representation_theory.maschke | Mathlib porting status

Changes since the initial port

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

Changes in mathlib3

70fd9563

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

31ca6f9c

bump to nightly-2023-12-20-06

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

058cd493

Diff

@@ -83,7 +83,7 @@ variable (π : W →ₗ[k] V)
 /-- We define the conjugate of `π` by `g`, as a `k`-linear map.
 -/
 def conjugate (g : G) : W →ₗ[k] V :=
-  ((GroupSmul.linearMap k V g⁻¹).comp π).comp (GroupSmul.linearMap k W g)
+  ((GroupSMul.linearMap k V g⁻¹).comp π).comp (GroupSMul.linearMap k W g)
 #align linear_map.conjugate LinearMap.conjugate
 -/

31ca6f9c

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,9 +3,9 @@ Copyright (c) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 -/
-import Mathbin.Algebra.MonoidAlgebra.Basic
-import Mathbin.Algebra.CharP.Invertible
-import Mathbin.LinearAlgebra.Basis
+import Algebra.MonoidAlgebra.Basic
+import Algebra.CharP.Invertible
+import LinearAlgebra.Basis
 
 #align_import representation_theory.maschke from "leanprover-community/mathlib"@"31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0"

31ca6f9c

bump to nightly-2023-08-17-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

60285dcc

Diff

@@ -156,7 +156,7 @@ theorem equivariantProjection_condition (v : V) : (π.equivariantProjection G) (
   rw [LinearMap.sum_apply]
   simp only [conjugate_i π i h]
   rw [Finset.sum_const, Finset.card_univ, nsmul_eq_smul_cast k, ← mul_smul,
-    Invertible.invOf_mul_self, one_smul]
+    Invertible.invOf_hMul_self, one_smul]
 #align linear_map.equivariant_projection_condition LinearMap.equivariantProjection_condition
 -/

31ca6f9c

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module representation_theory.maschke
-! leanprover-community/mathlib commit 31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.MonoidAlgebra.Basic
 import Mathbin.Algebra.CharP.Invertible
 import Mathbin.LinearAlgebra.Basis
 
+#align_import representation_theory.maschke from "leanprover-community/mathlib"@"31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0"
+
 /-!
 # Maschke's theorem

31ca6f9c

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -82,20 +82,19 @@ namespace LinearMap
 
 variable (π : W →ₗ[k] V)
 
-include π
-
+#print LinearMap.conjugate /-
 /-- We define the conjugate of `π` by `g`, as a `k`-linear map.
 -/
 def conjugate (g : G) : W →ₗ[k] V :=
   ((GroupSmul.linearMap k V g⁻¹).comp π).comp (GroupSmul.linearMap k W g)
 #align linear_map.conjugate LinearMap.conjugate
+-/
 
 variable (i : V →ₗ[MonoidAlgebra k G] W) (h : ∀ v : V, π (i v) = v)
 
 section
 
-include h
-
+#print LinearMap.conjugate_i /-
 theorem conjugate_i (g : G) (v : V) : (conjugate π g) (i v) = v :=
   by
   dsimp [conjugate]
@@ -103,11 +102,13 @@ theorem conjugate_i (g : G) (v : V) : (conjugate π g) (i v) = v :=
   change (1 : MonoidAlgebra k G) • v = v
   simp
 #align linear_map.conjugate_i LinearMap.conjugate_i
+-/
 
 end
 
 variable (G) [Fintype G]
 
+#print LinearMap.sumOfConjugates /-
 /-- The sum of the conjugates of `π` by each element `g : G`, as a `k`-linear map.
 
 (We postpone dividing by the size of the group as long as possible.)
@@ -115,7 +116,9 @@ variable (G) [Fintype G]
 def sumOfConjugates : W →ₗ[k] V :=
   ∑ g : G, π.conjugate g
 #align linear_map.sum_of_conjugates LinearMap.sumOfConjugates
+-/
 
+#print LinearMap.sumOfConjugatesEquivariant /-
 /-- In fact, the sum over `g : G` of the conjugate of `π` by `g` is a `k[G]`-linear map.
 -/
 def sumOfConjugatesEquivariant : W →ₗ[MonoidAlgebra k G] V :=
@@ -133,22 +136,22 @@ def sumOfConjugatesEquivariant : W →ₗ[MonoidAlgebra k G] V :=
     simp only [← mul_smul, single_mul_single, mul_inv_rev, mul_one, Function.Embedding.coeFn_mk,
       Finset.sum_map, inv_inv, inv_mul_cancel_right]
 #align linear_map.sum_of_conjugates_equivariant LinearMap.sumOfConjugatesEquivariant
+-/
 
 section
 
 variable [inv : Invertible (Fintype.card G : k)]
 
-include inv
-
+#print LinearMap.equivariantProjection /-
 /-- We construct our `k[G]`-linear retraction of `i` as
 $$ \frac{1}{|G|} \sum_{g \in G} g⁻¹ • π(g • -). $$
 -/
 def equivariantProjection : W →ₗ[MonoidAlgebra k G] V :=
   ⅟ (Fintype.card G : k) • π.sumOfConjugatesEquivariant G
 #align linear_map.equivariant_projection LinearMap.equivariantProjection
+-/
 
-include h
-
+#print LinearMap.equivariantProjection_condition /-
 theorem equivariantProjection_condition (v : V) : (π.equivariantProjection G) (i v) = v :=
   by
   rw [equivariant_projection, smul_apply, sum_of_conjugates_equivariant,
@@ -158,6 +161,7 @@ theorem equivariantProjection_condition (v : V) : (π.equivariantProjection G) (
   rw [Finset.sum_const, Finset.card_univ, nsmul_eq_smul_cast k, ← mul_smul,
     Invertible.invOf_mul_self, one_smul]
 #align linear_map.equivariant_projection_condition LinearMap.equivariantProjection_condition
+-/
 
 end
 
@@ -189,6 +193,7 @@ variable {W : Type u} [AddCommGroup W] [Module k W] [Module (MonoidAlgebra k G)
 
 variable [IsScalarTower k (MonoidAlgebra k G) W]
 
