toPreorder.{u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_8) (SetLike.partialOrder.{u4, u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_8) M₂ (Submodule.setLike.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_8)))) (LinearMap.ker.{u3, u5, u4, u6, max u4 u6} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u5} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃ (LinearMap.{u3, u5, u4, u6} R₂ R₃ (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u5} R₃ _inst_3) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6 _inst_8 _inst_9) (LinearMap.semilinearMapClass.{u3, u5, u4, u6} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u5} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃) g) (LinearMap.range.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (Eq.{succ u4} (LinearMap.{u3, u3, u4, u4} R₂ R₂ (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u3} R₂ _inst_2) (RingHom.id.{u3} R₂ (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_2))) (coeSort.{succ u4, succ (succ u4)} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_8) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_8) M₂ (Submodule.setLike.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_8)) (LinearMap.ker.{u3, u5, u4, u6, max u4 u6} R₂ R₃ 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_inst_7 _inst_8 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u3} R₂ _inst_2) (Submodule.addCommMonoid.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_8 (LinearMap.ker.{u3, u5, u4, u6, max u4 u6} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u5} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃ (LinearMap.{u3, u5, u4, u6} R₂ R₃ (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u5} R₃ _inst_3) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6 _inst_8 _inst_9) 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M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (Submodule.Quotient.addCommGroup.{u3, u4} R₂ M₂ _inst_2 _inst_5 _inst_8 (LinearMap.range.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f))) (Submodule.module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_8 (LinearMap.ker.{u3, u5, u4, u6, max u4 u6} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u5} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃ (LinearMap.{u3, u5, u4, u6} R₂ R₃ (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u5} R₃ _inst_3) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6 _inst_8 _inst_9) (LinearMap.semilinearMapClass.{u3, u5, u4, u6} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u5} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃) g)) (Submodule.Quotient.module.{u3, u4} R₂ M₂ _inst_2 _inst_5 _inst_8 (LinearMap.range.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (RingHom.id.{u3} R₂ (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_2))))))))
but is expected to have type
forall {R : Type.{u6}} {M : Type.{u4}} {R₂ : Type.{u5}} {M₂ : Type.{u3}} {R₃ : Type.{u2}} {M₃ : Type.{u1}} [_inst_1 : Ring.{u6} R] [_inst_2 : Ring.{u5} R₂] [_inst_3 : Ring.{u2} R₃] [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : AddCommGroup.{u3} M₂] [_inst_6 : AddCommMonoid.{u1} M₃] [_inst_7 : Module.{u6, u4} R M (Ring.toSemiring.{u6} R _inst_1) _inst_4] [_inst_8 : Module.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5)] [_inst_9 : Module.{u2, u1} R₃ M₃ (Ring.toSemiring.{u2} R₃ _inst_3) _inst_6] {τ₁₂ : RingHom.{u6, u5} R R₂ (Semiring.toNonAssocSemiring.{u6} R (Ring.toSemiring.{u6} R _inst_1)) (Semiring.toNonAssocSemiring.{u5} R₂ (Ring.toSemiring.{u5} R₂ _inst_2))} {τ₂₃ : RingHom.{u5, u2} R₂ R₃ (Semiring.toNonAssocSemiring.{u5} R₂ (Ring.toSemiring.{u5} R₂ _inst_2)) (Semiring.toNonAssocSemiring.{u2} R₃ (Ring.toSemiring.{u2} R₃ _inst_3))} [_inst_11 : RingHomSurjective.{u6, u5} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) τ₁₂] {f : LinearMap.{u6, u5, u4, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8} {g : LinearMap.{u5, u2, u3, u1} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9}, Iff (LE.le.{u3} (Submodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) (Preorder.toLE.{u3} (Submodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) (PartialOrder.toPreorder.{u3} (Submodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) 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(AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) M₂ (Submodule.setLike.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8)) x (LinearMap.ker.{u5, u2, u3, u1, max u3 u1} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃ (LinearMap.{u5, u2, u3, u1} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9) (LinearMap.instSemilinearMapClassLinearMap.{u5, u2, u3, u1} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃) g))) (HasQuotient.Quotient.{u3, u3} M₂ (Submodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) (Submodule.hasQuotient.{u5, u3} R₂ M₂ _inst_2 _inst_5 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(Ring.toSemiring.{u5} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u6, u5, u4, u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (RingHom.id.{u5} R₂ (Semiring.toNonAssocSemiring.{u5} R₂ (Ring.toSemiring.{u5} R₂ _inst_2)))))))
Case conversion may be inaccurate. Consider using '#align linear_map.ker_le_range_iff LinearMap.ker_le_range_iffₓ'. -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/08e1d8d4d989df3a6df86f385e9053ec8a372cc1
@@ -924,7 +924,7 @@ def Quotient.equiv {N : Type _} [AddCommGroup N] [Module R N] (P : Submodule R M
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} [_inst_7 : CommRing.{u1} R] [_inst_8 : AddCommGroup.{u2} M] [_inst_9 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8)] [_inst_10 : AddCommGroup.{u3} N] [_inst_11 : Module.{u1, u3} R N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_10)] (P : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) _inst_9) (Q : Submodule.{u1, u3} R N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_10) _inst_11) (f : LinearEquiv.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) (AddCommGroup.toAddCommMonoid.{u3} N _inst_10) _inst_9 _inst_11) (hf : Eq.{succ u3} (Submodule.{u1, u3} R N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_10) _inst_11) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R M N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) (AddCommGroup.toAddCommMonoid.{u3} N _inst_10) _inst_9 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7))) (LinearEquiv.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) (AddCommGroup.toAddCommMonoid.{u3} N _inst_10) _inst_9 _inst_11) (SemilinearEquivClass.semilinearMapClass.{u1, u1, u2, u3, max u2 u3} R R M N (LinearEquiv.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) (AddCommGroup.toAddCommMonoid.{u3} N _inst_10) _inst_9 _inst_11) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) (AddCommGroup.toAddCommMonoid.{u3} N _inst_10) _inst_9 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7))) (LinearEquiv.semilinearEquivClass.{u1, u1, u2, u3} R R M N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) (AddCommGroup.toAddCommMonoid.{u3} N _inst_10) _inst_9 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7))))) f P) Q), Eq.{max (succ u3) (succ u2)} (LinearEquiv.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)))) (Submodule.Quotient.equiv._proof_11.{u1} R (CommRing.toRing.{u1} R _inst_7)) (Submodule.Quotient.equiv._proof_10.{u1} R (CommRing.toRing.{u1} R _inst_7)) (HasQuotient.Quotient.{u3, u3} N (Submodule.{u1, u3} R N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_10) _inst_11) (Submodule.hasQuotient.{u1, u3} R N (CommRing.toRing.{u1} R _inst_7) _inst_10 _inst_11) Q) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) _inst_9) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_7) _inst_8 _inst_9) P) (AddCommGroup.toAddCommMonoid.{u3} (HasQuotient.Quotient.{u3, u3} N (Submodule.{u1, u3} R N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_10) _inst_11) (Submodule.hasQuotient.{u1, u3} R N (CommRing.toRing.{u1} R _inst_7) _inst_10 _inst_11) Q) (Submodule.Quotient.addCommGroup.{u1, u3} R N (CommRing.toRing.{u1} R _inst_7) _inst_10 _inst_11 Q)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) _inst_9) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_7) _inst_8 _inst_9) P) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_7) _inst_8 _inst_9 P)) (Submodule.Quotient.module.{u1, u3} R N (CommRing.toRing.{u1} R _inst_7) _inst_10 _inst_11 Q) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_7) _inst_8 _inst_9 P)) (LinearEquiv.symm.{u1, u1, u2, u3} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) _inst_9) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_7) _inst_8 _inst_9) P) (HasQuotient.Quotient.{u3, u3} N (Submodule.{u1, u3} R N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_10) _inst_11) (Submodule.hasQuotient.{u1, u3} R N (CommRing.toRing.{u1} R _inst_7) _inst_10 _inst_11) Q) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) _inst_9) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_7) _inst_8 _inst_9) P) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_7) _inst_8 _inst_9 P)) (AddCommGroup.toAddCommMonoid.{u3} (HasQuotient.Quotient.{u3, u3} N (Submodule.{u1, u3} R N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_10) _inst_11) (Submodule.hasQuotient.{u1, u3} R N (CommRing.toRing.{u1} R _inst_7) _inst_10 _inst_11) Q) (Submodule.Quotient.addCommGroup.{u1, u3} R N (CommRing.toRing.{u1} R _inst_7) _inst_10 _inst_11 Q)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_7) _inst_8 _inst_9 P) (Submodule.Quotient.module.{u1, u3} R N (CommRing.toRing.{u1} R _inst_7) _inst_10 _inst_11 Q) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)))) (Submodule.Quotient.equiv._proof_10.{u1} R (CommRing.toRing.{u1} R _inst_7)) (Submodule.Quotient.equiv._proof_11.{u1} R (CommRing.toRing.{u1} R _inst_7)) (Submodule.Quotient.equiv.{u1, u2, u3} R M (CommRing.toRing.{u1} R _inst_7) _inst_8 _inst_9 N _inst_10 _inst_11 P Q f hf)) (Submodule.Quotient.equiv.{u1, u3, u2} R N (CommRing.toRing.{u1} R _inst_7) _inst_10 _inst_11 M _inst_8 _inst_9 Q P (LinearEquiv.symm.{u1, u1, u2, u3} R R M N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) (AddCommGroup.toAddCommMonoid.{u3} N _inst_10) _inst_9 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7))) f) (Iff.mpr (Eq.{succ u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_7)) 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(LinearEquiv.{u1, u1, u3, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_7)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_7)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7))) N M (AddCommGroup.toAddCommMonoid.{u3} N _inst_10) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) _inst_11 _inst_9) (SemilinearEquivClass.semilinearMapClass.{u1, u1, u3, u2, max u3 u2} R R N M (LinearEquiv.{u1, u1, u3, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_7)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_7)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7))) N M (AddCommGroup.toAddCommMonoid.{u3} N _inst_10) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) _inst_11 _inst_9) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_7)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_10) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) _inst_11 _inst_9 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7))) (LinearEquiv.semilinearEquivClass.{u1, u1, u3, u2} R R N M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_7)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_10) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) _inst_11 _inst_9 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7))))) (LinearEquiv.symm.{u1, u1, u2, u3} R R M N (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_7)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) (AddCommGroup.toAddCommMonoid.{u3} N _inst_10) _inst_9 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7))) f) Q) P) (Eq.{succ u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_10) _inst_11) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R M N (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_7)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) (AddCommGroup.toAddCommMonoid.{u3} N _inst_10) _inst_9 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)))) (RingHomSurjective.invPair.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_7)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_7)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)))) (LinearEquiv.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_7)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_7)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) (AddCommGroup.toAddCommMonoid.{u3} N _inst_10) _inst_9 _inst_11) (SemilinearEquivClass.semilinearMapClass.{u1, u1, u2, u3, max u2 u3} R R M N (LinearEquiv.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_7)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_7)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) (AddCommGroup.toAddCommMonoid.{u3} N _inst_10) _inst_9 _inst_11) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_7)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) (AddCommGroup.toAddCommMonoid.{u3} N _inst_10) _inst_9 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7))) (LinearEquiv.semilinearEquivClass.{u1, u1, u2, u3} R R M N (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_7)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) (AddCommGroup.toAddCommMonoid.{u3} N _inst_10) _inst_9 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7))))) f P) Q) (Submodule.map_symm_eq_iff.{u1, u1, u2, u3} R R M N (CommRing.toCommSemiring.{u1} R _inst_7) (CommRing.toCommSemiring.{u1} R _inst_7) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) (AddCommGroup.toAddCommMonoid.{u3} N _inst_10) _inst_9 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_7))) P f Q) hf))
but is expected to have type
- forall {R : Type.{u3}} {M : Type.{u2}} {N : Type.{u1}} [_inst_7 : CommRing.{u3} R] [_inst_8 : AddCommGroup.{u2} M] [_inst_9 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8)] [_inst_10 : AddCommGroup.{u1} N] [_inst_11 : Module.{u3, u1} R N (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_10)] (P : Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) _inst_9) (Q : Submodule.{u3, u1} R N (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_10) _inst_11) (f : LinearEquiv.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) (AddCommGroup.toAddCommMonoid.{u1} N _inst_10) _inst_9 _inst_11) (hf : Eq.{succ u1} (Submodule.{u3, u1} R N (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_10) _inst_11) (Submodule.map.{u3, u3, u2, u1, max u2 u1} R R M N (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) (AddCommGroup.toAddCommMonoid.{u1} N _inst_10) _inst_9 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHomSurjective.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7))) (LinearEquiv.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) (AddCommGroup.toAddCommMonoid.{u1} N _inst_10) _inst_9 _inst_11) (SemilinearEquivClass.instSemilinearMapClass.{u3, u3, u2, u1, max u2 u1} R R M N (LinearEquiv.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) (AddCommGroup.toAddCommMonoid.{u1} N _inst_10) _inst_9 _inst_11) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) (AddCommGroup.toAddCommMonoid.{u1} N _inst_10) _inst_9 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u3, u3, u2, u1} R R M N (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) (AddCommGroup.toAddCommMonoid.{u1} N _inst_10) _inst_9 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7))))) f P) Q), Eq.{max (succ u2) (succ u1)} (LinearEquiv.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7))) (HasQuotient.Quotient.{u1, u1} N (Submodule.{u3, u1} R N (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_10) _inst_11) (Submodule.hasQuotient.{u3, u1} R N (CommRing.toRing.{u3} R _inst_7) _inst_10 _inst_11) Q) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) _inst_9) (Submodule.hasQuotient.{u3, u2} R M (CommRing.toRing.{u3} R _inst_7) _inst_8 _inst_9) P) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} N (Submodule.{u3, u1} R N (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_10) _inst_11) (Submodule.hasQuotient.{u3, u1} R N (CommRing.toRing.{u3} R _inst_7) _inst_10 _inst_11) Q) (Submodule.Quotient.addCommGroup.{u3, u1} R N (CommRing.toRing.{u3} R _inst_7) _inst_10 _inst_11 Q)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) _inst_9) (Submodule.hasQuotient.{u3, u2} R M (CommRing.toRing.{u3} R _inst_7) _inst_8 _inst_9) P) (Submodule.Quotient.addCommGroup.{u3, u2} R M (CommRing.toRing.{u3} R _inst_7) _inst_8 _inst_9 P)) (Submodule.Quotient.module.{u3, u1} R N (CommRing.toRing.{u3} R _inst_7) _inst_10 _inst_11 Q) (Submodule.Quotient.module.{u3, u2} R M (CommRing.toRing.{u3} R _inst_7) _inst_8 _inst_9 P)) (LinearEquiv.symm.{u3, u3, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) _inst_9) (Submodule.hasQuotient.{u3, u2} R M (CommRing.toRing.{u3} R _inst_7) _inst_8 _inst_9) P) (HasQuotient.Quotient.{u1, u1} N (Submodule.{u3, u1} R N (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_10) _inst_11) (Submodule.hasQuotient.{u3, u1} R N (CommRing.toRing.{u3} R _inst_7) _inst_10 _inst_11) Q) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) _inst_9) (Submodule.hasQuotient.{u3, u2} R M (CommRing.toRing.{u3} R _inst_7) _inst_8 _inst_9) P) (Submodule.Quotient.addCommGroup.{u3, u2} R M (CommRing.toRing.{u3} R _inst_7) _inst_8 _inst_9 P)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} N (Submodule.{u3, u1} R N (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_10) _inst_11) (Submodule.hasQuotient.{u3, u1} R N (CommRing.toRing.{u3} R _inst_7) _inst_10 _inst_11) Q) (Submodule.Quotient.addCommGroup.{u3, u1} R N (CommRing.toRing.{u3} R _inst_7) _inst_10 _inst_11 Q)) (Submodule.Quotient.module.{u3, u2} R M (CommRing.toRing.{u3} R _inst_7) _inst_8 _inst_9 P) (Submodule.Quotient.module.{u3, u1} R N (CommRing.toRing.{u3} R _inst_7) _inst_10 _inst_11 Q) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7))) (Submodule.Quotient.equiv.{u3, u2, u1} R M (CommRing.toRing.{u3} R _inst_7) _inst_8 _inst_9 N _inst_10 _inst_11 P Q f hf)) (Submodule.Quotient.equiv.{u3, u1, u2} R N (CommRing.toRing.{u3} R _inst_7) _inst_10 _inst_11 M _inst_8 _inst_9 Q P (LinearEquiv.symm.{u3, u3, u2, u1} R R M N (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) (AddCommGroup.toAddCommMonoid.{u1} N _inst_10) _inst_9 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7))) f) (Iff.mpr (Eq.{succ u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) _inst_9) (Submodule.map.{u3, u3, u1, u2, max u2 u1} R R N M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_10) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) _inst_11 _inst_9 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHomSurjective.invPair.{u3, u3} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (LinearEquiv.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7))) N M (AddCommGroup.toAddCommMonoid.{u1} N _inst_10) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) _inst_11 _inst_9) (SemilinearEquivClass.instSemilinearMapClass.{u3, u3, u1, u2, max u2 u1} R R N M (LinearEquiv.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7))) N M (AddCommGroup.toAddCommMonoid.{u1} N _inst_10) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) _inst_11 _inst_9) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_10) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) _inst_11 _inst_9 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u3, u3, u1, u2} R R N M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_10) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) _inst_11 _inst_9 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7))))) (LinearEquiv.symm.{u3, u3, u2, u1} R R M N (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) (AddCommGroup.toAddCommMonoid.{u1} N _inst_10) _inst_9 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7))) f) Q) P) (Eq.{succ u1} (Submodule.{u3, u1} R N (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_10) _inst_11) (Submodule.map.{u3, u3, u2, u1, max u2 u1} R R M N (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) (AddCommGroup.toAddCommMonoid.{u1} N _inst_10) _inst_9 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHomSurjective.invPair.{u3, u3} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (LinearEquiv.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) (AddCommGroup.toAddCommMonoid.{u1} N _inst_10) _inst_9 _inst_11) (SemilinearEquivClass.instSemilinearMapClass.{u3, u3, u2, u1, max u2 u1} R R M N (LinearEquiv.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) (AddCommGroup.toAddCommMonoid.{u1} N _inst_10) _inst_9 _inst_11) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) (AddCommGroup.toAddCommMonoid.{u1} N _inst_10) _inst_9 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u3, u3, u2, u1} R R M N (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) (AddCommGroup.toAddCommMonoid.{u1} N _inst_10) _inst_9 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7))))) f P) Q) (Submodule.map_symm_eq_iff.{u1, u2, u3, u3} R R M N (CommRing.toCommSemiring.{u3} R _inst_7) (CommRing.toCommSemiring.{u3} R _inst_7) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) (AddCommGroup.toAddCommMonoid.{u1} N _inst_10) _inst_9 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7)))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_7))) P f Q) hf))
+ forall {R : Type.{u3}} {M : Type.{u2}} {N : Type.{u1}} [_inst_7 : CommRing.{u3} R] [_inst_8 : AddCommGroup.{u2} M] [_inst_9 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8)] [_inst_10 : AddCommGroup.{u1} N] [_inst_11 : Module.{u3, u1} R N (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_10)] (P : Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) _inst_9) (Q : Submodule.{u3, u1} R N (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_10) _inst_11) (f : LinearEquiv.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) (AddCommGroup.toAddCommMonoid.{u1} N _inst_10) _inst_9 _inst_11) (hf : Eq.{succ u1} (Submodule.{u3, u1} R N (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_10) _inst_11) (Submodule.map.{u3, u3, u2, u1, max u2 u1} R R M N (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) (AddCommGroup.toAddCommMonoid.{u1} N _inst_10) _inst_9 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7))) (LinearEquiv.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) 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(Submodule.map.{u3, u3, u2, u1, max u2 u1} R R M N (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) (AddCommGroup.toAddCommMonoid.{u1} N _inst_10) _inst_9 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)))) (RingHomSurjective.invPair.{u3, u3} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)))) (LinearEquiv.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) (AddCommGroup.toAddCommMonoid.{u1} N _inst_10) _inst_9 _inst_11) (SemilinearEquivClass.instSemilinearMapClass.{u3, u3, u2, u1, max u2 u1} R R M N (LinearEquiv.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) (AddCommGroup.toAddCommMonoid.{u1} N _inst_10) _inst_9 _inst_11) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) (AddCommGroup.toAddCommMonoid.{u1} N _inst_10) _inst_9 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u3, u3, u2, u1} R R M N (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) (AddCommGroup.toAddCommMonoid.{u1} N _inst_10) _inst_9 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7))))) f P) Q) (Submodule.map_symm_eq_iff.{u1, u2, u3, u3} R R M N (CommRing.toCommSemiring.{u3} R _inst_7) (CommRing.toCommSemiring.{u3} R _inst_7) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) (AddCommGroup.toAddCommMonoid.{u1} N _inst_10) _inst_9 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_7))) P f Q) hf))
Case conversion may be inaccurate. Consider using '#align submodule.quotient.equiv_symm Submodule.Quotient.equiv_symmₓ'. -/
@[simp]
theorem Quotient.equiv_symm {R M N : Type _} [CommRing R] [AddCommGroup M] [Module R M]
mathlib commit https://github.com/leanprover-community/mathlib/commit/730c6d4cab72b9d84fcfb9e95e8796e9cd8f40ba
@@ -861,7 +861,7 @@ def Submodule.comapMkQOrderEmbedding : Submodule R (M ⧸ p) ↪o Submodule R M
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (p' : Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)), Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.setLike.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p))))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (fun (_x : RelEmbedding.{u2, u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LE.le.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) => (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) 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_inst_3 p) p')
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (p : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (p' : Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)), Eq.{succ u1} ((fun 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_inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))) (RelEmbedding.toEmbedding.{u1, u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) => LE.le.{u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.completeLattice.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)))))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => LE.le.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Submodule.comapMkQOrderEmbedding.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) p') (Submodule.comap.{u2, u2, u1, u1, u1} R R M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} 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))) M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.mkQ.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) p')
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (p : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (p' : Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)), Eq.{succ u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) => Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) p') (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.completeLattice.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)))))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))))) (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (fun (_x : Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) => Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.completeLattice.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)))))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))))) 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x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => LE.le.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Submodule.comapMkQOrderEmbedding.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) p') (Submodule.comap.{u2, u2, u1, u1, u1} R R M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} 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))) M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.mkQ.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) p')
Case conversion may be inaccurate. Consider using '#align submodule.comap_mkq_embedding_eq Submodule.comapMkQOrderEmbedding_eqₓ'. -/
@[simp]
theorem comapMkQOrderEmbedding_eq (p' : Submodule R (M ⧸ p)) :
mathlib commit https://github.com/leanprover-community/mathlib/commit/02ba8949f486ebecf93fe7460f1ed0564b5e442c
@@ -48,7 +48,7 @@ def quotientRel : Setoid M :=
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {x : M} {y : M}, Iff (Setoid.r.{succ u2} M (Submodule.quotientRel.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) x y) (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HSub.hSub.{u2, u2, u2} M M M (instHSub.{u2} M (SubNegMonoid.toHasSub.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)))) x y) p)
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {x : M} {y : M}, Iff (Setoid.r.{succ u2} M (Submodule.quotientRel.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) x y) (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HSub.hSub.{u2, u2, u2} M M M (instHSub.{u2} M (SubNegMonoid.toSub.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)))) x y) p)
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {x : M} {y : M}, Iff (Setoid.r.{succ u2} M (Submodule.quotientRel.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) x y) (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HSub.hSub.{u2, u2, u2} M M M (instHSub.{u2} M (SubNegMonoid.toSub.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)))) x y) p)
Case conversion may be inaccurate. Consider using '#align submodule.quotient_rel_r_def Submodule.quotientRel_r_defₓ'. -/
theorem quotientRel_r_def {x y : M} : @Setoid.r _ p.quotientRel x y ↔ x - y ∈ p :=
Iff.trans
@@ -112,7 +112,7 @@ theorem quot_mk_eq_mk {p : Submodule R M} (x : M) : (Quot.mk _ x : M ⧸ p) = mk
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {x : M} {y : M}, Iff (Eq.{succ u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p y)) (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)))))) (Neg.neg.{u2} M (SubNegMonoid.toHasNeg.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2))) x) y) p)
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {x : M} {y : M}, Iff (Eq.{succ u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p y)) (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)))))) (Neg.neg.{u2} M (NegZeroClass.toNeg.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) x) y) p)
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {x : M} {y : M}, Iff (Eq.{succ u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p y)) (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)))))) (Neg.neg.{u2} M (NegZeroClass.toNeg.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) x) y) p)
Case conversion may be inaccurate. Consider using '#align submodule.quotient.eq' Submodule.Quotient.eq'ₓ'. -/
protected theorem eq' {x y : M} : (mk x : M ⧸ p) = mk y ↔ -x + y ∈ p :=
QuotientAddGroup.eq
@@ -122,7 +122,7 @@ protected theorem eq' {x y : M} : (mk x : M ⧸ p) = mk y ↔ -x + y ∈ p :=
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {x : M} {y : M}, Iff (Eq.{succ u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p y)) (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HSub.hSub.{u2, u2, u2} M M M (instHSub.{u2} M (SubNegMonoid.toHasSub.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)))) x y) p)
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {x : M} {y : M}, Iff (Eq.{succ u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p y)) (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HSub.hSub.{u2, u2, u2} M M M (instHSub.{u2} M (SubNegMonoid.toSub.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)))) x y) p)
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {x : M} {y : M}, Iff (Eq.{succ u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p y)) (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HSub.hSub.{u2, u2, u2} M M M (instHSub.{u2} M (SubNegMonoid.toSub.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)))) x y) p)
Case conversion may be inaccurate. Consider using '#align submodule.quotient.eq Submodule.Quotient.eqₓ'. -/
protected theorem eq {x y : M} : (mk x : M ⧸ p) = mk y ↔ x - y ∈ p :=
p.Quotient.eq''.trans (leftRel_apply.symm.trans p.quotientRel_r_def)
@@ -149,7 +149,7 @@ theorem mk_zero : mk 0 = (0 : M ⧸ p) :=
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} {x : M} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), Iff (Eq.{succ u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x) (OfNat.ofNat.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) 0 (OfNat.mk.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) 0 (Zero.zero.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.HasQuotient.Quotient.hasZero.{u1, u2} R M _inst_1 _inst_2 _inst_3 p))))) (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x p)
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} {x : M} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), Iff (Eq.{succ u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x) (OfNat.ofNat.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) 0 (Zero.toOfNat0.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.instZeroQuotientSubmoduleToSemiringToAddCommMonoidHasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)))) (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x p)
+ forall {R : Type.{u1}} {M : Type.{u2}} {x : M} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), Iff (Eq.{succ u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x) (OfNat.ofNat.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) 0 (Zero.toOfNat0.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.instZeroQuotientSubmoduleToSemiringToAddCommMonoidHasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)))) (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x p)
Case conversion may be inaccurate. Consider using '#align submodule.quotient.mk_eq_zero Submodule.Quotient.mk_eq_zeroₓ'. -/
@[simp]
theorem mk_eq_zero : (mk x : M ⧸ p) = 0 ↔ x ∈ p := by simpa using (Quotient.eq' p : mk x = 0 ↔ _)
@@ -480,18 +480,14 @@ noncomputable instance Quotient.fintype [Fintype M] (S : Submodule R M) : Fintyp
#align submodule.quotient.fintype Submodule.Quotient.fintype
-/
-/- warning: submodule.card_eq_card_quotient_mul_card -> Submodule.card_eq_card_quotient_mul_card is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : Fintype.{u2} M] (S : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : DecidablePred.{succ u2} M (fun (_x : M) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) _x S)], Eq.{1} Nat (Fintype.card.{u2} M _inst_4) (HMul.hMul.{0, 0, 0} Nat Nat Nat (instHMul.{0} Nat Nat.hasMul) (Fintype.card.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) S) (Subtype.fintype.{u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x S) (fun (a : M) => _inst_5 a) _inst_4)) (Fintype.card.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (Submodule.Quotient.fintype.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 S)))
-but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : Fintype.{u2} M] (S : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : DecidablePred.{succ u2} M (fun (_x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) _x S)], Eq.{1} Nat (Fintype.card.{u2} M _inst_4) (HMul.hMul.{0, 0, 0} Nat Nat Nat (instHMul.{0} Nat instMulNat) (Fintype.card.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x S)) (Subtype.fintype.{u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x S) (fun (a : M) => _inst_5 a) _inst_4)) (Fintype.card.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (Submodule.Quotient.fintype.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 S)))
-Case conversion may be inaccurate. Consider using '#align submodule.card_eq_card_quotient_mul_card Submodule.card_eq_card_quotient_mul_cardₓ'. -/
+#print Submodule.card_eq_card_quotient_mul_card /-
theorem card_eq_card_quotient_mul_card [Fintype M] (S : Submodule R M) [DecidablePred (· ∈ S)] :
Fintype.card M = Fintype.card S * Fintype.card (M ⧸ S) :=
by
rw [mul_comm, ← Fintype.card_prod]
exact Fintype.card_congr AddSubgroup.addGroupEquivQuotientProdAddSubgroup
#align submodule.card_eq_card_quotient_mul_card Submodule.card_eq_card_quotient_mul_card
+-/
section
@@ -718,7 +714,7 @@ theorem mapQ_mkQ (f : M →ₛₗ[τ₁₂] M₂) {h} : (mapQ p q f h).comp p.mk
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (q : Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (h : optParam.{0} (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) 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_inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (Submodule.orderTop.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) p)))) trivial)), Eq.{max (succ u2) (succ u4)} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ 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M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} (HasQuotient.Quotient.{u4, u4} M₂ (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u3, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 q) τ₁₂))))
but is expected to have type
- forall {R : Type.{u3}} {M : Type.{u4}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u4} M] [_inst_3 : Module.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2)] (p : Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) {R₂ : Type.{u2}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u2} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u2, u1} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u3, u2} R R₂ (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R₂ (Ring.toSemiring.{u2} R₂ _inst_4))} (q : Submodule.{u2, u1} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (h : optParam.{0} (LE.le.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Preorder.toLE.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Submodule.completeLattice.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3))))) p (Submodule.comap.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) 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_inst_3) (Submodule.hasQuotient.{u3, u4} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u2, u1} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} (HasQuotient.Quotient.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u4} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u4} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u2, u1} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.Quotient.module.{u3, u4} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q) τ₁₂)))
+ forall {R : Type.{u3}} {M : Type.{u4}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u4} M] [_inst_3 : Module.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2)] (p : Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) {R₂ : Type.{u2}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u2} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u2, u1} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u3, u2} R R₂ (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R₂ (Ring.toSemiring.{u2} R₂ _inst_4))} (q : Submodule.{u2, u1} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (h : optParam.{0} (LE.le.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Preorder.toLE.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Submodule.completeLattice.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3))))) p (Submodule.comap.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u3, u2, u4, u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) (OfNat.ofNat.{max u4 u1} (LinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) 0 (Zero.toOfNat0.{max u4 u1} (LinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instZeroLinearMap.{u3, u2, u4, u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂))) q)) (of_eq_true (LE.le.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Preorder.toLE.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Submodule.completeLattice.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3))))) p (Submodule.comap.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u3, u2, u4, u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) (OfNat.ofNat.{max u4 u1} (LinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) 0 (Zero.toOfNat0.{max u4 u1} (LinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instZeroLinearMap.{u3, u2, u4, u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂))) q)) (Eq.trans.{1} Prop (LE.le.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Preorder.toLE.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Submodule.completeLattice.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3))))) p (Submodule.comap.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u3, u2, u4, u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) (OfNat.ofNat.{max u4 u1} (LinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) 0 (Zero.toOfNat0.{max u4 u1} (LinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instZeroLinearMap.{u3, u2, u4, u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂))) q)) (LE.le.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Preorder.toLE.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Submodule.completeLattice.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3))))) p (Top.top.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3))) True (congrArg.{succ u4, 1} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) Prop (Submodule.comap.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u3, u2, u4, u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) (OfNat.ofNat.{max u4 u1} (LinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) 0 (Zero.toOfNat0.{max u4 u1} (LinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instZeroLinearMap.{u3, u2, u4, u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂))) q) (Top.top.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3)) (LE.le.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Preorder.toLE.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Submodule.completeLattice.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3))))) p) (Submodule.comap_zero.{u1, u2, u3, u4} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ q)) (Mathlib.Order.BoundedOrder._auxLemma.1.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Preorder.toLE.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Submodule.completeLattice.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3))))) (Submodule.instOrderTopSubmoduleToLEToPreorderInstPartialOrderSetLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) p)))), Eq.{max (succ u4) (succ u1)} (LinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} 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(Submodule.hasQuotient.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.Quotient.module.{u3, u4} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.mapQ.{u3, u4, u2, u1} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ q (OfNat.ofNat.{max u4 u1} (LinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) 0 (Zero.toOfNat0.{max u4 u1} (LinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instZeroLinearMap.{u3, u2, u4, u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂))) h) (OfNat.ofNat.{max u4 u1} (LinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u4} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u2, u1} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (AddCommGroup.toAddCommMonoid.{u4} (HasQuotient.Quotient.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u4} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u4} R M _inst_1 _inst_2 _inst_3 p)) 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_inst_3) (Submodule.hasQuotient.{u3, u4} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u2, u1} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} (HasQuotient.Quotient.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u4} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u4} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u2, u1} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.Quotient.module.{u3, u4} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u2, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q) τ₁₂)))
Case conversion may be inaccurate. Consider using '#align submodule.mapq_zero Submodule.mapQ_zeroₓ'. -/
@[simp]
theorem mapQ_zero (h : p ≤ q.comap (0 : M →ₛₗ[τ₁₂] M₂) := (by simp)) :
@@ -877,7 +873,7 @@ theorem comapMkQOrderEmbedding_eq (p' : Submodule R (M ⧸ p)) :
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} [_inst_7 : RingHomSurjective.{u1, u3} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂] {f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6} {s : Set.{u4} M₂}, (Set.Nonempty.{u4} M₂ s) -> (HasSubset.Subset.{u4} (Set.{u4} M₂) (Set.hasSubset.{u4} M₂) s ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Set.{u4} M₂) (HasLiftT.mk.{succ u4, succ u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Set.{u4} M₂) (CoeTCₓ.coe.{succ u4, succ u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Set.{u4} M₂) (SetLike.Set.hasCoeT.{u4, u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) M₂ (Submodule.setLike.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6)))) (LinearMap.range.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) _inst_7 f))) -> (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Set.preimage.{u2, u4} M M₂ (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f) s)) (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f (Submodule.span.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6 s)))
but is expected to have type
- forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} [_inst_7 : RingHomSurjective.{u4, u3} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂] {f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6} {s : Set.{u1} M₂}, (Set.Nonempty.{u1} M₂ s) -> (HasSubset.Subset.{u1} (Set.{u1} M₂) (Set.instHasSubsetSet.{u1} M₂) s (SetLike.coe.{u1, u1} (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) M₂ (Submodule.instSetLikeSubmodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (LinearMap.range.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) _inst_7 f))) -> (Eq.{succ u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Set.preimage.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f) s)) (Submodule.comap.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f (Submodule.span.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6 s)))
+ forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} [_inst_7 : RingHomSurjective.{u4, u3} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂] {f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6} {s : Set.{u1} M₂}, (Set.Nonempty.{u1} M₂ s) -> (HasSubset.Subset.{u1} (Set.{u1} M₂) (Set.instHasSubsetSet.{u1} M₂) s (SetLike.coe.{u1, u1} (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) M₂ (Submodule.setLike.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (LinearMap.range.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) _inst_7 f))) -> (Eq.{succ u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Set.preimage.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f) s)) (Submodule.comap.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f (Submodule.span.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6 s)))
Case conversion may be inaccurate. Consider using '#align submodule.span_preimage_eq Submodule.span_preimage_eqₓ'. -/
theorem span_preimage_eq [RingHomSurjective τ₁₂] {f : M →ₛₗ[τ₁₂] M₂} {s : Set M₂} (h₀ : s.Nonempty)
(h₁ : s ⊆ range f) : span R (f ⁻¹' s) = (span R₂ s).comap f :=
@@ -993,7 +989,7 @@ theorem range_mkQ_comp (f : M →ₛₗ[τ₁₂] M₂) : f.range.mkQ.comp f = 0