+#print MonoidAlgebra.exists_leftInverse_of_injective /-
 theorem exists_leftInverse_of_injective (f : V →ₗ[MonoidAlgebra k G] W) (hf : f.ker = ⊥) :
     ∃ g : W →ₗ[MonoidAlgebra k G] V, g.comp f = LinearMap.id :=
   by
@@ -204,19 +209,24 @@ theorem exists_leftInverse_of_injective (f : V →ₗ[MonoidAlgebra k G] W) (hf
   have := congr_arg LinearMap.toFun hφ
   exact congr_fun this v
 #align monoid_algebra.exists_left_inverse_of_injective MonoidAlgebra.exists_leftInverse_of_injective
+-/
 
 namespace Submodule
 
+#print MonoidAlgebra.Submodule.exists_isCompl /-
 theorem exists_isCompl (p : Submodule (MonoidAlgebra k G) V) :
     ∃ q : Submodule (MonoidAlgebra k G) V, IsCompl p q :=
   let ⟨f, hf⟩ := MonoidAlgebra.exists_leftInverse_of_injective p.Subtype p.ker_subtype
   ⟨f.ker, LinearMap.isCompl_of_proj <| LinearMap.ext_iff.1 hf⟩
 #align monoid_algebra.submodule.exists_is_compl MonoidAlgebra.Submodule.exists_isCompl
+-/
 
+#print MonoidAlgebra.Submodule.complementedLattice /-
 /-- This also implies an instance `is_semisimple_module (monoid_algebra k G) V`. -/
 instance complementedLattice : ComplementedLattice (Submodule (MonoidAlgebra k G) V) :=
   ⟨exists_isCompl⟩
 #align monoid_algebra.submodule.complemented_lattice MonoidAlgebra.Submodule.complementedLattice
+-/
 
 end Submodule

31ca6f9c

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -48,7 +48,7 @@ open Module
 
 open MonoidAlgebra
 
-open BigOperators
+open scoped BigOperators
 
 section

31ca6f9c

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -84,9 +84,6 @@ variable (π : W →ₗ[k] V)
 
 include π
 
-/- warning: linear_map.conjugate -> LinearMap.conjugate is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.conjugate LinearMap.conjugateₓ'. -/
 /-- We define the conjugate of `π` by `g`, as a `k`-linear map.
 -/
 def conjugate (g : G) : W →ₗ[k] V :=
@@ -99,9 +96,6 @@ section
 
 include h
 
-/- warning: linear_map.conjugate_i -> LinearMap.conjugate_i is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.conjugate_i LinearMap.conjugate_iₓ'. -/
 theorem conjugate_i (g : G) (v : V) : (conjugate π g) (i v) = v :=
   by
   dsimp [conjugate]
@@ -114,9 +108,6 @@ end
 
 variable (G) [Fintype G]
 
-/- warning: linear_map.sum_of_conjugates -> LinearMap.sumOfConjugates is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.sum_of_conjugates LinearMap.sumOfConjugatesₓ'. -/
 /-- The sum of the conjugates of `π` by each element `g : G`, as a `k`-linear map.
 
 (We postpone dividing by the size of the group as long as possible.)
@@ -125,9 +116,6 @@ def sumOfConjugates : W →ₗ[k] V :=
   ∑ g : G, π.conjugate g
 #align linear_map.sum_of_conjugates LinearMap.sumOfConjugates
 
-/- warning: linear_map.sum_of_conjugates_equivariant -> LinearMap.sumOfConjugatesEquivariant is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.sum_of_conjugates_equivariant LinearMap.sumOfConjugatesEquivariantₓ'. -/
 /-- In fact, the sum over `g : G` of the conjugate of `π` by `g` is a `k[G]`-linear map.
 -/
 def sumOfConjugatesEquivariant : W →ₗ[MonoidAlgebra k G] V :=
@@ -152,9 +140,6 @@ variable [inv : Invertible (Fintype.card G : k)]
 
 include inv
 
-/- warning: linear_map.equivariant_projection -> LinearMap.equivariantProjection is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.equivariant_projection LinearMap.equivariantProjectionₓ'. -/
 /-- We construct our `k[G]`-linear retraction of `i` as
 $$ \frac{1}{|G|} \sum_{g \in G} g⁻¹ • π(g • -). $$
 -/
@@ -164,9 +149,6 @@ def equivariantProjection : W →ₗ[MonoidAlgebra k G] V :=
 
 include h
 
-/- warning: linear_map.equivariant_projection_condition -> LinearMap.equivariantProjection_condition is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.equivariant_projection_condition LinearMap.equivariantProjection_conditionₓ'. -/
 theorem equivariantProjection_condition (v : V) : (π.equivariantProjection G) (i v) = v :=
   by
   rw [equivariant_projection, smul_apply, sum_of_conjugates_equivariant,
@@ -207,9 +189,6 @@ variable {W : Type u} [AddCommGroup W] [Module k W] [Module (MonoidAlgebra k G)
 
 variable [IsScalarTower k (MonoidAlgebra k G) W]
 
-/- warning: monoid_algebra.exists_left_inverse_of_injective -> MonoidAlgebra.exists_leftInverse_of_injective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align monoid_algebra.exists_left_inverse_of_injective MonoidAlgebra.exists_leftInverse_of_injectiveₓ'. -/
 theorem exists_leftInverse_of_injective (f : V →ₗ[MonoidAlgebra k G] W) (hf : f.ker = ⊥) :
     ∃ g : W →ₗ[MonoidAlgebra k G] V, g.comp f = LinearMap.id :=
   by
@@ -228,18 +207,12 @@ theorem exists_leftInverse_of_injective (f : V →ₗ[MonoidAlgebra k G] W) (hf
 
 namespace Submodule
 
-/- warning: monoid_algebra.submodule.exists_is_compl -> MonoidAlgebra.Submodule.exists_isCompl is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align monoid_algebra.submodule.exists_is_compl MonoidAlgebra.Submodule.exists_isComplₓ'. -/
 theorem exists_isCompl (p : Submodule (MonoidAlgebra k G) V) :
     ∃ q : Submodule (MonoidAlgebra k G) V, IsCompl p q :=
   let ⟨f, hf⟩ := MonoidAlgebra.exists_leftInverse_of_injective p.Subtype p.ker_subtype
   ⟨f.ker, LinearMap.isCompl_of_proj <| LinearMap.ext_iff.1 hf⟩
 #align monoid_algebra.submodule.exists_is_compl MonoidAlgebra.Submodule.exists_isCompl
 