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} {R₂ : Type.{u3}} {M₂ : Type.{u4}} {R₃ : Type.{u5}} {M₃ : Type.{u6}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u3} R₂] [_inst_3 : Ring.{u5} R₃] [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : AddCommMonoid.{u6} M₃] [_inst_7 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_8 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] [_inst_9 : Module.{u5, u6} R₃ M₃ (Ring.toSemiring.{u5} R₃ _inst_3) _inst_6] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_2))} {τ₂₃ : RingHom.{u3, u5} R₂ R₃ (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u5} R₃ (Ring.toNonAssocRing.{u5} R₃ _inst_3))} [_inst_11 : RingHomSurjective.{u1, u3} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂] {f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8} {g : LinearMap.{u3, u5, u4, u6} R₂ R₃ (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u5} R₃ _inst_3) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6 _inst_8 _inst_9}, Iff (LE.le.{u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_8) (Preorder.toLE.{u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_8) (PartialOrder.toPreorder.{u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_8) (SetLike.partialOrder.{u4, u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_8) M₂ (Submodule.setLike.{u3, 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_inst_5) _inst_6 _inst_8 _inst_9 τ₂₃ (LinearMap.{u3, u5, u4, u6} R₂ R₃ (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u5} R₃ _inst_3) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6 _inst_8 _inst_9) (LinearMap.semilinearMapClass.{u3, u5, u4, u6} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u5} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃) g)) (Submodule.Quotient.module.{u3, u4} R₂ M₂ _inst_2 _inst_5 _inst_8 (LinearMap.range.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (RingHom.id.{u3} R₂ (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_2))))))))
but is expected to have type
- forall {R : Type.{u6}} {M : Type.{u4}} {R₂ : Type.{u5}} {M₂ : Type.{u3}} {R₃ : Type.{u2}} {M₃ : Type.{u1}} [_inst_1 : Ring.{u6} R] [_inst_2 : Ring.{u5} R₂] [_inst_3 : Ring.{u2} R₃] [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : AddCommGroup.{u3} M₂] [_inst_6 : AddCommMonoid.{u1} M₃] [_inst_7 : Module.{u6, u4} R M (Ring.toSemiring.{u6} R _inst_1) _inst_4] [_inst_8 : Module.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5)] [_inst_9 : Module.{u2, u1} R₃ M₃ (Ring.toSemiring.{u2} R₃ _inst_3) _inst_6] {τ₁₂ : RingHom.{u6, u5} R R₂ (Semiring.toNonAssocSemiring.{u6} R (Ring.toSemiring.{u6} R _inst_1)) (Semiring.toNonAssocSemiring.{u5} R₂ (Ring.toSemiring.{u5} R₂ _inst_2))} {τ₂₃ : RingHom.{u5, u2} R₂ R₃ (Semiring.toNonAssocSemiring.{u5} R₂ (Ring.toSemiring.{u5} R₂ _inst_2)) (Semiring.toNonAssocSemiring.{u2} R₃ (Ring.toSemiring.{u2} R₃ _inst_3))} [_inst_11 : RingHomSurjective.{u6, u5} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) τ₁₂] {f : LinearMap.{u6, u5, u4, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8} {g : LinearMap.{u5, u2, u3, u1} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9}, Iff (LE.le.{u3} (Submodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) (Preorder.toLE.{u3} (Submodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) (PartialOrder.toPreorder.{u3} (Submodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) (Submodule.completeLattice.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8))))) (LinearMap.ker.{u5, u2, u3, u1, max u3 u1} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃ (LinearMap.{u5, u2, u3, u1} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9) (LinearMap.instSemilinearMapClassLinearMap.{u5, u2, u3, u1} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃) g) (LinearMap.range.{u6, u5, u4, u3, max u4 u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u6, u5, u4, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u6, u5, u4, u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (Eq.{succ u3} (LinearMap.{u5, u5, u3, u3} R₂ R₂ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u5} R₂ _inst_2) (RingHom.id.{u5} R₂ (Semiring.toNonAssocSemiring.{u5} R₂ (Ring.toSemiring.{u5} R₂ _inst_2))) (Subtype.{succ u3} M₂ (fun (x : M₂) => Membership.mem.{u3, u3} M₂ (Submodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) (SetLike.instMembership.{u3, u3} (Submodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) M₂ (Submodule.instSetLikeSubmodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8)) x (LinearMap.ker.{u5, u2, u3, u1, max u3 u1} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃ (LinearMap.{u5, u2, u3, u1} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9) (LinearMap.instSemilinearMapClassLinearMap.{u5, u2, u3, u1} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃) g))) (HasQuotient.Quotient.{u3, u3} M₂ (Submodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) (Submodule.hasQuotient.{u5, u3} R₂ M₂ _inst_2 _inst_5 _inst_8) (LinearMap.range.{u6, u5, u4, u3, max u4 u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u6, u5, u4, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u6, u5, u4, u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8 (LinearMap.ker.{u5, u2, u3, u1, max u3 u1} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃ (LinearMap.{u5, u2, u3, u1} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9) (LinearMap.instSemilinearMapClassLinearMap.{u5, u2, u3, u1} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃) g)) (AddCommGroup.toAddCommMonoid.{u3} (HasQuotient.Quotient.{u3, u3} M₂ (Submodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) (Submodule.hasQuotient.{u5, u3} R₂ M₂ _inst_2 _inst_5 _inst_8) (LinearMap.range.{u6, u5, u4, u3, max u4 u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u6, u5, u4, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u6, u5, u4, u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (Submodule.Quotient.addCommGroup.{u5, u3} R₂ M₂ _inst_2 _inst_5 _inst_8 (LinearMap.range.{u6, u5, u4, u3, max u4 u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u6, u5, u4, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u6, u5, u4, u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8 (LinearMap.ker.{u5, u2, u3, u1, max u3 u1} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃ (LinearMap.{u5, u2, u3, u1} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9) (LinearMap.instSemilinearMapClassLinearMap.{u5, u2, u3, u1} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃) g)) (Submodule.Quotient.module.{u5, u3} R₂ M₂ _inst_2 _inst_5 _inst_8 (LinearMap.range.{u6, u5, u4, u3, max u4 u3} R R₂ M M₂ (Ring.toSemiring.{u6} R 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(Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8)) x (LinearMap.ker.{u5, u2, u3, u1, max u3 u1} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃ (LinearMap.{u5, u2, u3, u1} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9) (LinearMap.instSemilinearMapClassLinearMap.{u5, u2, u3, u1} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃) g))) (HasQuotient.Quotient.{u3, u3} M₂ (Submodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) (Submodule.hasQuotient.{u5, u3} R₂ M₂ _inst_2 _inst_5 _inst_8) (LinearMap.range.{u6, u5, u4, u3, max u4 u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u6, u5, u4, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u6, u5, u4, u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u5} R₂ _inst_2) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8 (LinearMap.ker.{u5, u2, u3, u1, max u3 u1} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃ (LinearMap.{u5, u2, u3, u1} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9) (LinearMap.instSemilinearMapClassLinearMap.{u5, u2, u3, u1} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃) g)) (AddCommGroup.toAddCommMonoid.{u3} (HasQuotient.Quotient.{u3, u3} M₂ (Submodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) (Submodule.hasQuotient.{u5, u3} R₂ M₂ _inst_2 _inst_5 _inst_8) (LinearMap.range.{u6, u5, u4, u3, max u4 u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u6, u5, u4, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u6, u5, u4, u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (Submodule.Quotient.addCommGroup.{u5, u3} R₂ M₂ _inst_2 _inst_5 _inst_8 (LinearMap.range.{u6, u5, u4, u3, max u4 u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u6, u5, u4, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u6, u5, u4, u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8 (LinearMap.ker.{u5, u2, u3, u1, max u3 u1} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃ (LinearMap.{u5, u2, u3, u1} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9) (LinearMap.instSemilinearMapClassLinearMap.{u5, u2, u3, u1} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃) g)) (Submodule.Quotient.module.{u5, u3} R₂ M₂ _inst_2 _inst_5 _inst_8 (LinearMap.range.{u6, u5, u4, u3, max u4 u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u6, u5, u4, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u6, u5, u4, u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (RingHom.id.{u5} R₂ (Semiring.toNonAssocSemiring.{u5} R₂ (Ring.toSemiring.{u5} R₂ _inst_2)))))))
+ forall {R : Type.{u6}} {M : Type.{u4}} {R₂ : Type.{u5}} {M₂ : Type.{u3}} {R₃ : Type.{u2}} {M₃ : Type.{u1}} [_inst_1 : Ring.{u6} R] [_inst_2 : Ring.{u5} R₂] [_inst_3 : Ring.{u2} R₃] [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : AddCommGroup.{u3} M₂] [_inst_6 : AddCommMonoid.{u1} M₃] [_inst_7 : Module.{u6, u4} R M (Ring.toSemiring.{u6} R _inst_1) _inst_4] [_inst_8 : Module.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5)] [_inst_9 : Module.{u2, u1} R₃ M₃ (Ring.toSemiring.{u2} R₃ _inst_3) _inst_6] {τ₁₂ : RingHom.{u6, u5} R R₂ (Semiring.toNonAssocSemiring.{u6} R (Ring.toSemiring.{u6} R _inst_1)) (Semiring.toNonAssocSemiring.{u5} R₂ (Ring.toSemiring.{u5} R₂ _inst_2))} {τ₂₃ : RingHom.{u5, u2} R₂ R₃ (Semiring.toNonAssocSemiring.{u5} R₂ (Ring.toSemiring.{u5} R₂ _inst_2)) (Semiring.toNonAssocSemiring.{u2} R₃ (Ring.toSemiring.{u2} R₃ _inst_3))} [_inst_11 : RingHomSurjective.{u6, u5} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) τ₁₂] {f : LinearMap.{u6, u5, u4, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8} {g : LinearMap.{u5, u2, u3, u1} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9}, Iff (LE.le.{u3} (Submodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) (Preorder.toLE.{u3} (Submodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) (PartialOrder.toPreorder.{u3} (Submodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) (Submodule.completeLattice.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8))))) (LinearMap.ker.{u5, u2, u3, u1, max u3 u1} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃ (LinearMap.{u5, u2, u3, u1} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9) (LinearMap.instSemilinearMapClassLinearMap.{u5, u2, u3, u1} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃) g) (LinearMap.range.{u6, u5, u4, u3, max u4 u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u6, u5, u4, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u6, u5, u4, u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (Eq.{succ u3} (LinearMap.{u5, u5, u3, u3} R₂ R₂ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u5} R₂ _inst_2) (RingHom.id.{u5} R₂ (Semiring.toNonAssocSemiring.{u5} R₂ (Ring.toSemiring.{u5} R₂ _inst_2))) (Subtype.{succ u3} M₂ (fun (x : M₂) => Membership.mem.{u3, u3} M₂ (Submodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) (SetLike.instMembership.{u3, u3} (Submodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) M₂ (Submodule.setLike.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8)) x (LinearMap.ker.{u5, u2, u3, u1, max u3 u1} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃ (LinearMap.{u5, u2, u3, u1} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9) (LinearMap.instSemilinearMapClassLinearMap.{u5, u2, u3, u1} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃) g))) (HasQuotient.Quotient.{u3, u3} M₂ (Submodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) (Submodule.hasQuotient.{u5, u3} R₂ M₂ _inst_2 _inst_5 _inst_8) (LinearMap.range.{u6, u5, u4, u3, max u4 u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u6, u5, u4, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u6, u5, u4, u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (Submodule.addCommMonoid.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8 (LinearMap.ker.{u5, u2, u3, u1, max u3 u1} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃ (LinearMap.{u5, u2, u3, u1} R₂ R₃ (Ring.toSemiring.{u5} R₂ 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(LinearMap.instSemilinearMapClassLinearMap.{u6, u5, u4, u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (Submodule.Quotient.addCommGroup.{u5, u3} R₂ M₂ _inst_2 _inst_5 _inst_8 (LinearMap.range.{u6, u5, u4, u3, max u4 u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u6, u5, u4, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u6, u5, u4, u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f))) (Submodule.module.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) 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M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u6, u5, u4, u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u5} R₂ _inst_2) (Submodule.addCommMonoid.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8 (LinearMap.ker.{u5, u2, u3, u1, max u3 u1} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃ (LinearMap.{u5, u2, u3, u1} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9) (LinearMap.instSemilinearMapClassLinearMap.{u5, u2, u3, u1} R₂ R₃ M₂ M₃ 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_inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u6, u5, u4, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u6, u5, u4, u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (Submodule.Quotient.addCommGroup.{u5, u3} R₂ M₂ _inst_2 _inst_5 _inst_8 (LinearMap.range.{u6, u5, u4, u3, max u4 u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u6, u5, u4, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u6, u5, u4, u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f))) (Submodule.module.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8 (LinearMap.ker.{u5, u2, u3, u1, max u3 u1} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃ (LinearMap.{u5, u2, u3, u1} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9) (LinearMap.instSemilinearMapClassLinearMap.{u5, u2, u3, u1} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃) g)) (Submodule.Quotient.module.{u5, u3} R₂ M₂ _inst_2 _inst_5 _inst_8 (LinearMap.range.{u6, u5, u4, u3, max u4 u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u6, u5, u4, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u6, u5, u4, u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f))) (LinearMap.instZeroLinearMap.{u5, u5, u3, u3} R₂ R₂ (Subtype.{succ u3} M₂ (fun (x : M₂) => Membership.mem.{u3, u3} M₂ (Submodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) (SetLike.instMembership.{u3, u3} (Submodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) M₂ (Submodule.setLike.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8)) x (LinearMap.ker.{u5, u2, u3, u1, max u3 u1} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃ (LinearMap.{u5, u2, u3, u1} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9) (LinearMap.instSemilinearMapClassLinearMap.{u5, u2, u3, u1} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃) g))) (HasQuotient.Quotient.{u3, u3} M₂ (Submodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) (Submodule.hasQuotient.{u5, u3} R₂ M₂ _inst_2 _inst_5 _inst_8) (LinearMap.range.{u6, u5, u4, u3, max u4 u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u6, u5, u4, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u6, u5, u4, u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u5} R₂ _inst_2) (Submodule.addCommMonoid.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8 (LinearMap.ker.{u5, u2, u3, u1, max u3 u1} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃ (LinearMap.{u5, u2, u3, u1} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9) (LinearMap.instSemilinearMapClassLinearMap.{u5, u2, u3, u1} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃) g)) (AddCommGroup.toAddCommMonoid.{u3} (HasQuotient.Quotient.{u3, u3} M₂ (Submodule.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8) (Submodule.hasQuotient.{u5, u3} R₂ M₂ _inst_2 _inst_5 _inst_8) (LinearMap.range.{u6, u5, u4, u3, max u4 u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u6, u5, u4, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u6, u5, u4, u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (Submodule.Quotient.addCommGroup.{u5, u3} R₂ M₂ _inst_2 _inst_5 _inst_8 (LinearMap.range.{u6, u5, u4, u3, max u4 u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u6, u5, u4, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u6, u5, u4, u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f))) (Submodule.module.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_8 (LinearMap.ker.{u5, u2, u3, u1, max u3 u1} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃ (LinearMap.{u5, u2, u3, u1} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) τ₂₃ M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9) (LinearMap.instSemilinearMapClassLinearMap.{u5, u2, u3, u1} R₂ R₃ M₂ M₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u2} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_8 _inst_9 τ₂₃) g)) (Submodule.Quotient.module.{u5, u3} R₂ M₂ _inst_2 _inst_5 _inst_8 (LinearMap.range.{u6, u5, u4, u3, max u4 u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂ (LinearMap.{u6, u5, u4, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) τ₁₂ M M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8) (LinearMap.instSemilinearMapClassLinearMap.{u6, u5, u4, u3} R R₂ M M₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_7 _inst_8 τ₁₂) _inst_11 f)) (RingHom.id.{u5} R₂ (Semiring.toNonAssocSemiring.{u5} R₂ (Ring.toSemiring.{u5} R₂ _inst_2)))))))
Case conversion may be inaccurate. Consider using '#align linear_map.ker_le_range_iff LinearMap.ker_le_range_iffₓ'. -/
theorem ker_le_range_iff {f : M →ₛₗ[τ₁₂] M₂} {g : M₂ →ₛₗ[τ₂₃] M₃} :
g.ker ≤ f.range ↔ f.range.mkQ.comp g.ker.Subtype = 0 := by
@@ -1128,12 +1124,7 @@ variable {R M M₂ : Type _} {r : R} {x y : M} [CommRing R] [AddCommGroup M] [Mo
namespace Submodule
-/- warning: submodule.mapq_linear -> Submodule.mapQLinear is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} {M₂ : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : AddCommGroup.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (q : Submodule.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5), LinearMap.{u1, u1, max u2 u3, max u2 u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (coeSort.{succ (max u2 u3), succ (succ (max u2 u3))} (Submodule.{u1, max u2 u3} R (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R M M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u3} R R R M M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_5 (Submodule.mapQLinear._proof_1.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5))) Type.{max u2 u3} (SetLike.hasCoeToSort.{max u2 u3, max u2 u3} (Submodule.{u1, max u2 u3} R (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R M M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u3} R R R M M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} 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(max u2 u3)} (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5) (fun (x : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5) => Membership.mem.{max u2 u3, max u2 u3} (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R M M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u3} R R R M M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_5 (smulCommClass_self.{u1, u3} R M₂ (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u3} R M₂ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5))))) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5) (Submodule.instSetLikeSubmodule.{u1, max u2 u3} R (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R M M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5)))))) x (Submodule.compatibleMaps.{u1, u2, u3} R M M₂ (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 p q))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) p) (HasQuotient.Quotient.{u3, u3} M₂ (Submodule.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5) (Submodule.hasQuotient.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5) q) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u3} (HasQuotient.Quotient.{u3, u3} M₂ (Submodule.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5) (Submodule.hasQuotient.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5) q) (Submodule.Quotient.addCommGroup.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5 q)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R 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_inst_1))) (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5)))) (Submodule.compatibleMaps.{u1, u2, u3} R M M₂ (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 p q)) (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) p) (HasQuotient.Quotient.{u3, u3} M₂ (Submodule.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5) (Submodule.hasQuotient.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5) q) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u3} (HasQuotient.Quotient.{u3, u3} M₂ (Submodule.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5) (Submodule.hasQuotient.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5) q) (Submodule.Quotient.addCommGroup.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5 q)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5 q) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, max u2 u3} R (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R M M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u3} R R R M M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_5 (smulCommClass_self.{u1, u3} R M₂ (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u3} R M₂ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5)))) (Submodule.compatibleMaps.{u1, u2, u3} R M M₂ (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 p q)) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u3} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) p) (HasQuotient.Quotient.{u3, u3} M₂ (Submodule.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5) (Submodule.hasQuotient.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5) q) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u3} (HasQuotient.Quotient.{u3, u3} M₂ (Submodule.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5) (Submodule.hasQuotient.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5) q) (Submodule.Quotient.addCommGroup.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5 q)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5 q) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Submodule.Quotient.module.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5 q) (Submodule.Quotient.smulCommClass.{u1, u3, u1, u1} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5 R (SMulZeroClass.toSMul.{u1, u1} R R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulZeroClass.toSMulWithZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u3} R M₂ (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4))) (SMulWithZero.toSMulZeroClass.{u1, u3} R M₂ (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M₂ (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5)))) (IsScalarTower.left.{u1, u3} R M₂ (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u3} R M₂ (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_4))))) (Module.toMulActionWithZero.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5))) q R (SMulZeroClass.toSMul.{u1, u1} R R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulZeroClass.toSMulWithZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u3} R M₂ (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4))) (SMulWithZero.toSMulZeroClass.{u1, u3} R M₂ (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M₂ (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5)))) (IsScalarTower.left.{u1, u3} R M₂ (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u3} R M₂ (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_4))))) (Module.toMulActionWithZero.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5))) (smulCommClass_self.{u1, u3} R M₂ (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u3} R M₂ (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_4))))) (Module.toMulActionWithZero.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5)))))
-Case conversion may be inaccurate. Consider using '#align submodule.mapq_linear Submodule.mapQLinearₓ'. -/
+#print Submodule.mapQLinear /-
/-- Given modules `M`, `M₂` over a commutative ring, together with submodules `p ⊆ M`, `q ⊆ M₂`,
the natural map $\{f ∈ Hom(M, M₂) | f(p) ⊆ q \} \to Hom(M/p, M₂/q)$ is linear. -/
def mapQLinear : compatibleMaps p q →ₗ[R] M ⧸ p →ₗ[R] M₂ ⧸ q
@@ -1146,6 +1137,7 @@ def mapQLinear : compatibleMaps p q →ₗ[R] M ⧸ p →ₗ[R] M₂ ⧸ q
ext
rfl
#align submodule.mapq_linear Submodule.mapQLinear
+-/
end Submodule
mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212
@@ -501,7 +501,7 @@ variable {M₂ : Type _} [AddCommGroup M₂] [Module R M₂]
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {M₂ : Type.{u3}} [_inst_4 : AddCommGroup.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4)] {{f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5}} {{g : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5}}, (forall (x : M), Eq.{succ u3} M₂ (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5) => (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) -> M₂) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5) => (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) -> M₂) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) g (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x))) -> (Eq.{max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5) f g)
but is expected to have type
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(Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4) (Submodule.Quotient.module.{u3, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5) (g : LinearMap.{u3, u3, u2, u1} 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))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4) (Submodule.Quotient.module.{u3, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5), (forall (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) => M₂) (Submodule.Quotient.mk.{u3, u2} R M _inst_1 _inst_2 _inst_3 p x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} 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))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4) (Submodule.Quotient.module.{u3, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (fun (_x : HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, 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(Ring.toSemiring.{u3} R _inst_1)))) f (Submodule.Quotient.mk.{u3, u2} R M _inst_1 _inst_2 _inst_3 p x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} 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))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4) (Submodule.Quotient.module.{u3, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (fun (_x : HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4) (Submodule.Quotient.module.{u3, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) g (Submodule.Quotient.mk.{u3, u2} R M _inst_1 _inst_2 _inst_3 p x))) -> (Eq.{max (succ u2) (succ u1)} (LinearMap.{u3, u3, u2, u1} 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))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4) (Submodule.Quotient.module.{u3, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5) f g)
+ forall {R : Type.{u3}} {M : Type.{u2}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {M₂ : Type.{u1}} [_inst_4 : AddCommGroup.{u1} M₂] [_inst_5 : Module.{u3, u1} R M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4)] (f : LinearMap.{u3, u3, u2, u1} 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))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4) (Submodule.Quotient.module.{u3, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5) (g : LinearMap.{u3, u3, u2, u1} 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))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4) (Submodule.Quotient.module.{u3, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5), (forall (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) => M₂) (Submodule.Quotient.mk.{u3, u2} R M _inst_1 _inst_2 _inst_3 p x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} 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))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 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_inst_5) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (fun (_x : HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4) (Submodule.Quotient.module.{u3, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) g (Submodule.Quotient.mk.{u3, u2} R M _inst_1 _inst_2 _inst_3 p x))) -> (Eq.{max (succ u2) (succ u1)} (LinearMap.{u3, u3, u2, u1} 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))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u3, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u3, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_4) (Submodule.Quotient.module.{u3, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_5) f g)
Case conversion may be inaccurate. Consider using '#align submodule.quot_hom_ext Submodule.quot_hom_extₓ'. -/
theorem quot_hom_ext ⦃f g : M ⧸ p →ₗ[R] M₂⦄ (h : ∀ x, f (Quotient.mk x) = g (Quotient.mk x)) :
f = g :=
@@ -521,7 +521,7 @@ def mkQ : M →ₗ[R] M ⧸ p where
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (x : M), Eq.{succ u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) => M -> (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p)) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) x) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x)
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (x : M), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) x) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) x) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x)
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (x : M), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) x) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) x) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x)
Case conversion may be inaccurate. Consider using '#align submodule.mkq_apply Submodule.mkQ_applyₓ'. -/
@[simp]
theorem mkQ_apply (x : M) : p.mkQ x = Quotient.mk x :=
@@ -532,7 +532,7 @@ theorem mkQ_apply (x : M) : p.mkQ x = Quotient.mk x :=
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (A : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), Function.Surjective.{succ u2, succ u2} M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) A) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) A) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) A) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 A)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 A)) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) A) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) A) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 A)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 A)) => M -> (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) A)) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) A) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) A) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 A)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 A) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 A))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (A : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3), Function.Surjective.{succ u1, succ u1} M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) A) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} 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))) M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) A) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) A) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 A)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 A)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) A) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) A) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) A) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 A)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 A) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.mkQ.{u2, u1} R M _inst_1 _inst_2 _inst_3 A))
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (A : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3), Function.Surjective.{succ u1, succ u1} M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) A) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} 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))) M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) A) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) A) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 A)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 A)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) A) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) A) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) A) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 A)) _inst_3 (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 A) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.mkQ.{u2, u1} R M _inst_1 _inst_2 _inst_3 A))
Case conversion may be inaccurate. Consider using '#align submodule.mkq_surjective Submodule.mkQ_surjectiveₓ'. -/
theorem mkQ_surjective (A : Submodule R M) : Function.Surjective A.mkQ := by
rintro ⟨x⟩ <;> exact ⟨x, rfl⟩
@@ -574,7 +574,7 @@ def liftQ (f : M →ₛₗ[τ₁₂] M₂) (h : p ≤ f.ker) : M ⧸ p →ₛₗ
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) {h : LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (LinearMap.ker.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)} (x : M), Eq.{succ u4} M₂ (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) (fun (_x : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) => (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) -> M₂) (LinearMap.hasCoeToFun.{u1, u3, u2, u4} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) (Submodule.liftQ.{u1, u2, u3, u4} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 p x)) (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f x)
but is expected to have type
- forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) {h : LE.le.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (LinearMap.ker.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)} (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) => M₂) (Submodule.Quotient.mk.{u4, u2} R M _inst_1 _inst_2 _inst_3 p x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (fun (_x : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) (Submodule.liftQ.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h) (Submodule.Quotient.mk.{u4, u2} R M _inst_1 _inst_2 _inst_3 p x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f x)
+ forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) {h : LE.le.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (LinearMap.ker.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f)} (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) => M₂) (Submodule.Quotient.mk.{u4, u2} R M _inst_1 _inst_2 _inst_3 p x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (fun (_x : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_6 τ₁₂) (Submodule.liftQ.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ f h) (Submodule.Quotient.mk.{u4, u2} R M _inst_1 _inst_2 _inst_3 p x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f x)
Case conversion may be inaccurate. Consider using '#align submodule.liftq_apply Submodule.liftQ_applyₓ'. -/
@[simp]
theorem liftQ_apply (f : M →ₛₗ[τ₁₂] M₂) {h} (x : M) : p.liftQ f h (Quotient.mk x) = f x :=
@@ -595,7 +595,7 @@ theorem liftQ_mkQ (f : M →ₛₗ[τ₁₂] M₂) (h) : (p.liftQ f h).comp p.mk
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (x : M) (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6), (Eq.{succ u4} M₂ (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f x) (OfNat.ofNat.{u4} M₂ 0 (OfNat.mk.{u4} M₂ 0 (Zero.zero.{u4} M₂ (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (SubNegMonoid.toAddMonoid.{u4} M₂ (AddGroup.toSubNegMonoid.{u4} M₂ (AddCommGroup.toAddGroup.{u4} M₂ _inst_5))))))))) -> (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x)))) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))) _inst_6)
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (x : M) (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6), (Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) x) (FunLike.coe.{max (succ u2) (succ u4), succ u2, succ u4} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f x) (OfNat.ofNat.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) x) 0 (Zero.toOfNat0.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) x) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) x) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) x) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) x) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) x) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) x) _inst_5)))))))) -> (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x)))) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) _inst_6)
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (x : M) (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6), (Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) x) (FunLike.coe.{max (succ u2) (succ u4), succ u2, succ u4} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f x) (OfNat.ofNat.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) x) 0 (Zero.toOfNat0.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) x) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) x) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) x) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) x) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) x) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) x) _inst_5)))))))) -> (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x)))) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) _inst_6)
Case conversion may be inaccurate. Consider using '#align submodule.liftq_span_singleton Submodule.liftQSpanSingletonₓ'. -/
/-- Special case of `liftq` when `p` is the span of `x`. In this case, the condition on `f` simply
becomes vanishing at `x`.-/
@@ -607,7 +607,7 @@ def liftQSpanSingleton (x : M) (f : M →ₛₗ[τ₁₂] M₂) (h : f x = 0) :
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (x : M) (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (h : Eq.{succ u4} M₂ (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} 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(AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x)))) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))) _inst_6) => (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))) -> M₂) (LinearMap.hasCoeToFun.{u1, u3, u2, u4} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))) M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M 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_inst_1 _inst_2 _inst_3 R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ x f h) (Submodule.Quotient.mk.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x)) y)) (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f y)
but is expected to have type
- forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (x : M) (f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (h : Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ 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(Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) (fun (_x : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x)))) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) _inst_6 τ₁₂) (Submodule.liftQSpanSingleton.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ x f h) (Submodule.Quotient.mk.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x)) y)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f y)
+ forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (x : M) (f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (h : Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) x) (NegZeroClass.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) x) (SubNegZeroMonoid.toNegZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) x) (SubtractionMonoid.toSubNegZeroMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) x) (SubtractionCommMonoid.toSubtractionMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) x) (AddCommGroup.toDivisionAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) x) _inst_5)))))))) (y : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) => M₂) (Submodule.Quotient.mk.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x)) y)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) M₂ (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x)))) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) _inst_6) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) (fun (_x : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x)))) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))) _inst_6 τ₁₂) (Submodule.liftQSpanSingleton.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ x f h) (Submodule.Quotient.mk.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x)) y)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f y)
Case conversion may be inaccurate. Consider using '#align submodule.liftq_span_singleton_apply Submodule.liftQSpanSingleton_applyₓ'. -/
@[simp]
theorem liftQSpanSingleton_apply (x : M) (f : M →ₛₗ[τ₁₂] M₂) (h : f x = 0) (y : M) :
@@ -696,7 +696,7 @@ def mapQ (f : M →ₛₗ[τ₁₂] M₂) (h : p ≤ comap f q) : M ⧸ p →ₛ
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} (q : Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) {h : LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) p (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R 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but is expected to have type
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(Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q) τ₁₂) (Submodule.mapQ.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ q f h) (Submodule.Quotient.mk.{u4, u2} R M _inst_1 _inst_2 _inst_3 p x)) (Submodule.Quotient.mk.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f x))
+ forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} (q : Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) {h : LE.le.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p (Submodule.comap.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f q)} (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) => HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.mk.{u4, u2} R M _inst_1 _inst_2 _inst_3 p x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (fun (_x : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) => HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u4, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u4, u2} R M _inst_1 _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Submodule.hasQuotient.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) q) (Submodule.Quotient.addCommGroup.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q)) (Submodule.Quotient.module.{u4, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.Quotient.module.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q) τ₁₂) (Submodule.mapQ.{u4, u2, u3, u1} R M _inst_1 _inst_2 _inst_3 p R₂ M₂ _inst_4 _inst_5 _inst_6 τ₁₂ q f h) (Submodule.Quotient.mk.{u4, u2} R M _inst_1 _inst_2 _inst_3 p x)) (Submodule.Quotient.mk.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 q (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f x))
Case conversion may be inaccurate. Consider using '#align submodule.mapq_apply Submodule.mapQ_applyₓ'. -/
@[simp]
theorem mapQ_apply (f : M →ₛₗ[τ₁₂] M₂) {h} (x : M) :
@@ -877,7 +877,7 @@ theorem comapMkQOrderEmbedding_eq (p' : Submodule R (M ⧸ p)) :
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {R₂ : Type.{u3}} {M₂ : Type.{u4}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_4))} [_inst_7 : RingHomSurjective.{u1, u3} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂] {f : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6} {s : Set.{u4} M₂}, (Set.Nonempty.{u4} M₂ s) -> (HasSubset.Subset.{u4} (Set.{u4} M₂) (Set.hasSubset.{u4} M₂) s ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Set.{u4} M₂) (HasLiftT.mk.{succ u4, succ u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Set.{u4} M₂) (CoeTCₓ.coe.{succ u4, succ u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) (Set.{u4} M₂) (SetLike.Set.hasCoeT.{u4, u4} (Submodule.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6) M₂ (Submodule.setLike.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6)))) (LinearMap.range.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) _inst_7 f))) -> (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Set.preimage.{u2, u4} M M₂ (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f) s)) (Submodule.comap.{u1, u3, u2, u4, max u2 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u1, u3, u2, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u3, u2, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f (Submodule.span.{u3, u4} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_6 s)))
but is expected to have type
- forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} [_inst_7 : RingHomSurjective.{u4, u3} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂] {f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6} {s : Set.{u1} M₂}, (Set.Nonempty.{u1} M₂ s) -> (HasSubset.Subset.{u1} (Set.{u1} M₂) (Set.instHasSubsetSet.{u1} M₂) s (SetLike.coe.{u1, u1} (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) M₂ (Submodule.instSetLikeSubmodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (LinearMap.range.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) _inst_7 f))) -> (Eq.{succ u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Set.preimage.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f) s)) (Submodule.comap.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f (Submodule.span.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6 s)))