-/- warning: monoid_algebra.submodule.complemented_lattice -> MonoidAlgebra.Submodule.complementedLattice is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align monoid_algebra.submodule.complemented_lattice MonoidAlgebra.Submodule.complementedLatticeₓ'. -/
 /-- This also implies an instance `is_semisimple_module (monoid_algebra k G) V`. -/
 instance complementedLattice : ComplementedLattice (Submodule (MonoidAlgebra k G) V) :=
   ⟨exists_isCompl⟩

31ca6f9c

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -85,10 +85,7 @@ variable (π : W →ₗ[k] V)
 include π
 
 /- warning: linear_map.conjugate -> LinearMap.conjugate is a dubious translation:
-lean 3 declaration is
-  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] {G : Type.{u}} [_inst_2 : Group.{u} G] {V : Type.{u}} [_inst_3 : AddCommGroup.{u} V] [_inst_4 : Module.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_5 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_5)))) (SMulZeroClass.toHasSmul.{u, u} k V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} k V (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} k V (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_4))))] {W : Type.{u}} [_inst_7 : AddCommGroup.{u} W] [_inst_8 : Module.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_9 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_9)))) (SMulZeroClass.toHasSmul.{u, u} k W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} k W (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} k W (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_8))))], (LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) -> G -> (LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4)
-but is expected to have type
-  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] {G : Type.{u}} [_inst_2 : Group.{u} G] {V : Type.{v}} [_inst_3 : AddCommGroup.{v} V] [_inst_4 : Module.{u, v} k V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_5 : Module.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, v} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u, v} k V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} k V (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} k V (Semiring.toMonoidWithZero.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} k V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_4))))] {W : Type.{w}} [_inst_7 : AddCommGroup.{w} W] [_inst_8 : Module.{u, w} k W (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_9 : Module.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, w} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_9)))) (SMulZeroClass.toSMul.{u, w} k W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} k W (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} k W (Semiring.toMonoidWithZero.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} k W (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_8))))], (LinearMap.{u, u, w, v} k k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) -> G -> (LinearMap.{u, u, w, v} k k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4)
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.conjugate LinearMap.conjugateₓ'. -/
 /-- We define the conjugate of `π` by `g`, as a `k`-linear map.
 -/
@@ -103,10 +100,7 @@ section
 include h
 
 /- warning: linear_map.conjugate_i -> LinearMap.conjugate_i is a dubious translation:
-lean 3 declaration is
-  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] {G : Type.{u}} [_inst_2 : Group.{u} G] {V : Type.{u}} [_inst_3 : AddCommGroup.{u} V] [_inst_4 : Module.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_5 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_5)))) (SMulZeroClass.toHasSmul.{u, u} k V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} k V (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} k V (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_4))))] {W : Type.{u}} [_inst_7 : AddCommGroup.{u} W] [_inst_8 : Module.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_9 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_9)))) (SMulZeroClass.toHasSmul.{u, u} k W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} k W (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} k W (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_8))))] (π : LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) (i : LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9), (forall (v : V), Eq.{succ u} V (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) (fun (_x : LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) => W -> V) (LinearMap.hasCoeToFun.{u, u, u, u} k k W V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4 (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))))) π (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9) (fun (_x : LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9) => V -> W) (LinearMap.hasCoeToFun.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v) -> (forall (g : G) (v : V), Eq.{succ u} V (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) (fun (_x : LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) => W -> V) (LinearMap.hasCoeToFun.{u, u, u, u} k k W V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4 (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))))) (LinearMap.conjugate.{u} k _inst_1 G _inst_2 V _inst_3 _inst_4 _inst_5 _inst_6 W _inst_7 _inst_8 _inst_9 _inst_10 π g) (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9) (fun (_x : LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9) => V -> W) (LinearMap.hasCoeToFun.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v)
-but is expected to have type
-  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] {G : Type.{u}} [_inst_2 : Group.{u} G] {V : Type.{v}} [_inst_3 : AddCommGroup.{v} V] [_inst_4 : Module.{u, v} k V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_5 : Module.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, v} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u, v} k V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} k V (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} k V (Semiring.toMonoidWithZero.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} k V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_4))))] {W : Type.{w}} [_inst_7 : AddCommGroup.{w} W] [_inst_8 : Module.{u, w} k W (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_9 : Module.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, w} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_9)))) (SMulZeroClass.toSMul.{u, w} k W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} k W (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} k W (Semiring.toMonoidWithZero.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} k W (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_8))))] (π : LinearMap.{u, u, w, v} k k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) (i : LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k 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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.conjugate_i LinearMap.conjugate_iₓ'. -/
 theorem conjugate_i (g : G) (v : V) : (conjugate π g) (i v) = v :=
   by
@@ -121,10 +115,7 @@ end
 variable (G) [Fintype G]
 
 /- warning: linear_map.sum_of_conjugates -> LinearMap.sumOfConjugates is a dubious translation:
-lean 3 declaration is
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(CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_5)))) (SMulZeroClass.toHasSmul.{u, u} k V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} k V (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} k V (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_4))))] {W : Type.{u}} [_inst_7 : AddCommGroup.{u} W] [_inst_8 : Module.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_9 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_9)))) (SMulZeroClass.toHasSmul.{u, u} k W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} k W (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} k W (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_8))))], (LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) -> (forall [_inst_11 : Fintype.{u} G], LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4)
-but is expected to have type
-  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] (G : Type.{u}) [_inst_2 : Group.{u} G] {V : Type.{v}} [_inst_3 : AddCommGroup.{v} V] [_inst_4 : Module.{u, v} k V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_5 : Module.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, v} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u, v} k V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} k V (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} k V (Semiring.toMonoidWithZero.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} k V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_4))))] {W : Type.{w}} [_inst_7 : AddCommGroup.{w} W] [_inst_8 : Module.{u, w} k W (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_9 : Module.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, w} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_9)))) (SMulZeroClass.toSMul.{u, w} k W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} k W (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} k W (Semiring.toMonoidWithZero.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} k W (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_8))))], (LinearMap.{u, u, w, v} k k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) -> (forall [_inst_11 : Fintype.{u} G], LinearMap.{u, u, w, v} k k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4)
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.sum_of_conjugates LinearMap.sumOfConjugatesₓ'. -/
 /-- The sum of the conjugates of `π` by each element `g : G`, as a `k`-linear map.
 