+ forall {R : Type.{u4}} {M : Type.{u2}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {R₂ : Type.{u3}} {M₂ : Type.{u1}} [_inst_4 : Ring.{u3} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_4))} [_inst_7 : RingHomSurjective.{u4, u3} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂] {f : LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6} {s : Set.{u1} M₂}, (Set.Nonempty.{u1} M₂ s) -> (HasSubset.Subset.{u1} (Set.{u1} M₂) (Set.instHasSubsetSet.{u1} M₂) s (SetLike.coe.{u1, u1} (Submodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) M₂ (Submodule.instSetLikeSubmodule.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (LinearMap.range.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) _inst_7 f))) -> (Eq.{succ u2} (Submodule.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.span.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Set.preimage.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f) s)) (Submodule.comap.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_3 _inst_6 τ₁₂) f (Submodule.span.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6 s)))
Case conversion may be inaccurate. Consider using '#align submodule.span_preimage_eq Submodule.span_preimage_eqₓ'. -/
theorem span_preimage_eq [RingHomSurjective τ₁₂] {f : M →ₛₗ[τ₁₂] M₂} {s : Set M₂} (h₀ : s.Nonempty)
(h₁ : s ⊆ range f) : span R (f ⁻¹' s) = (span R₂ s).comap f :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/195fcd60ff2bfe392543bceb0ec2adcdb472db4c
@@ -224,11 +224,11 @@ theorem mk_smul (r : S) (x : M) : (mk (r • x) : M ⧸ p) = r • mk x :=
rfl
#align submodule.quotient.mk_smul Submodule.Quotient.mk_smul
-#print Submodule.Quotient.sMulCommClass /-
-instance sMulCommClass (T : Type _) [SMul T R] [SMul T M] [IsScalarTower T R M]
+#print Submodule.Quotient.smulCommClass /-
+instance smulCommClass (T : Type _) [SMul T R] [SMul T M] [IsScalarTower T R M]
[SMulCommClass S T M] : SMulCommClass S T (M ⧸ P)
where smul_comm x y := Quotient.ind' fun z => congr_arg mk (smul_comm _ _ _)
-#align submodule.quotient.smul_comm_class Submodule.Quotient.sMulCommClass
+#align submodule.quotient.smul_comm_class Submodule.Quotient.smulCommClass
-/
#print Submodule.Quotient.isScalarTower /-
@@ -1132,7 +1132,7 @@ namespace Submodule
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} {M₂ : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : AddCommGroup.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (q : Submodule.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5), LinearMap.{u1, u1, max u2 u3, max u2 u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (coeSort.{succ (max u2 u3), succ (succ (max u2 u3))} (Submodule.{u1, max u2 u3} R (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R M M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u3} R R R M M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_5 (Submodule.mapQLinear._proof_1.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5))) Type.{max u2 u3} (SetLike.hasCoeToSort.{max u2 u3, max u2 u3} (Submodule.{u1, max u2 u3} R (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R M M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u3} R R R M M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_5 (Submodule.mapQLinear._proof_1.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5))) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5) (Submodule.setLike.{u1, max u2 u3} R (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R M M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u3} R R R M M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_5 (Submodule.mapQLinear._proof_1.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5)))) (Submodule.compatibleMaps.{u1, u2, u3} R M M₂ (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 p q)) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) p) (HasQuotient.Quotient.{u3, u3} M₂ (Submodule.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5) (Submodule.hasQuotient.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5) q) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u3} (HasQuotient.Quotient.{u3, u3} M₂ (Submodule.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5) (Submodule.hasQuotient.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5) q) (Submodule.Quotient.addCommGroup.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5 q)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5 q)) (Submodule.addCommMonoid.{u1, max u2 u3} R (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R M M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u3} R R R M M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_5 (Submodule.mapQLinear._proof_1.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5)) (Submodule.compatibleMaps.{u1, u2, u3} R M M₂ (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 p q)) (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) p) (HasQuotient.Quotient.{u3, u3} M₂ (Submodule.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5) (Submodule.hasQuotient.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5) q) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u3} (HasQuotient.Quotient.{u3, u3} M₂ (Submodule.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5) (Submodule.hasQuotient.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5) q) (Submodule.Quotient.addCommGroup.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5 q)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5 q) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, max u2 u3} R (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R M M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u3} R R R M M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_5 (Submodule.mapQLinear._proof_1.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5)) (Submodule.compatibleMaps.{u1, u2, u3} R M M₂ (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 p q)) (LinearMap.module.{u1, u1, u1, u2, u3} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) p) (HasQuotient.Quotient.{u3, u3} M₂ (Submodule.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5) (Submodule.hasQuotient.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5) q) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u3} (HasQuotient.Quotient.{u3, u3} M₂ (Submodule.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5) (Submodule.hasQuotient.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5) q) (Submodule.Quotient.addCommGroup.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5 q)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5 q) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Submodule.Quotient.module.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5 q) (Submodule.mapQLinear._proof_2.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5 q))
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} {M₂ : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : AddCommGroup.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (q : Submodule.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5), LinearMap.{u1, u1, max u2 u3, max u3 u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Subtype.{succ (max u2 u3)} (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5) (fun (x : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5) => Membership.mem.{max u2 u3, max u2 u3} (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5) (Submodule.{u1, max u3 u2} R (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R M M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u3} R R R M M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_5 (smulCommClass_self.{u1, u3} R M₂ (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u3} R M₂ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5))))) (SetLike.instMembership.{max u2 u3, max u2 u3} (Submodule.{u1, max u3 u2} R (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R M M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u3} R R R M M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_5 (smulCommClass_self.{u1, u3} R M₂ (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u3} R M₂ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5))))) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5) (Submodule.instSetLikeSubmodule.{u1, max u2 u3} R (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R M M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u3} R R R M M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_5 (smulCommClass_self.{u1, u3} R M₂ (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u3} R M₂ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5)))))) x (Submodule.compatibleMaps.{u1, u2, u3} R M M₂ (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 p q))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) p) (HasQuotient.Quotient.{u3, u3} M₂ (Submodule.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5) (Submodule.hasQuotient.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5) q) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u3} (HasQuotient.Quotient.{u3, u3} M₂ (Submodule.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5) (Submodule.hasQuotient.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5) q) (Submodule.Quotient.addCommGroup.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5 q)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5 q)) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, max u2 u3} R (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R M M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u3} R R R M M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_5 (smulCommClass_self.{u1, u3} R M₂ (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u3} R M₂ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5)))) (Submodule.compatibleMaps.{u1, u2, u3} R M M₂ (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 p q)) (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) p) (HasQuotient.Quotient.{u3, u3} M₂ (Submodule.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5) (Submodule.hasQuotient.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5) q) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u3} (HasQuotient.Quotient.{u3, u3} M₂ (Submodule.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5) (Submodule.hasQuotient.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5) q) (Submodule.Quotient.addCommGroup.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5 q)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5 q) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, max u2 u3} R (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R M M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u3} R R R M M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_5 (smulCommClass_self.{u1, u3} R M₂ (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u3} R M₂ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5)))) (Submodule.compatibleMaps.{u1, u2, u3} R M M₂ (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 p q)) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u3} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) p) (HasQuotient.Quotient.{u3, u3} M₂ (Submodule.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5) (Submodule.hasQuotient.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5) q) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u3} (HasQuotient.Quotient.{u3, u3} M₂ (Submodule.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5) (Submodule.hasQuotient.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5) q) (Submodule.Quotient.addCommGroup.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5 q)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5 q) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Submodule.Quotient.module.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5 q) (Submodule.Quotient.sMulCommClass.{u1, u3, u1, u1} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5 R (SMulZeroClass.toSMul.{u1, u1} R R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulZeroClass.toSMulWithZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u3} R M₂ (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4))) (SMulWithZero.toSMulZeroClass.{u1, u3} R M₂ (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M₂ (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5)))) (IsScalarTower.left.{u1, u3} R M₂ (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u3} R M₂ (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_4))))) (Module.toMulActionWithZero.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5))) q R (SMulZeroClass.toSMul.{u1, u1} R R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulZeroClass.toSMulWithZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u3} R M₂ (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4))) (SMulWithZero.toSMulZeroClass.{u1, u3} R M₂ (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M₂ (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5)))) (IsScalarTower.left.{u1, u3} R M₂ (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u3} R M₂ (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_4))))) (Module.toMulActionWithZero.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5))) (smulCommClass_self.{u1, u3} R M₂ (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u3} R M₂ (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_4))))) (Module.toMulActionWithZero.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5)))))
+ forall {R : Type.{u1}} {M : Type.{u2}} {M₂ : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : AddCommGroup.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (q : Submodule.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5), LinearMap.{u1, u1, max u2 u3, max u3 u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Subtype.{succ (max u2 u3)} (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5) (fun (x : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5) => Membership.mem.{max u2 u3, max u2 u3} (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5) (Submodule.{u1, max u3 u2} R (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R M M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u3} R R R M M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_5 (smulCommClass_self.{u1, u3} R M₂ (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u3} R M₂ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5))))) (SetLike.instMembership.{max u2 u3, max u2 u3} (Submodule.{u1, max u3 u2} R (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R M M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u3} R R R M M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_5 (smulCommClass_self.{u1, u3} R M₂ (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u3} R M₂ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5))))) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5) (Submodule.instSetLikeSubmodule.{u1, max u2 u3} R (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R M M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u3} R R R M M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_5 (smulCommClass_self.{u1, u3} R M₂ (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u3} R M₂ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5)))))) x (Submodule.compatibleMaps.{u1, u2, u3} R M M₂ (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 p q))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) p) (HasQuotient.Quotient.{u3, u3} M₂ (Submodule.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5) (Submodule.hasQuotient.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5) q) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u3} (HasQuotient.Quotient.{u3, u3} M₂ (Submodule.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5) (Submodule.hasQuotient.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5) q) (Submodule.Quotient.addCommGroup.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5 q)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R 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(AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u3} R R R M M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_5 (smulCommClass_self.{u1, u3} R M₂ (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u3} R M₂ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5)))) (Submodule.compatibleMaps.{u1, u2, u3} R M M₂ (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 p q)) (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) p) (HasQuotient.Quotient.{u3, u3} M₂ (Submodule.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5) (Submodule.hasQuotient.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5) q) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 p)) (AddCommGroup.toAddCommMonoid.{u3} (HasQuotient.Quotient.{u3, u3} M₂ (Submodule.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5) (Submodule.hasQuotient.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5) q) (Submodule.Quotient.addCommGroup.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5 q)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 p) (Submodule.Quotient.module.{u1, u3} R M₂ (CommRing.toRing.{u1} R _inst_1) _inst_4 _inst_5 q) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, max u2 u3} R (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R M M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u3} R R R M M₂ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_5 (smulCommClass_self.{u1, u3} R M₂ 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(CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulZeroClass.toSMulWithZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u3} R M₂ (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4))) (SMulWithZero.toSMulZeroClass.{u1, u3} R M₂ (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M₂ (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5)))) (IsScalarTower.left.{u1, u3} R M₂ (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u3} R M₂ (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_4))))) (Module.toMulActionWithZero.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5))) q R (SMulZeroClass.toSMul.{u1, u1} R R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SMulWithZero.toSMulZeroClass.{u1, u1} R R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulZeroClass.toSMulWithZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u3} R M₂ (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4))) (SMulWithZero.toSMulZeroClass.{u1, u3} R M₂ (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M₂ (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5)))) (IsScalarTower.left.{u1, u3} R M₂ (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u3} R M₂ (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_4))))) (Module.toMulActionWithZero.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5))) (smulCommClass_self.{u1, u3} R M₂ (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u3} R M₂ (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_4))))) (Module.toMulActionWithZero.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5)))))
Case conversion may be inaccurate. Consider using '#align submodule.mapq_linear Submodule.mapQLinearₓ'. -/
/-- Given modules `M`, `M₂` over a commutative ring, together with submodules `p ⊆ M`, `q ⊆ M₂`,
the natural map $\{f ∈ Hom(M, M₂) | f(p) ⊆ q \} \to Hom(M/p, M₂/q)$ is linear. -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211
@@ -659,9 +659,9 @@ theorem mkQ_map_self : map p.mkQ p = ⊥ := by
/- warning: submodule.comap_map_mkq -> Submodule.comap_map_mkQ is a dubious translation:
lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (p' : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.comap.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.map.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) p')) (HasSup.sup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p p')
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (p' : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.comap.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.map.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) p')) (Sup.sup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p p')
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (p' : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.comap.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.map.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) p')) (HasSup.sup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p p')
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (p' : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.comap.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.map.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) p')) (Sup.sup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p p')
Case conversion may be inaccurate. Consider using '#align submodule.comap_map_mkq Submodule.comap_map_mkQₓ'. -/
@[simp]
theorem comap_map_mkQ : comap p.mkQ (map p.mkQ p') = p ⊔ p' := by simp [comap_map_eq, sup_comm]
@@ -669,9 +669,9 @@ theorem comap_map_mkQ : comap p.mkQ (map p.mkQ p') = p ⊔ p' := by simp [comap_
/- warning: submodule.map_mkq_eq_top -> Submodule.map_mkQ_eq_top is a dubious translation:
lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (p' : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), Iff (Eq.{succ u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.map.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) p') (Top.top.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.hasTop.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)))) (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HasSup.sup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p p') (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (p' : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), Iff (Eq.{succ u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.map.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) p') (Top.top.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.hasTop.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)))) (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Sup.sup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p p') (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (p' : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), Iff (Eq.{succ u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.map.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) p') (Top.top.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.instTopSubmodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)))) (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (HasSup.sup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p p') (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (p' : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), Iff (Eq.{succ u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.map.{u1, u1, u2, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) p') (Top.top.{u2} (Submodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.instTopSubmodule.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p)))) (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Sup.sup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) p p') (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))
Case conversion may be inaccurate. Consider using '#align submodule.map_mkq_eq_top Submodule.map_mkQ_eq_topₓ'. -/
@[simp]
theorem map_mkQ_eq_top : map p.mkQ p' = ⊤ ↔ p ⊔ p' = ⊤ := by
mathlib commit https://github.com/leanprover-community/mathlib/commit/3ade05ac9447ae31a22d2ea5423435e054131240
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Kevin Buzzard, Yury Kudryashov
! This file was ported from Lean 3 source module linear_algebra.quotient
-! leanprover-community/mathlib commit 0d17cfb64a04ded3972434625fa74505ea1780f0
+! leanprover-community/mathlib commit 23aa88e32dcc9d2a24cca7bc23268567ed4cd7d6
! 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.Span
/-!