@@ -135,10 +126,7 @@ def sumOfConjugates : W →ₗ[k] V :=
 #align linear_map.sum_of_conjugates LinearMap.sumOfConjugates
 
 /- warning: linear_map.sum_of_conjugates_equivariant -> LinearMap.sumOfConjugatesEquivariant is a dubious translation:
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(AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_4))))] {W : Type.{u}} [_inst_7 : AddCommGroup.{u} W] [_inst_8 : Module.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_9 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} 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(Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u, v} k V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} k V (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} k V (Semiring.toMonoidWithZero.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} k V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_4))))] {W : Type.{w}} [_inst_7 : AddCommGroup.{w} W] [_inst_8 : Module.{u, w} k W (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_9 : Module.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, w} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_9)))) (SMulZeroClass.toSMul.{u, w} k W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} k W (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} k W (Semiring.toMonoidWithZero.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} k W (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_8))))], (LinearMap.{u, u, w, v} k k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) -> (forall [_inst_11 : Fintype.{u} G], LinearMap.{u, u, w, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_9 _inst_5)
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.sum_of_conjugates_equivariant LinearMap.sumOfConjugatesEquivariantₓ'. -/
 /-- In fact, the sum over `g : G` of the conjugate of `π` by `g` is a `k[G]`-linear map.
 -/
@@ -165,10 +153,7 @@ variable [inv : Invertible (Fintype.card G : k)]
 include inv
 
 /- warning: linear_map.equivariant_projection -> LinearMap.equivariantProjection is a dubious translation:
-lean 3 declaration is
-  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] (G : Type.{u}) [_inst_2 : Group.{u} G] {V : Type.{u}} [_inst_3 : AddCommGroup.{u} V] [_inst_4 : Module.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_5 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_5)))) (SMulZeroClass.toHasSmul.{u, u} k V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} k V (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} k V (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_4))))] {W : Type.{u}} [_inst_7 : AddCommGroup.{u} W] [_inst_8 : Module.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_9 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_9)))) (SMulZeroClass.toHasSmul.{u, u} k W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} k W (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} k W (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_8))))], (LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) -> (forall [_inst_11 : Fintype.{u} G] [inv : Invertible.{u} k (Distrib.toHasMul.{u} k (Ring.toDistrib.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoidWithOne.toOne.{u} k (AddGroupWithOne.toAddMonoidWithOne.{u} k (AddCommGroupWithOne.toAddGroupWithOne.{u} k (Ring.toAddCommGroupWithOne.{u} k (CommRing.toRing.{u} k _inst_1))))) ((fun (a : Type) (b : Type.{u}) [self : HasLiftT.{1, succ u} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u} Nat k (CoeTCₓ.coe.{1, succ u} Nat k (Nat.castCoe.{u} k (AddMonoidWithOne.toNatCast.{u} k (AddGroupWithOne.toAddMonoidWithOne.{u} k (AddCommGroupWithOne.toAddGroupWithOne.{u} k (Ring.toAddCommGroupWithOne.{u} k (CommRing.toRing.{u} k _inst_1)))))))) (Fintype.card.{u} G _inst_11))], LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_9 _inst_5)
-but is expected to have type
-  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] (G : Type.{u}) [_inst_2 : Group.{u} G] {V : Type.{v}} [_inst_3 : AddCommGroup.{v} V] [_inst_4 : Module.{u, v} k V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_5 : Module.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, v} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u, v} k V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} k V (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} k V (Semiring.toMonoidWithZero.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} k V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_4))))] {W : Type.{w}} [_inst_7 : AddCommGroup.{w} W] [_inst_8 : Module.{u, w} k W (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_9 : Module.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, w} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_9)))) (SMulZeroClass.toSMul.{u, w} k W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} k W (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} k W (Semiring.toMonoidWithZero.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} k W (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_8))))], (LinearMap.{u, u, w, v} k k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) -> (forall [_inst_11 : Fintype.{u} G] [inv : Invertible.{u} k (NonUnitalNonAssocRing.toMul.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))) (Semiring.toOne.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Nat.cast.{u} k (Semiring.toNatCast.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Fintype.card.{u} G _inst_11))], LinearMap.{u, u, w, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_9 _inst_5)
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.equivariant_projection LinearMap.equivariantProjectionₓ'. -/
 /-- We construct our `k[G]`-linear retraction of `i` as
 $$ \frac{1}{|G|} \sum_{g \in G} g⁻¹ • π(g • -). $$
@@ -180,10 +165,7 @@ def equivariantProjection : W →ₗ[MonoidAlgebra k G] V :=
 include h
 