# Quotients by submodules
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
* If `p` is a submodule of `M`, `M ⧸ p` is the quotient of `M` with respect to `p`:
that is, elements of `M` are identified if their difference is in `p`. This is itself a module.
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
Purely automatic replacement. If this is in any way controversial; I'm happy to just close this PR.
@@ -365,7 +365,7 @@ theorem liftQ_mkQ (f : M →ₛₗ[τ₁₂] M₂) (h) : (p.liftQ f h).comp p.mk
#align submodule.liftq_mkq Submodule.liftQ_mkQ
/-- Special case of `submodule.liftQ` when `p` is the span of `x`. In this case, the condition on
-`f` simply becomes vanishing at `x`.-/
+`f` simply becomes vanishing at `x`. -/
def liftQSpanSingleton (x : M) (f : M →ₛₗ[τ₁₂] M₂) (h : f x = 0) : (M ⧸ R ∙ x) →ₛₗ[τ₁₂] M₂ :=
(R ∙ x).liftQ f <| by rw [span_singleton_le_iff_mem, LinearMap.mem_ker, h]
#align submodule.liftq_span_singleton Submodule.liftQSpanSingleton
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)
@@ -22,7 +22,6 @@ section Ring
namespace Submodule
variable {R M : Type*} {r : R} {x y : M} [Ring R] [AddCommGroup M] [Module R M]
-
variable (p p' : Submodule R M)
open LinearMap QuotientAddGroup
@@ -572,15 +571,10 @@ namespace LinearMap
section Ring
variable {R M R₂ M₂ R₃ M₃ : Type*}
-
variable [Ring R] [Ring R₂] [Ring R₃]
-
variable [AddCommMonoid M] [AddCommGroup M₂] [AddCommMonoid M₃]
-
variable [Module R M] [Module R₂ M₂] [Module R₃ M₃]
-
variable {τ₁₂ : R →+* R₂} {τ₂₃ : R₂ →+* R₃} {τ₁₃ : R →+* R₃}
-
variable [RingHomCompTriple τ₁₂ τ₂₃ τ₁₃] [RingHomSurjective τ₁₂]
theorem range_mkQ_comp (f : M →ₛₗ[τ₁₂] M₂) : f.range.mkQ.comp f = 0 :=
@@ -609,7 +603,6 @@ open LinearMap
namespace Submodule
variable {R M : Type*} {r : R} {x y : M} [Ring R] [AddCommGroup M] [Module R M]
-
variable (p p' : Submodule R M)
/-- If `p = ⊥`, then `M / p ≃ₗ[R] M`. -/
Homogenises porting notes via capitalisation and addition of whitespace.
It makes the following changes:
@@ -130,7 +130,7 @@ instance instSMul' : SMul S (M ⧸ P) :=
leftRel_apply.mpr <| by simpa using Submodule.smul_mem P (a • (1 : R)) (leftRel_apply.mp h)⟩
#align submodule.quotient.has_smul' Submodule.Quotient.instSMul'
--- porting note: should this be marked as a `@[default_instance]`?
+-- Porting note: should this be marked as a `@[default_instance]`?
/-- Shortcut to help the elaborator in the common case. -/
instance instSMul : SMul R (M ⧸ P) :=
Quotient.instSMul' P
@@ -170,7 +170,7 @@ instance mulAction' [Monoid S] [SMul S R] [MulAction S M] [IsScalarTower S R M]
toSMul := instSMul' _ }
#align submodule.quotient.mul_action' Submodule.Quotient.mulAction'
--- porting note: should this be marked as a `@[default_instance]`?
+-- Porting note: should this be marked as a `@[default_instance]`?
instance mulAction (P : Submodule R M) : MulAction R (M ⧸ P) :=
Quotient.mulAction' P
#align submodule.quotient.mul_action Submodule.Quotient.mulAction
@@ -180,7 +180,7 @@ instance smulZeroClass' [SMul S R] [SMulZeroClass S M] [IsScalarTower S R M] (P
ZeroHom.smulZeroClass ⟨mk, mk_zero _⟩ <| Submodule.Quotient.mk_smul P
#align submodule.quotient.smul_zero_class' Submodule.Quotient.smulZeroClass'
--- porting note: should this be marked as a `@[default_instance]`?
+-- Porting note: should this be marked as a `@[default_instance]`?
instance smulZeroClass (P : Submodule R M) : SMulZeroClass R (M ⧸ P) :=
Quotient.smulZeroClass' P
#align submodule.quotient.smul_zero_class Submodule.Quotient.smulZeroClass
@@ -194,7 +194,7 @@ instance distribSMul' [SMul S R] [DistribSMul S M] [IsScalarTower S R M] (P : Su
toSMulZeroClass := smulZeroClass' _ }
#align submodule.quotient.distrib_smul' Submodule.Quotient.distribSMul'
--- porting note: should this be marked as a `@[default_instance]`?
+-- Porting note: should this be marked as a `@[default_instance]`?
instance distribSMul (P : Submodule R M) : DistribSMul R (M ⧸ P) :=
Quotient.distribSMul' P
#align submodule.quotient.distrib_smul Submodule.Quotient.distribSMul
@@ -208,7 +208,7 @@ instance distribMulAction' [Monoid S] [SMul S R] [DistribMulAction S M] [IsScala
toMulAction := mulAction' _ }
#align submodule.quotient.distrib_mul_action' Submodule.Quotient.distribMulAction'
--- porting note: should this be marked as a `@[default_instance]`?
+-- Porting note: should this be marked as a `@[default_instance]`?
instance distribMulAction (P : Submodule R M) : DistribMulAction R (M ⧸ P) :=
Quotient.distribMulAction' P
#align submodule.quotient.distrib_mul_action Submodule.Quotient.distribMulAction
@@ -222,7 +222,7 @@ instance module' [Semiring S] [SMul S R] [Module S M] [IsScalarTower S R M] (P :
toDistribMulAction := distribMulAction' _ }
#align submodule.quotient.module' Submodule.Quotient.module'
--- porting note: should this be marked as a `@[default_instance]`?
+-- Porting note: should this be marked as a `@[default_instance]`?
instance module (P : Submodule R M) : Module R (M ⧸ P) :=
Quotient.module' P
#align submodule.quotient.module Submodule.Quotient.module
@@ -344,7 +344,7 @@ variable {R₂ M₂ : Type*} [Ring R₂] [AddCommGroup M₂] [Module R₂ M₂]
`submodule.mkQ` are equal.
See note [partially-applied ext lemmas]. -/
-@[ext 1100] -- porting note: increase priority so this applies before `LinearMap.ext`
+@[ext 1100] -- Porting note: increase priority so this applies before `LinearMap.ext`
theorem linearMap_qext ⦃f g : M ⧸ p →ₛₗ[τ₁₂] M₂⦄ (h : f.comp p.mkQ = g.comp p.mkQ) : f = g :=
LinearMap.ext fun x => Quotient.inductionOn' x <| (LinearMap.congr_fun h : _)
#align submodule.linear_map_qext Submodule.linearMap_qext
@@ -401,7 +401,7 @@ theorem comap_map_mkQ : comap p.mkQ (map p.mkQ p') = p ⊔ p' := by simp [comap_
@[simp]
theorem map_mkQ_eq_top : map p.mkQ p' = ⊤ ↔ p ⊔ p' = ⊤ := by
- -- porting note: ambiguity of `map_eq_top_iff` is no longer automatically resolved by preferring
+ -- Porting note: ambiguity of `map_eq_top_iff` is no longer automatically resolved by preferring
-- the current namespace
simp only [LinearMap.map_eq_top_iff p.range_mkQ, sup_comm, ker_mkQ]
#align submodule.map_mkq_eq_top Submodule.map_mkQ_eq_top
@@ -456,7 +456,7 @@ theorem mapQ_pow {f : M →ₗ[R] M} (h : p ≤ p.comap f) (k : ℕ)
induction' k with k ih
· simp [LinearMap.one_eq_id]
· simp only [LinearMap.iterate_succ]
- -- porting note: why does any of these `optParams` need to be applied? Why didn't `simp` handle
+ -- Porting note: why does any of these `optParams` need to be applied? Why didn't `simp` handle
-- all of this for us?
convert mapQ_comp p p p f (f ^ k) h (p.le_comap_pow_of_le_comap h k)
(h.trans (comap_mono <| p.le_comap_pow_of_le_comap h k))
(· op ·) a
by (a op ·)
(#8843)
I used the regex \(\(· (.) ·\) (.)\)
, replacing with ($2 $1 ·)
.
@@ -126,7 +126,7 @@ variable {S : Type*} [SMul S R] [SMul S M] [IsScalarTower S R M] (P : Submodule
instance instSMul' : SMul S (M ⧸ P) :=
⟨fun a =>
- Quotient.map' ((· • ·) a) fun x y h =>
+ Quotient.map' (a • ·) fun x y h =>
leftRel_apply.mpr <| by simpa using Submodule.smul_mem P (a • (1 : R)) (leftRel_apply.mp h)⟩
#align submodule.quotient.has_smul' Submodule.Quotient.instSMul'
We replace the calls to Function.Surjective.x
for constructing instances with a more direct inheritance pattern.
Co-authored-by: Chris Hughes <33847686+ChrisHughes24@users.noreply.github.com> Co-authored-by: Matthew Ballard <matt@mrb.email>
@@ -162,9 +162,12 @@ section Module
variable {S : Type*}
+-- Performance of `Function.Surjective.mulAction` is worse since it has to unify data to apply
+-- TODO: leanprover-community/mathlib4#7432
instance mulAction' [Monoid S] [SMul S R] [MulAction S M] [IsScalarTower S R M]
(P : Submodule R M) : MulAction S (M ⧸ P) :=
- Function.Surjective.mulAction mk (surjective_quot_mk _) <| Submodule.Quotient.mk_smul P
+ { Function.Surjective.mulAction mk (surjective_quot_mk _) <| Submodule.Quotient.mk_smul P with
+ toSMul := instSMul' _ }
#align submodule.quotient.mul_action' Submodule.Quotient.mulAction'
-- porting note: should this be marked as a `@[default_instance]`?
@@ -182,10 +185,13 @@ instance smulZeroClass (P : Submodule R M) : SMulZeroClass R (M ⧸ P) :=
Quotient.smulZeroClass' P
#align submodule.quotient.smul_zero_class Submodule.Quotient.smulZeroClass
+-- Performance of `Function.Surjective.distribSMul` is worse since it has to unify data to apply
+-- TODO: leanprover-community/mathlib4#7432
instance distribSMul' [SMul S R] [DistribSMul S M] [IsScalarTower S R M] (P : Submodule R M) :
DistribSMul S (M ⧸ P) :=
- Function.Surjective.distribSMul {toFun := mk, map_zero' := rfl, map_add' := fun _ _ => rfl}
- (surjective_quot_mk _) (Submodule.Quotient.mk_smul P)
+ { Function.Surjective.distribSMul {toFun := mk, map_zero' := rfl, map_add' := fun _ _ => rfl}
+ (surjective_quot_mk _) (Submodule.Quotient.mk_smul P) with
+ toSMulZeroClass := smulZeroClass' _ }
#align submodule.quotient.distrib_smul' Submodule.Quotient.distribSMul'
-- porting note: should this be marked as a `@[default_instance]`?
@@ -193,10 +199,13 @@ instance distribSMul (P : Submodule R M) : DistribSMul R (M ⧸ P) :=
Quotient.distribSMul' P
#align submodule.quotient.distrib_smul Submodule.Quotient.distribSMul
+-- Performance of `Function.Surjective.distribMulAction` is worse since it has to unify data
+-- TODO: leanprover-community/mathlib4#7432
instance distribMulAction' [Monoid S] [SMul S R] [DistribMulAction S M] [IsScalarTower S R M]
(P : Submodule R M) : DistribMulAction S (M ⧸ P) :=
- Function.Surjective.distribMulAction {toFun := mk, map_zero' := rfl, map_add' := fun _ _ => rfl}
- (surjective_quot_mk _) (Submodule.Quotient.mk_smul P)
+ { Function.Surjective.distribMulAction {toFun := mk, map_zero' := rfl, map_add' := fun _ _ => rfl}
+ (surjective_quot_mk _) (Submodule.Quotient.mk_smul P) with
+ toMulAction := mulAction' _ }
#align submodule.quotient.distrib_mul_action' Submodule.Quotient.distribMulAction'
-- porting note: should this be marked as a `@[default_instance]`?
@@ -204,10 +213,13 @@ instance distribMulAction (P : Submodule R M) : DistribMulAction R (M ⧸ P) :=
Quotient.distribMulAction' P
#align submodule.quotient.distrib_mul_action Submodule.Quotient.distribMulAction
+-- Performance of `Function.Surjective.module` is worse since it has to unify data to apply
+-- TODO: leanprover-community/mathlib4#7432
instance module' [Semiring S] [SMul S R] [Module S M] [IsScalarTower S R M] (P : Submodule R M) :
Module S (M ⧸ P) :=
- Function.Surjective.module _ {toFun := mk, map_zero' := rfl, map_add' := fun _ _ => rfl}
- (surjective_quot_mk _) (Submodule.Quotient.mk_smul P)
+ { Function.Surjective.module _ {toFun := mk, map_zero' := by rfl, map_add' := fun _ _ => by rfl}
+ (surjective_quot_mk _) (Submodule.Quotient.mk_smul P) with
+ toDistribMulAction := distribMulAction' _ }
#align submodule.quotient.module' Submodule.Quotient.module'
-- porting note: should this be marked as a `@[default_instance]`?