 /- warning: linear_map.equivariant_projection_condition -> LinearMap.equivariantProjection_condition is a dubious translation:
-lean 3 declaration is
-  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] (G : Type.{u}) [_inst_2 : Group.{u} G] {V : Type.{u}} [_inst_3 : AddCommGroup.{u} V] [_inst_4 : Module.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_5 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_5)))) (SMulZeroClass.toHasSmul.{u, u} k V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} k V (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} k V (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_4))))] {W : Type.{u}} [_inst_7 : AddCommGroup.{u} W] [_inst_8 : Module.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_9 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_9)))) (SMulZeroClass.toHasSmul.{u, u} k W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} k W (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} k W (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_8))))] (π : LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) (i : LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9), (forall (v : V), Eq.{succ u} V (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) (fun (_x : LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) => W -> V) (LinearMap.hasCoeToFun.{u, u, u, u} k k W V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4 (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))))) π (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9) (fun (_x : LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9) => V -> W) (LinearMap.hasCoeToFun.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v) -> (forall [_inst_11 : Fintype.{u} G] [inv : Invertible.{u} k (Distrib.toHasMul.{u} k (Ring.toDistrib.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoidWithOne.toOne.{u} k (AddGroupWithOne.toAddMonoidWithOne.{u} k (AddCommGroupWithOne.toAddGroupWithOne.{u} k (Ring.toAddCommGroupWithOne.{u} k (CommRing.toRing.{u} k _inst_1))))) ((fun (a : Type) (b : Type.{u}) [self : HasLiftT.{1, succ u} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u} Nat k (CoeTCₓ.coe.{1, succ u} Nat k (Nat.castCoe.{u} k (AddMonoidWithOne.toNatCast.{u} k (AddGroupWithOne.toAddMonoidWithOne.{u} k (AddCommGroupWithOne.toAddGroupWithOne.{u} k (Ring.toAddCommGroupWithOne.{u} k (CommRing.toRing.{u} k _inst_1)))))))) (Fintype.card.{u} G _inst_11))] (v : V), Eq.{succ u} V (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_9 _inst_5) (fun (_x : LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_9 _inst_5) => W -> V) (LinearMap.hasCoeToFun.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_9 _inst_5 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) (LinearMap.equivariantProjection.{u} k _inst_1 G _inst_2 V _inst_3 _inst_4 _inst_5 _inst_6 W _inst_7 _inst_8 _inst_9 _inst_10 π _inst_11 inv) (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9) (fun (_x : LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9) => V -> W) (LinearMap.hasCoeToFun.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v)
-but is expected to have type
-  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] (G : Type.{u}) [_inst_2 : Group.{u} G] {V : Type.{v}} [_inst_3 : AddCommGroup.{v} V] [_inst_4 : Module.{u, v} k V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_5 : Module.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, v} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u, v} k V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} k V (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} k V (Semiring.toMonoidWithZero.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} k V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_4))))] {W : Type.{w}} [_inst_7 : AddCommGroup.{w} W] [_inst_8 : Module.{u, w} k W (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_9 : Module.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, w} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_9)))) (SMulZeroClass.toSMul.{u, w} k W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} k W (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} k W (Semiring.toMonoidWithZero.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} k W (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_8))))] (π : LinearMap.{u, u, w, v} k k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) (i : LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k 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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.equivariant_projection_condition LinearMap.equivariantProjection_conditionₓ'. -/
 theorem equivariantProjection_condition (v : V) : (π.equivariantProjection G) (i v) = v :=
   by
@@ -226,10 +208,7 @@ variable {W : Type u} [AddCommGroup W] [Module k W] [Module (MonoidAlgebra k G)
 variable [IsScalarTower k (MonoidAlgebra k G) W]
 
 /- warning: monoid_algebra.exists_left_inverse_of_injective -> MonoidAlgebra.exists_leftInverse_of_injective is a dubious translation:
-lean 3 declaration is
-  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] {G : Type.{u1}} [_inst_2 : Fintype.{u1} G] [_inst_3 : Invertible.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u1} Nat k (CoeTCₓ.coe.{1, succ u1} Nat k (Nat.castCoe.{u1} k (AddMonoidWithOne.toNatCast.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))))) (Fintype.card.{u1} G _inst_2))] [_inst_4 : Group.{u1} G] {V : Type.{u1}} [_inst_5 : AddCommGroup.{u1} V] [_inst_6 : Module.{u1, u1} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_7 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_8 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (SMulZeroClass.toHasSmul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.addCommMonoid.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MonoidAlgebra.smulZeroClass.{u1, u1, u1} k G k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (SMulWithZero.toSmulZeroClass.{u1, u1} k k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MulZeroClass.toSMulWithZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))))))) (SMulZeroClass.toHasSmul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MulZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MulZeroOneClass.toMulZeroClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))) (SMulZeroClass.toHasSmul.{u1, u1} k V (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, u1} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, u1} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (Module.toMulActionWithZero.{u1, u1} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_6))))] {W : Type.{u1}} [_inst_9 : AddCommGroup.{u1} W] [_inst_10 : Module.{u1, u1} k W (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)] [_inst_11 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) W (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)] [_inst_12 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) W (SMulZeroClass.toHasSmul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.addCommMonoid.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MonoidAlgebra.smulZeroClass.{u1, u1, u1} k G k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (SMulWithZero.toSmulZeroClass.{u1, u1} k k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MulZeroClass.toSMulWithZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))))))) (SMulZeroClass.toHasSmul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) W (AddZeroClass.toHasZero.{u1} W (AddMonoid.toAddZeroClass.{u1} W (AddCommMonoid.toAddMonoid.{u1} W (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)))) (SMulWithZero.toSmulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) W (MulZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MulZeroOneClass.toMulZeroClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))))) (AddZeroClass.toHasZero.{u1} W (AddMonoid.toAddZeroClass.{u1} W (AddCommMonoid.toAddMonoid.{u1} W (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) W (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (AddZeroClass.toHasZero.{u1} W (AddMonoid.toAddZeroClass.{u1} W (AddCommMonoid.toAddMonoid.{u1} W (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) W (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_11)))) (SMulZeroClass.toHasSmul.{u1, u1} k W (AddZeroClass.toHasZero.{u1} W (AddMonoid.toAddZeroClass.{u1} W (AddCommMonoid.toAddMonoid.{u1} W (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)))) (SMulWithZero.toSmulZeroClass.{u1, u1} k W (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (AddZeroClass.toHasZero.{u1} W (AddMonoid.toAddZeroClass.{u1} W (AddCommMonoid.toAddMonoid.{u1} W (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)))) (MulActionWithZero.toSMulWithZero.{u1, u1} k W (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} W (AddMonoid.toAddZeroClass.{u1} W (AddCommMonoid.toAddMonoid.{u1} W (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)))) (Module.toMulActionWithZero.{u1, u1} k W (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_10))))] (f : LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) V W (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11), (Eq.{succ u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (LinearMap.ker.{u1, u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V W (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11 (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) V W (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11) (LinearMap.semilinearMapClass.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V W (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11 (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))))) f) (Bot.bot.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.hasBot.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))) -> (Exists.{succ u1} (LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) W V (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_11 _inst_7) (fun (g : LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) W V (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_11 _inst_7) => Eq.{succ u1} (LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) V V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7 _inst_7) (LinearMap.comp.{u1, u1, u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V W V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7 _inst_11 _inst_7 (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (RingHomCompTriple.right_ids.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))))) g f) (LinearMap.id.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))
-but is expected to have type
-  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] {G : Type.{u1}} [_inst_2 : Fintype.{u1} G] [_inst_3 : Invertible.{u1} k (NonUnitalNonAssocRing.toMul.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toOne.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Nat.cast.{u1} k (Semiring.toNatCast.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Fintype.card.{u1} G _inst_2))] [_inst_4 : Group.{u1} G] {V : Type.{u1}} [_inst_5 : AddCommGroup.{u1} V] [_inst_6 : Module.{u1, u1} k V (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_7 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_8 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (Algebra.toSMul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.algebra.{u1, u1, u1} k G k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Algebra.id.{u1} k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (SMulZeroClass.toSMul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidWithZero.toZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))) (SMulZeroClass.toSMul.{u1, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, u1} k V (CommMonoidWithZero.toZero.{u1} k (CommGroupWithZero.toCommMonoidWithZero.{u1} k (Semifield.toCommGroupWithZero.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, u1} k V (Semiring.toMonoidWithZero.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (Module.toMulActionWithZero.{u1, u1} k V (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_6))))] {W : Type.{u1}} [_inst_9 : AddCommGroup.{u1} W] [_inst_10 : Module.{u1, u1} k W (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)] [_inst_11 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)] [_inst_12 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (Algebra.toSMul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.algebra.{u1, u1, u1} k G k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Algebra.id.{u1} k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (SMulZeroClass.toSMul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (NegZeroClass.toZero.{u1} W (SubNegZeroMonoid.toNegZeroClass.{u1} W (SubtractionMonoid.toSubNegZeroMonoid.{u1} W (SubtractionCommMonoid.toSubtractionMonoid.{u1} W (AddCommGroup.toDivisionAddCommMonoid.{u1} W _inst_9))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (MonoidWithZero.toZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (NegZeroClass.toZero.{u1} W (SubNegZeroMonoid.toNegZeroClass.{u1} W (SubtractionMonoid.toSubNegZeroMonoid.{u1} W (SubtractionCommMonoid.toSubtractionMonoid.{u1} W (AddCommGroup.toDivisionAddCommMonoid.{u1} W _inst_9))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (NegZeroClass.toZero.{u1} W (SubNegZeroMonoid.toNegZeroClass.{u1} W (SubtractionMonoid.toSubNegZeroMonoid.{u1} W (SubtractionCommMonoid.toSubtractionMonoid.{u1} W (AddCommGroup.toDivisionAddCommMonoid.{u1} W _inst_9))))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_11)))) (SMulZeroClass.toSMul.{u1, u1} k W (NegZeroClass.toZero.{u1} W (SubNegZeroMonoid.toNegZeroClass.{u1} W (SubtractionMonoid.toSubNegZeroMonoid.{u1} W (SubtractionCommMonoid.toSubtractionMonoid.{u1} W (AddCommGroup.toDivisionAddCommMonoid.{u1} W _inst_9))))) (SMulWithZero.toSMulZeroClass.{u1, u1} k W (CommMonoidWithZero.toZero.{u1} k (CommGroupWithZero.toCommMonoidWithZero.{u1} k (Semifield.toCommGroupWithZero.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} W (SubNegZeroMonoid.toNegZeroClass.{u1} W (SubtractionMonoid.toSubNegZeroMonoid.{u1} W (SubtractionCommMonoid.toSubtractionMonoid.{u1} W (AddCommGroup.toDivisionAddCommMonoid.{u1} W _inst_9))))) (MulActionWithZero.toSMulWithZero.{u1, u1} k W (Semiring.toMonoidWithZero.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} W (SubNegZeroMonoid.toNegZeroClass.{u1} W (SubtractionMonoid.toSubNegZeroMonoid.{u1} W (SubtractionCommMonoid.toSubtractionMonoid.{u1} W (AddCommGroup.toDivisionAddCommMonoid.{u1} W _inst_9))))) (Module.toMulActionWithZero.{u1, u1} k W (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_10))))] (f : LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) V W (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11), (Eq.{succ u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (LinearMap.ker.{u1, u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V W (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11 (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) V W (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11) (LinearMap.semilinearMapClass.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V W (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11 (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))))) f) (Bot.bot.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.instBotSubmodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))) -> (Exists.{succ u1} (LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) W V (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_11 _inst_7) (fun (g : LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k 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(MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) V V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7 _inst_7) (LinearMap.comp.{u1, u1, u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V W V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7 _inst_11 _inst_7 (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (RingHomCompTriple.ids.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))))) g f) (LinearMap.id.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align monoid_algebra.exists_left_inverse_of_injective MonoidAlgebra.exists_leftInverse_of_injectiveₓ'. -/
 theorem exists_leftInverse_of_injective (f : V →ₗ[MonoidAlgebra k G] W) (hf : f.ker = ⊥) :
     ∃ g : W →ₗ[MonoidAlgebra k G] V, g.comp f = LinearMap.id :=
@@ -250,10 +229,7 @@ theorem exists_leftInverse_of_injective (f : V →ₗ[MonoidAlgebra k G] W) (hf
 namespace Submodule
 