@@ -142,18 +142,18 @@ theorem mk_smul (r : S) (x : M) : (mk (r • x) : M ⧸ p) = r • mk x :=
#align submodule.quotient.mk_smul Submodule.Quotient.mk_smul
instance smulCommClass (T : Type*) [SMul T R] [SMul T M] [IsScalarTower T R M]
- [SMulCommClass S T M] : SMulCommClass S T (M ⧸ P)
- where smul_comm _x _y := Quotient.ind' fun _z => congr_arg mk (smul_comm _ _ _)
+ [SMulCommClass S T M] : SMulCommClass S T (M ⧸ P) where
+ smul_comm _x _y := Quotient.ind' fun _z => congr_arg mk (smul_comm _ _ _)
#align submodule.quotient.smul_comm_class Submodule.Quotient.smulCommClass
instance isScalarTower (T : Type*) [SMul T R] [SMul T M] [IsScalarTower T R M] [SMul S T]
- [IsScalarTower S T M] : IsScalarTower S T (M ⧸ P)
- where smul_assoc _x _y := Quotient.ind' fun _z => congr_arg mk (smul_assoc _ _ _)
+ [IsScalarTower S T M] : IsScalarTower S T (M ⧸ P) where
+ smul_assoc _x _y := Quotient.ind' fun _z => congr_arg mk (smul_assoc _ _ _)
#align submodule.quotient.is_scalar_tower Submodule.Quotient.isScalarTower
instance isCentralScalar [SMul Sᵐᵒᵖ R] [SMul Sᵐᵒᵖ M] [IsScalarTower Sᵐᵒᵖ R M]
- [IsCentralScalar S M] : IsCentralScalar S (M ⧸ P)
- where op_smul_eq_smul _x := Quotient.ind' fun _z => congr_arg mk <| op_smul_eq_smul _ _
+ [IsCentralScalar S M] : IsCentralScalar S (M ⧸ P) where
+ op_smul_eq_smul _x := Quotient.ind' fun _z => congr_arg mk <| op_smul_eq_smul _ _
#align submodule.quotient.is_central_scalar Submodule.Quotient.isCentralScalar
end SMul
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -21,7 +21,7 @@ section Ring
namespace Submodule
-variable {R M : Type _} {r : R} {x y : M} [Ring R] [AddCommGroup M] [Module R M]
+variable {R M : Type*} {r : R} {x y : M} [Ring R] [AddCommGroup M] [Module R M]
variable (p p' : Submodule R M)
@@ -122,7 +122,7 @@ theorem mk_sub : (mk (x - y) : M ⧸ p) = (mk x : M ⧸ p) - (mk y : M ⧸ p) :=
section SMul
-variable {S : Type _} [SMul S R] [SMul S M] [IsScalarTower S R M] (P : Submodule R M)
+variable {S : Type*} [SMul S R] [SMul S M] [IsScalarTower S R M] (P : Submodule R M)
instance instSMul' : SMul S (M ⧸ P) :=
⟨fun a =>
@@ -141,12 +141,12 @@ theorem mk_smul (r : S) (x : M) : (mk (r • x) : M ⧸ p) = r • mk x :=
rfl
#align submodule.quotient.mk_smul Submodule.Quotient.mk_smul
-instance smulCommClass (T : Type _) [SMul T R] [SMul T M] [IsScalarTower T R M]
+instance smulCommClass (T : Type*) [SMul T R] [SMul T M] [IsScalarTower T R M]
[SMulCommClass S T M] : SMulCommClass S T (M ⧸ P)
where smul_comm _x _y := Quotient.ind' fun _z => congr_arg mk (smul_comm _ _ _)
#align submodule.quotient.smul_comm_class Submodule.Quotient.smulCommClass
-instance isScalarTower (T : Type _) [SMul T R] [SMul T M] [IsScalarTower T R M] [SMul S T]
+instance isScalarTower (T : Type*) [SMul T R] [SMul T M] [IsScalarTower T R M] [SMul S T]
[IsScalarTower S T M] : IsScalarTower S T (M ⧸ P)
where smul_assoc _x _y := Quotient.ind' fun _z => congr_arg mk (smul_assoc _ _ _)
#align submodule.quotient.is_scalar_tower Submodule.Quotient.isScalarTower
@@ -160,7 +160,7 @@ end SMul
section Module
-variable {S : Type _}
+variable {S : Type*}
instance mulAction' [Monoid S] [SMul S R] [MulAction S M] [IsScalarTower S R M]
(P : Submodule R M) : MulAction S (M ⧸ P) :=
@@ -301,7 +301,7 @@ theorem card_eq_card_quotient_mul_card [Fintype M] (S : Submodule R M) [Decidabl
section
-variable {M₂ : Type _} [AddCommGroup M₂] [Module R M₂]
+variable {M₂ : Type*} [AddCommGroup M₂] [Module R M₂]
theorem quot_hom_ext (f g : (M ⧸ p) →ₗ[R] M₂) (h : ∀ x : M, f (Quotient.mk x) = g (Quotient.mk x)) :
f = g :=
@@ -326,7 +326,7 @@ theorem mkQ_surjective (A : Submodule R M) : Function.Surjective A.mkQ := by
end
-variable {R₂ M₂ : Type _} [Ring R₂] [AddCommGroup M₂] [Module R₂ M₂] {τ₁₂ : R →+* R₂}
+variable {R₂ M₂ : Type*} [Ring R₂] [AddCommGroup M₂] [Module R₂ M₂] {τ₁₂ : R →+* R₂}
/-- Two `LinearMap`s from a quotient module are equal if their compositions with
`submodule.mkQ` are equal.
@@ -422,7 +422,7 @@ theorem mapQ_zero (h : p ≤ q.comap (0 : M →ₛₗ[τ₁₂] M₂) := (by sim
/-- Given submodules `p ⊆ M`, `p₂ ⊆ M₂`, `p₃ ⊆ M₃` and maps `f : M → M₂`, `g : M₂ → M₃` inducing
`mapQ f : M ⧸ p → M₂ ⧸ p₂` and `mapQ g : M₂ ⧸ p₂ → M₃ ⧸ p₃` then
`mapQ (g ∘ f) = (mapQ g) ∘ (mapQ f)`. -/
-theorem mapQ_comp {R₃ M₃ : Type _} [Ring R₃] [AddCommGroup M₃] [Module R₃ M₃] (p₂ : Submodule R₂ M₂)
+theorem mapQ_comp {R₃ M₃ : Type*} [Ring R₃] [AddCommGroup M₃] [Module R₃ M₃] (p₂ : Submodule R₂ M₂)
(p₃ : Submodule R₃ M₃) {τ₂₃ : R₂ →+* R₃} {τ₁₃ : R →+* R₃} [RingHomCompTriple τ₁₂ τ₂₃ τ₁₃]
(f : M →ₛₗ[τ₁₂] M₂) (g : M₂ →ₛₗ[τ₂₃] M₃) (hf : p ≤ p₂.comap f) (hg : p₂ ≤ p₃.comap g)
(h := hf.trans (comap_mono hg)) :
@@ -515,7 +515,7 @@ theorem span_preimage_eq [RingHomSurjective τ₁₂] {f : M →ₛₗ[τ₁₂]
/-- If `P` is a submodule of `M` and `Q` a submodule of `N`,
and `f : M ≃ₗ N` maps `P` to `Q`, then `M ⧸ P` is equivalent to `N ⧸ Q`. -/
@[simps]
-def Quotient.equiv {N : Type _} [AddCommGroup N] [Module R N] (P : Submodule R M)
+def Quotient.equiv {N : Type*} [AddCommGroup N] [Module R N] (P : Submodule R M)
(Q : Submodule R N) (f : M ≃ₗ[R] N) (hf : P.map f = Q) : (M ⧸ P) ≃ₗ[R] N ⧸ Q :=
{ P.mapQ Q (f : M →ₗ[R] N) fun x hx => hf ▸ Submodule.mem_map_of_mem hx with
toFun := P.mapQ Q (f : M →ₗ[R] N) fun x hx => hf ▸ Submodule.mem_map_of_mem hx
@@ -530,7 +530,7 @@ def Quotient.equiv {N : Type _} [AddCommGroup N] [Module R N] (P : Submodule R M
#align submodule.quotient.equiv_apply Submodule.Quotient.equiv_apply
@[simp]
-theorem Quotient.equiv_symm {R M N : Type _} [CommRing R] [AddCommGroup M] [Module R M]
+theorem Quotient.equiv_symm {R M N : Type*} [CommRing R] [AddCommGroup M] [Module R M]
[AddCommGroup N] [Module R N] (P : Submodule R M) (Q : Submodule R N) (f : M ≃ₗ[R] N)
(hf : P.map f = Q) :
(Quotient.equiv P Q f hf).symm =
@@ -539,7 +539,7 @@ theorem Quotient.equiv_symm {R M N : Type _} [CommRing R] [AddCommGroup M] [Modu
#align submodule.quotient.equiv_symm Submodule.Quotient.equiv_symm
@[simp]
-theorem Quotient.equiv_trans {N O : Type _} [AddCommGroup N] [Module R N] [AddCommGroup O]
+theorem Quotient.equiv_trans {N O : Type*} [AddCommGroup N] [Module R N] [AddCommGroup O]
[Module R O] (P : Submodule R M) (Q : Submodule R N) (S : Submodule R O) (e : M ≃ₗ[R] N)
(f : N ≃ₗ[R] O) (he : P.map e = Q) (hf : Q.map f = S) (hef : P.map (e.trans f) = S) :
Quotient.equiv P S (e.trans f) hef =
@@ -559,7 +559,7 @@ namespace LinearMap
section Ring
-variable {R M R₂ M₂ R₃ M₃ : Type _}
+variable {R M R₂ M₂ R₃ M₃ : Type*}
variable [Ring R] [Ring R₂] [Ring R₃]
@@ -596,7 +596,7 @@ open LinearMap
namespace Submodule
-variable {R M : Type _} {r : R} {x y : M} [Ring R] [AddCommGroup M] [Module R M]
+variable {R M : Type*} {r : R} {x y : M} [Ring R] [AddCommGroup M] [Module R M]
variable (p p' : Submodule R M)
@@ -657,7 +657,7 @@ end Ring
section CommRing
-variable {R M M₂ : Type _} {r : R} {x y : M} [CommRing R] [AddCommGroup M] [Module R M]
+variable {R M M₂ : Type*} {r : R} {x y : M} [CommRing R] [AddCommGroup M] [Module R M]
[AddCommGroup M₂] [Module R M₂] (p : Submodule R M) (q : Submodule R M₂)
namespace Submodule
@@ -124,17 +124,17 @@ section SMul
variable {S : Type _} [SMul S R] [SMul S M] [IsScalarTower S R M] (P : Submodule R M)
-instance hasSmul' : SMul S (M ⧸ P) :=
+instance instSMul' : SMul S (M ⧸ P) :=
⟨fun a =>
Quotient.map' ((· • ·) a) fun x y h =>
leftRel_apply.mpr <| by simpa using Submodule.smul_mem P (a • (1 : R)) (leftRel_apply.mp h)⟩
-#align submodule.quotient.has_smul' Submodule.Quotient.hasSmul'
+#align submodule.quotient.has_smul' Submodule.Quotient.instSMul'
-- porting note: should this be marked as a `@[default_instance]`?
/-- Shortcut to help the elaborator in the common case. -/
-instance hasSmul : SMul R (M ⧸ P) :=
- Quotient.hasSmul' P
-#align submodule.quotient.has_smul Submodule.Quotient.hasSmul
+instance instSMul : SMul R (M ⧸ P) :=
+ Quotient.instSMul' P
+#align submodule.quotient.has_smul Submodule.Quotient.instSMul
@[simp]
theorem mk_smul (r : S) (x : M) : (mk (r • x) : M ⧸ p) = r • mk x :=
@@ -182,16 +182,16 @@ instance smulZeroClass (P : Submodule R M) : SMulZeroClass R (M ⧸ P) :=
Quotient.smulZeroClass' P
#align submodule.quotient.smul_zero_class Submodule.Quotient.smulZeroClass
-instance distribSmul' [SMul S R] [DistribSMul S M] [IsScalarTower S R M] (P : Submodule R M) :
+instance distribSMul' [SMul S R] [DistribSMul S M] [IsScalarTower S R M] (P : Submodule R M) :
DistribSMul S (M ⧸ P) :=
Function.Surjective.distribSMul {toFun := mk, map_zero' := rfl, map_add' := fun _ _ => rfl}
(surjective_quot_mk _) (Submodule.Quotient.mk_smul P)
-#align submodule.quotient.distrib_smul' Submodule.Quotient.distribSmul'
+#align submodule.quotient.distrib_smul' Submodule.Quotient.distribSMul'
-- porting note: should this be marked as a `@[default_instance]`?
-instance distribSmul (P : Submodule R M) : DistribSMul R (M ⧸ P) :=
- Quotient.distribSmul' P
-#align submodule.quotient.distrib_smul Submodule.Quotient.distribSmul
+instance distribSMul (P : Submodule R M) : DistribSMul R (M ⧸ P) :=
+ Quotient.distribSMul' P
+#align submodule.quotient.distrib_smul Submodule.Quotient.distribSMul
instance distribMulAction' [Monoid S] [SMul S R] [DistribMulAction S M] [IsScalarTower S R M]
(P : Submodule R M) : DistribMulAction S (M ⧸ P) :=
@@ -222,9 +222,7 @@ where `P : Submodule R M`.
-/
def restrictScalarsEquiv [Ring S] [SMul S R] [Module S M] [IsScalarTower S R M]
(P : Submodule R M) : (M ⧸ P.restrictScalars S) ≃ₗ[S] M ⧸ P :=
- {
- Quotient.congrRight fun _ _ =>
- Iff.rfl with
+ { Quotient.congrRight fun _ _ => Iff.rfl with
map_add' := fun x y => Quotient.inductionOn₂' x y fun _x' _y' => rfl
map_smul' := fun _c x => Quotient.inductionOn' x fun _x' => rfl }
#align submodule.quotient.restrict_scalars_equiv Submodule.Quotient.restrictScalarsEquiv
@@ -263,8 +261,7 @@ instance QuotientBot.infinite [Infinite M] : Infinite (M ⧸ (⊥ : Submodule R
sub_eq_zero.mp <| (Submodule.Quotient.eq ⊥).mp h
#align submodule.quotient_bot.infinite Submodule.QuotientBot.infinite
-instance QuotientTop.unique : Unique (M ⧸ (⊤ : Submodule R M))
- where
+instance QuotientTop.unique : Unique (M ⧸ (⊤ : Submodule R M)) where
default := 0
uniq x := Quotient.inductionOn' x fun _x => (Submodule.Quotient.eq ⊤).mpr Submodule.mem_top
#align submodule.quotient_top.unique Submodule.QuotientTop.unique
@@ -286,9 +283,8 @@ theorem subsingleton_quotient_iff_eq_top : Subsingleton (M ⧸ p) ↔ p = ⊤ :=
#align submodule.subsingleton_quotient_iff_eq_top Submodule.subsingleton_quotient_iff_eq_top
theorem unique_quotient_iff_eq_top : Nonempty (Unique (M ⧸ p)) ↔ p = ⊤ :=
- ⟨fun ⟨h⟩ => subsingleton_quotient_iff_eq_top.mp (@Unique.instSubsingleton _ h), by
- rintro rfl
- exact ⟨QuotientTop.unique⟩⟩
+ ⟨fun ⟨h⟩ => subsingleton_quotient_iff_eq_top.mp (@Unique.instSubsingleton _ h),
+ by rintro rfl; exact ⟨QuotientTop.unique⟩⟩
#align submodule.unique_quotient_iff_eq_top Submodule.unique_quotient_iff_eq_top
variable (p)
@@ -480,8 +476,7 @@ theorem ker_liftQ_eq_bot (f : M →ₛₗ[τ₁₂] M₂) (h) (h' : ker f ≤ p)
/-- The correspondence theorem for modules: there is an order isomorphism between submodules of the
quotient of `M` by `p`, and submodules of `M` larger than `p`. -/
-def comapMkQRelIso : Submodule R (M ⧸ p) ≃o { p' : Submodule R M // p ≤ p' }
- where
+def comapMkQRelIso : Submodule R (M ⧸ p) ≃o { p' : Submodule R M // p ≤ p' } where
toFun p' := ⟨comap p.mkQ p', le_comap_mkQ p _⟩
invFun q := map p.mkQ q
left_inv p' := map_comap_eq_self <| by simp
@@ -522,11 +517,7 @@ and `f : M ≃ₗ N` maps `P` to `Q`, then `M ⧸ P` is equivalent to `N ⧸ Q`.