 /- warning: monoid_algebra.submodule.exists_is_compl -> MonoidAlgebra.Submodule.exists_isCompl is a dubious translation:
-lean 3 declaration is
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V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_7 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_8 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (SMulZeroClass.toHasSmul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k 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(Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))) (SMulZeroClass.toHasSmul.{u1, u1} k V (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, u1} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, u1} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (Module.toMulActionWithZero.{u1, u1} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_6))))] (p : Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7), Exists.{succ u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (fun (q : Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) => IsCompl.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.completeLattice.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))) (CompleteLattice.toBoundedOrder.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.completeLattice.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)) p q)
-but is expected to have type
-  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] {G : Type.{u1}} [_inst_2 : Fintype.{u1} G] [_inst_3 : Invertible.{u1} k (NonUnitalNonAssocRing.toMul.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toOne.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Nat.cast.{u1} k (Semiring.toNatCast.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Fintype.card.{u1} G _inst_2))] [_inst_4 : Group.{u1} G] {V : Type.{u1}} [_inst_5 : AddCommGroup.{u1} V] [_inst_6 : Module.{u1, u1} k V (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_7 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_8 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (Algebra.toSMul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.algebra.{u1, u1, u1} k G k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Algebra.id.{u1} k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (SMulZeroClass.toSMul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidWithZero.toZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))) (SMulZeroClass.toSMul.{u1, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, u1} k V (CommMonoidWithZero.toZero.{u1} k (CommGroupWithZero.toCommMonoidWithZero.{u1} k (Semifield.toCommGroupWithZero.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, u1} k V (Semiring.toMonoidWithZero.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (Module.toMulActionWithZero.{u1, u1} k V (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_6))))] (p : Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7), Exists.{succ u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (fun (q : Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) => IsCompl.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.completeLattice.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))) (CompleteLattice.toBoundedOrder.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.completeLattice.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)) p q)
+<too large>
 Case conversion may be inaccurate. Consider using '#align monoid_algebra.submodule.exists_is_compl MonoidAlgebra.Submodule.exists_isComplₓ'. -/
 theorem exists_isCompl (p : Submodule (MonoidAlgebra k G) V) :
     ∃ q : Submodule (MonoidAlgebra k G) V, IsCompl p q :=
@@ -262,10 +238,7 @@ theorem exists_isCompl (p : Submodule (MonoidAlgebra k G) V) :
 #align monoid_algebra.submodule.exists_is_compl MonoidAlgebra.Submodule.exists_isCompl
 
 /- warning: monoid_algebra.submodule.complemented_lattice -> MonoidAlgebra.Submodule.complementedLattice is a dubious translation:
-lean 3 declaration is
-  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] {G : Type.{u1}} [_inst_2 : Fintype.{u1} G] [_inst_3 : Invertible.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u1} Nat k (CoeTCₓ.coe.{1, succ u1} Nat k (Nat.castCoe.{u1} k (AddMonoidWithOne.toNatCast.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))))) (Fintype.card.{u1} G _inst_2))] [_inst_4 : Group.{u1} G] {V : Type.{u1}} [_inst_5 : AddCommGroup.{u1} V] [_inst_6 : Module.{u1, u1} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_7 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_8 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (SMulZeroClass.toHasSmul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.addCommMonoid.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MonoidAlgebra.smulZeroClass.{u1, u1, u1} k G k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (SMulWithZero.toSmulZeroClass.{u1, u1} k k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MulZeroClass.toSMulWithZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))))))) (SMulZeroClass.toHasSmul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MulZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MulZeroOneClass.toMulZeroClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))) (SMulZeroClass.toHasSmul.{u1, u1} k V (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, u1} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, u1} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (Module.toMulActionWithZero.{u1, u1} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_6))))], ComplementedLattice.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (ConditionallyCompleteLattice.toLattice.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.completeLattice.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))) (CompleteLattice.toBoundedOrder.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.completeLattice.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))
-but is expected to have type
-  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] {G : Type.{u1}} [_inst_2 : Fintype.{u1} G] [_inst_3 : Invertible.{u1} k (NonUnitalNonAssocRing.toMul.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toOne.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Nat.cast.{u1} k (Semiring.toNatCast.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Fintype.card.{u1} G _inst_2))] [_inst_4 : Group.{u1} G] {V : Type.{u1}} [_inst_5 : AddCommGroup.{u1} V] [_inst_6 : Module.{u1, u1} k V (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_7 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_8 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (Algebra.toSMul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.algebra.{u1, u1, u1} k G k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Algebra.id.{u1} k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (SMulZeroClass.toSMul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidWithZero.toZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))) (SMulZeroClass.toSMul.{u1, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, u1} k V (CommMonoidWithZero.toZero.{u1} k (CommGroupWithZero.toCommMonoidWithZero.{u1} k (Semifield.toCommGroupWithZero.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, u1} k V (Semiring.toMonoidWithZero.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (Module.toMulActionWithZero.{u1, u1} k V (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_6))))], ComplementedLattice.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (ConditionallyCompleteLattice.toLattice.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.completeLattice.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))) (CompleteLattice.toBoundedOrder.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.completeLattice.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))
+<too large>
 Case conversion may be inaccurate. Consider using '#align monoid_algebra.submodule.complemented_lattice MonoidAlgebra.Submodule.complementedLatticeₓ'. -/
 /-- This also implies an instance `is_semisimple_module (monoid_algebra k G) V`. -/
 instance complementedLattice : ComplementedLattice (Submodule (MonoidAlgebra k G) V) :=