@[simps]
def Quotient.equiv {N : Type _} [AddCommGroup N] [Module R N] (P : Submodule R M)
(Q : Submodule R N) (f : M ≃ₗ[R] N) (hf : P.map f = Q) : (M ⧸ P) ≃ₗ[R] N ⧸ Q :=
- {
- P.mapQ Q (f : M →ₗ[R] N) fun x hx =>
- hf ▸
- Submodule.mem_map_of_mem
- hx with
+ { P.mapQ Q (f : M →ₗ[R] N) fun x hx => hf ▸ Submodule.mem_map_of_mem hx with
toFun := P.mapQ Q (f : M →ₗ[R] N) fun x hx => hf ▸ Submodule.mem_map_of_mem hx
invFun :=
Q.mapQ P (f.symm : N →ₗ[R] M) fun x hx => by
@@ -29,7 +29,7 @@ open LinearMap QuotientAddGroup
/-- The equivalence relation associated to a submodule `p`, defined by `x ≈ y` iff `-x + y ∈ p`.
-Note this is equivalent to `y - x ∈ p`, but defined this way to be be defeq to the `AddSubgroup`
+Note this is equivalent to `y - x ∈ p`, but defined this way to be defeq to the `AddSubgroup`
version, where commutativity can't be assumed. -/
def quotientRel : Setoid M :=
QuotientAddGroup.leftRel p.toAddSubgroup
@@ -2,15 +2,12 @@
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Kevin Buzzard, Yury Kudryashov
-
-! This file was ported from Lean 3 source module linear_algebra.quotient
-! leanprover-community/mathlib commit 48085f140e684306f9e7da907cd5932056d1aded
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.GroupTheory.QuotientGroup
import Mathlib.LinearAlgebra.Span
+#align_import linear_algebra.quotient from "leanprover-community/mathlib"@"48085f140e684306f9e7da907cd5932056d1aded"
+
/-!
# Quotients by submodules
fix-comments.py
on all files.@@ -32,7 +32,7 @@ open LinearMap QuotientAddGroup
/-- The equivalence relation associated to a submodule `p`, defined by `x ≈ y` iff `-x + y ∈ p`.
-Note this is equivalent to `y - x ∈ p`, but defined this way to be be defeq to the `add_subgroup`
+Note this is equivalent to `y - x ∈ p`, but defined this way to be be defeq to the `AddSubgroup`
version, where commutativity can't be assumed. -/
def quotientRel : Setoid M :=
QuotientAddGroup.leftRel p.toAddSubgroup
@@ -221,7 +221,7 @@ instance module (P : Submodule R M) : Module R (M ⧸ P) :=
variable (S)
/-- The quotient of `P` as an `S`-submodule is the same as the quotient of `P` as an `R`-submodule,
-where `P : submodule R M`.
+where `P : Submodule R M`.
-/
def restrictScalarsEquiv [Ring S] [SMul S R] [Module S M] [IsScalarTower S R M]
(P : Submodule R M) : (M ⧸ P.restrictScalars S) ≃ₗ[S] M ⧸ P :=
@@ -335,7 +335,7 @@ end
variable {R₂ M₂ : Type _} [Ring R₂] [AddCommGroup M₂] [Module R₂ M₂] {τ₁₂ : R →+* R₂}
-/-- Two `linear_map`s from a quotient module are equal if their compositions with
+/-- Two `LinearMap`s from a quotient module are equal if their compositions with
`submodule.mkQ` are equal.
See note [partially-applied ext lemmas]. -/
@@ -19,7 +19,6 @@ import Mathlib.LinearAlgebra.Span
-/
-
-- For most of this file we work over a noncommutative ring
section Ring
@@ -19,10 +19,6 @@ import Mathlib.LinearAlgebra.Span
-/
-section deinstance_nonassocring
--- porting note: because we're missing lean4#2074 we need this, see:
--- https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/LinearAlgebra.2ESpan.20!4.232248
-attribute [-instance] Ring.toNonAssocRing
-- For most of this file we work over a noncommutative ring
section Ring
@@ -695,5 +691,3 @@ def mapQLinear : compatibleMaps p q →ₗ[R] M ⧸ p →ₗ[R] M₂ ⧸ q
end Submodule
end CommRing
-
-end deinstance_nonassocring
Now that leanprover/lean4#2210 has been merged, this PR:
set_option synthInstance.etaExperiment true
commands (and some etaExperiment%
term elaborators)set_option maxHeartbeats
commandsCo-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>
@@ -91,8 +91,11 @@ protected theorem eq {x y : M} : (mk x : M ⧸ p) = (mk y : M ⧸ p) ↔ x - y
(Submodule.Quotient.eq' p).trans (leftRel_apply.symm.trans p.quotientRel_r_def)
#align submodule.quotient.eq Submodule.Quotient.eq
-instance : Zero (M ⧸ p) :=
- ⟨mk 0⟩
+instance : Zero (M ⧸ p) where
+ -- Use Quotient.mk'' instead of mk here because mk is not reducible.
+ -- This would lead to non-defeq diamonds.
+ -- See also the same comment at the One instance for Con.
+ zero := Quotient.mk'' 0
instance : Inhabited (M ⧸ p) :=
⟨0⟩
by
s! (#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 by
s".
@@ -291,8 +291,7 @@ theorem subsingleton_quotient_iff_eq_top : Subsingleton (M ⧸ p) ↔ p = ⊤ :=
#align submodule.subsingleton_quotient_iff_eq_top Submodule.subsingleton_quotient_iff_eq_top
theorem unique_quotient_iff_eq_top : Nonempty (Unique (M ⧸ p)) ↔ p = ⊤ :=
- ⟨fun ⟨h⟩ => subsingleton_quotient_iff_eq_top.mp (@Unique.instSubsingleton _ h),
- by
+ ⟨fun ⟨h⟩ => subsingleton_quotient_iff_eq_top.mp (@Unique.instSubsingleton _ h), by
rintro rfl
exact ⟨QuotientTop.unique⟩⟩
#align submodule.unique_quotient_iff_eq_top Submodule.unique_quotient_iff_eq_top
@@ -510,8 +509,7 @@ theorem comapMkQOrderEmbedding_eq (p' : Submodule R (M ⧸ p)) :
theorem span_preimage_eq [RingHomSurjective τ₁₂] {f : M →ₛₗ[τ₁₂] M₂} {s : Set M₂} (h₀ : s.Nonempty)
(h₁ : s ⊆ range f) : span R (f ⁻¹' s) = (span R₂ s).comap f := by
suffices (span R₂ s).comap f ≤ span R (f ⁻¹' s) by exact le_antisymm (span_preimage_le f s) this
- have hk : ker f ≤ span R (f ⁻¹' s) :=
- by
+ have hk : ker f ≤ span R (f ⁻¹' s) := by
let y := Classical.choose h₀
have hy : y ∈ s := Classical.choose_spec h₀
rw [ker_le_iff]
@@ -536,8 +534,7 @@ def Quotient.equiv {N : Type _} [AddCommGroup N] [Module R N] (P : Submodule R M
hx with
toFun := P.mapQ Q (f : M →ₗ[R] N) fun x hx => hf ▸ Submodule.mem_map_of_mem hx
invFun :=
- Q.mapQ P (f.symm : N →ₗ[R] M) fun x hx =>
- by
+ Q.mapQ P (f.symm : N →ₗ[R] M) fun x hx => by
rw [← hf, Submodule.mem_map] at hx
obtain ⟨y, hy, rfl⟩ := hx
simpa
@@ -643,9 +640,7 @@ theorem coe_quotEquivOfEqBot_symm (hp : p = ⊥) :
/-- Quotienting by equal submodules gives linearly equivalent quotients. -/
def quotEquivOfEq (h : p = p') : (M ⧸ p) ≃ₗ[R] M ⧸ p' :=
- {
- @Quotient.congr _ _ (quotientRel p) (quotientRel p') (Equiv.refl _) fun a b =>
- by
+ { @Quotient.congr _ _ (quotientRel p) (quotientRel p') (Equiv.refl _) fun a b => by
subst h
rfl with
map_add' := by
finset
lemmas around (#3748)
Match https://github.com/leanprover-community/mathlib/pull/18900
Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
@@ -399,7 +399,9 @@ theorem comap_map_mkQ : comap p.mkQ (map p.mkQ p') = p ⊔ p' := by simp [comap_
@[simp]
theorem map_mkQ_eq_top : map p.mkQ p' = ⊤ ↔ p ⊔ p' = ⊤ := by
- simp only [map_eq_top_iff p.range_mkQ, sup_comm, ker_mkQ]
+ -- porting note: ambiguity of `map_eq_top_iff` is no longer automatically resolved by preferring
+ -- the current namespace
+ simp only [LinearMap.map_eq_top_iff p.range_mkQ, sup_comm, ker_mkQ]
#align submodule.map_mkq_eq_top Submodule.map_mkQ_eq_top
variable (q : Submodule R₂ M₂)
This PR fixes two things:
align
statements for definitions and theorems and instances that are separated by two newlines from the relevant declaration (s/\n\n#align/\n#align
). This is often seen in the mathport output after ending calc
blocks.#align
statements. (This was needed for a script I wrote for #3630.)@@ -497,7 +497,6 @@ def comapMkQRelIso : Submodule R (M ⧸ p) ≃o { p' : Submodule R M // p ≤ p'
of `M`. -/
def comapMkQOrderEmbedding : Submodule R (M ⧸ p) ↪o Submodule R M :=
(RelIso.toRelEmbedding <| comapMkQRelIso p).trans (Subtype.relEmbedding (· ≤ ·) _)
-
#align submodule.comap_mkq.order_embedding Submodule.comapMkQOrderEmbedding
@[simp]
@@ -342,7 +342,7 @@ variable {R₂ M₂ : Type _} [Ring R₂] [AddCommGroup M₂] [Module R₂ M₂]
`submodule.mkQ` are equal.
See note [partially-applied ext lemmas]. -/
-@[ext 1001] -- porting note: increase priority so this applies before `LinearMap.ext`
+@[ext 1100] -- porting note: increase priority so this applies before `LinearMap.ext`
theorem linearMap_qext ⦃f g : M ⧸ p →ₛₗ[τ₁₂] M₂⦄ (h : f.comp p.mkQ = g.comp p.mkQ) : f = g :=
LinearMap.ext fun x => Quotient.inductionOn' x <| (LinearMap.congr_fun h : _)
#align submodule.linear_map_qext Submodule.linearMap_qext
@@ -146,10 +146,10 @@ theorem mk_smul (r : S) (x : M) : (mk (r • x) : M ⧸ p) = r • mk x :=
rfl
#align submodule.quotient.mk_smul Submodule.Quotient.mk_smul
-instance sMulCommClass (T : Type _) [SMul T R] [SMul T M] [IsScalarTower T R M]
+instance smulCommClass (T : Type _) [SMul T R] [SMul T M] [IsScalarTower T R M]
[SMulCommClass S T M] : SMulCommClass S T (M ⧸ P)
where smul_comm _x _y := Quotient.ind' fun _z => congr_arg mk (smul_comm _ _ _)
-#align submodule.quotient.smul_comm_class Submodule.Quotient.sMulCommClass
+#align submodule.quotient.smul_comm_class Submodule.Quotient.smulCommClass
instance isScalarTower (T : Type _) [SMul T R] [SMul T M] [IsScalarTower T R M] [SMul S T]
[IsScalarTower S T M] : IsScalarTower S T (M ⧸ P)
initialize_simps_projections
now by default generates all projections of all parent structures, and doesn't generate the projections to those parent structures.TwoPointed
)Internal changes:
ParsedProjectionData
to avoid the bug reported here (and to another bug where it seemed that the wrong data was inserted in ParsedProjectionData
, but it was hard to minimize because of all the crashes). If we manage to fix the bug in that Zulip thread, I'll see if I can track down the other bug in commit 97454284Co-authored-by: Johan Commelin <johan@commelin.net>
@@ -560,7 +560,7 @@ theorem Quotient.equiv_trans {N O : Type _} [AddCommGroup N] [Module R N] [AddCo
(f : N ≃ₗ[R] O) (he : P.map e = Q) (hf : Q.map f = S) (hef : P.map (e.trans f) = S) :
Quotient.equiv P S (e.trans f) hef =
(Quotient.equiv P Q e he).trans (Quotient.equiv Q S f hf) := by
- ext x
+ ext
-- `simp` can deal with `hef` depending on `e` and `f`
simp only [Quotient.equiv_apply, LinearEquiv.trans_apply, LinearEquiv.coe_trans]
-- `rw` can deal with `mapQ_comp` needing extra hypotheses coming from the RHS
@@ -543,16 +543,7 @@ def Quotient.equiv {N : Type _} [AddCommGroup N] [Module R N] (P : Submodule R M
left_inv := fun x => Quotient.inductionOn' x (by simp)
right_inv := fun x => Quotient.inductionOn' x (by simp) }
#align submodule.quotient.equiv Submodule.Quotient.equiv
-
--- porting note: `simps` didn't generate this?
-@[simp]
-theorem Quotient.equiv_apply {N : Type _} [AddCommGroup N] [Module R N]
- (P : Submodule R M) (Q : Submodule R N) (f : M ≃ₗ[R] N) (hf : P.map f = Q)
- (hf' := fun _ hx => hf ▸ Submodule.mem_map_of_mem hx) (x : M ⧸ P) :
- (Quotient.equiv P Q f hf) x = (P.mapQ Q (f : M →ₗ[R] N) hf') x :=
- rfl
--- porting note: this is `align`ed with an `ₓ` because I had to add `hf'` as an `optParam`.
-#align submodule.quotient.equiv_apply Submodule.Quotient.equiv_applyₓ
+#align submodule.quotient.equiv_apply Submodule.Quotient.equiv_apply
@[simp]
theorem Quotient.equiv_symm {R M N : Type _} [CommRing R] [AddCommGroup M] [Module R M]
@@ -569,19 +560,11 @@ theorem Quotient.equiv_trans {N O : Type _} [AddCommGroup N] [Module R N] [AddCo
(f : N ≃ₗ[R] O) (he : P.map e = Q) (hf : Q.map f = S) (hef : P.map (e.trans f) = S) :
Quotient.equiv P S (e.trans f) hef =
(Quotient.equiv P Q e he).trans (Quotient.equiv Q S f hf) := by
- ext
+ ext x
-- `simp` can deal with `hef` depending on `e` and `f`
- -- porting note: this doesn't work in Lean 4?
- simp only [Quotient.equiv_apply P S (e.trans f)
- hef (fun _ hx => hef ▸ Submodule.mem_map_of_mem hx) _,
- Quotient.equiv_apply P Q e he (fun _ hx => he ▸ Submodule.mem_map_of_mem hx) _,
- Quotient.equiv_apply Q S f hf (fun _ hx => hf ▸ Submodule.mem_map_of_mem hx) _]
- simp only [LinearEquiv.trans_apply, LinearEquiv.coe_trans]
+ simp only [Quotient.equiv_apply, LinearEquiv.trans_apply, LinearEquiv.coe_trans]
-- `rw` can deal with `mapQ_comp` needing extra hypotheses coming from the RHS
- -- porting note: this doesn't work in Lean 4?
- rw [mapQ_comp P Q S e.toLinearMap f.toLinearMap (fun _ hx => he ▸ Submodule.mem_map_of_mem hx)
- (fun _ hx => hf ▸ Submodule.mem_map_of_mem hx) _]
- rfl
+ rw [mapQ_comp, LinearMap.comp_apply]
#align submodule.quotient.equiv_trans Submodule.Quotient.equiv_trans
end Submodule
porting notes:
mk
or mk x
and friends greatly speeds up elaboration issues.mkq
or liftq
(and variants). Is is mkq
, or mkQ
? Edit: we've gone with mkQ
, liftQ
and mapQ
.submodule.comap_mkq.rel_iso
be called according to our naming conventions? Edit: unclear, but here it's been changed to Submodule.comapMkQRelIso
.optParams
automatically in simp
or rw
?optParam
in Submodule.Quotient.equiv_apply
that wasn't needed in Lean 3, so this has been #align
ed with an ₓ
, and why didn't simps
generate this lemma?default_instance
s, but I'm not sure. Edit: this can always be added later if necessary, so it's not urgent here.The unported dependencies are