31ca6f9c

bump to nightly-2023-05-24-06

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

fbc7b476

Diff

@@ -106,7 +106,7 @@ include h
 lean 3 declaration is
   forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] {G : Type.{u}} [_inst_2 : Group.{u} G] {V : Type.{u}} [_inst_3 : AddCommGroup.{u} V] [_inst_4 : Module.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_5 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_5)))) (SMulZeroClass.toHasSmul.{u, u} k V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} k V (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} k V (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_4))))] {W : Type.{u}} [_inst_7 : AddCommGroup.{u} W] [_inst_8 : Module.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_9 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_9)))) (SMulZeroClass.toHasSmul.{u, u} k W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} k W (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} k W (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_8))))] (π : LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) (i : LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9), (forall (v : V), Eq.{succ u} V (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) (fun (_x : LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) => W -> V) (LinearMap.hasCoeToFun.{u, u, u, u} k k W V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4 (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))))) π (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9) (fun (_x : LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9) => V -> W) (LinearMap.hasCoeToFun.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v) -> (forall (g : G) (v : V), Eq.{succ u} V (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) (fun (_x : LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) => W -> V) (LinearMap.hasCoeToFun.{u, u, u, u} k k W V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4 (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))))) (LinearMap.conjugate.{u} k _inst_1 G _inst_2 V _inst_3 _inst_4 _inst_5 _inst_6 W _inst_7 _inst_8 _inst_9 _inst_10 π g) (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9) (fun (_x : LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9) => V -> W) (LinearMap.hasCoeToFun.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v)
 but is expected to have type
-  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] {G : Type.{u}} [_inst_2 : Group.{u} G] {V : Type.{v}} [_inst_3 : AddCommGroup.{v} V] [_inst_4 : Module.{u, v} k V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_5 : Module.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, v} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u, v} k V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} k V (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} k V (Semiring.toMonoidWithZero.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} k V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_4))))] {W : Type.{w}} [_inst_7 : AddCommGroup.{w} W] [_inst_8 : Module.{u, w} k W (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_9 : Module.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, w} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W 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(CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9), (forall (v : V), Eq.{succ v} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : W) => V) (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, 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_inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) (FunLike.coe.{max (succ v) (succ w), succ w, succ v} (LinearMap.{u, u, w, v} k k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) W (fun (_x : W) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : W) => V) _x) (LinearMap.instFunLikeLinearMap.{u, u, w, v} k k W V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4 (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))))) π (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V) => W) _x) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} 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(DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9) V (fun (a : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V) => W) a) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) (FunLike.coe.{max (succ v) (succ w), succ w, succ v} (LinearMap.{u, u, w, v} k k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) W (fun (_x : W) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : W) => V) _x) (LinearMap.instFunLikeLinearMap.{u, u, w, v} k k W V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4 (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))))) (LinearMap.conjugate.{u, v, w} k _inst_1 G _inst_2 V _inst_3 _inst_4 _inst_5 _inst_6 W _inst_7 _inst_8 _inst_9 _inst_10 π g) (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V) => W) _x) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v)
+  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] {G : Type.{u}} [_inst_2 : Group.{u} G] {V : Type.{v}} [_inst_3 : AddCommGroup.{v} V] [_inst_4 : Module.{u, v} k V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_5 : Module.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, v} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u, v} k V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} k V (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} k V (Semiring.toMonoidWithZero.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} k V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_4))))] {W : Type.{w}} [_inst_7 : AddCommGroup.{w} W] [_inst_8 : Module.{u, w} k W (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_9 : Module.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, w} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_9)))) (SMulZeroClass.toSMul.{u, w} k W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} k W (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} k W (Semiring.toMonoidWithZero.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} k W (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_8))))] (π : LinearMap.{u, u, w, v} k k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) (i : LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9), (forall (v : V), Eq.{succ v} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : W) => V) (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9) V (fun (a : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V) => W) a) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) (FunLike.coe.{max (succ v) (succ w), succ w, succ v} (LinearMap.{u, u, w, v} k k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) W (fun (_x : W) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : W) => V) _x) (LinearMap.instFunLikeLinearMap.{u, u, w, v} k k W V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4 (RingHom.id.{u} k 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(MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v) -> (forall (g : G) (v : V), Eq.{succ v} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : W) => V) (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9) V (fun (a : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V) => W) a) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) (FunLike.coe.{max (succ v) (succ w), succ w, succ v} (LinearMap.{u, u, w, v} k k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) W (fun (_x : W) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : W) => V) _x) (LinearMap.instFunLikeLinearMap.{u, u, w, v} k k W V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4 (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))))) (LinearMap.conjugate.{u, v, w} k _inst_1 G _inst_2 V _inst_3 _inst_4 _inst_5 _inst_6 W _inst_7 _inst_8 _inst_9 _inst_10 π g) (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V) => W) _x) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v)
 Case conversion may be inaccurate. Consider using '#align linear_map.conjugate_i LinearMap.conjugate_iₓ'. -/
 theorem conjugate_i (g : G) (v : V) : (conjugate π g) (i v) = v :=
   by
@@ -183,7 +183,7 @@ include h
 lean 3 declaration is
   forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] (G : Type.{u}) [_inst_2 : Group.{u} G] {V : Type.{u}} [_inst_3 : AddCommGroup.{u} V] [_inst_4 : Module.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_5 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_5)))) (SMulZeroClass.toHasSmul.{u, u} k V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} k V (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} k V (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_4))))] {W : Type.{u}} [_inst_7 : AddCommGroup.{u} W] [_inst_8 : Module.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_9 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_9)))) (SMulZeroClass.toHasSmul.{u, u} k W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} k W (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} k W (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_8))))] (π : LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) (i : LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9), (forall (v : V), Eq.{succ u} V (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) (fun (_x : LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) => W -> V) (LinearMap.hasCoeToFun.{u, u, u, u} k k W V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4 (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))))) π (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9) (fun (_x : LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9) => V -> W) (LinearMap.hasCoeToFun.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v) -> (forall [_inst_11 : Fintype.{u} G] [inv : Invertible.{u} k (Distrib.toHasMul.{u} k (Ring.toDistrib.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoidWithOne.toOne.{u} k (AddGroupWithOne.toAddMonoidWithOne.{u} k (AddCommGroupWithOne.toAddGroupWithOne.{u} k (Ring.toAddCommGroupWithOne.{u} k (CommRing.toRing.{u} k _inst_1))))) ((fun (a : Type) (b : Type.{u}) [self : HasLiftT.{1, succ u} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u} Nat k (CoeTCₓ.coe.{1, succ u} Nat k (Nat.castCoe.{u} k (AddMonoidWithOne.toNatCast.{u} k (AddGroupWithOne.toAddMonoidWithOne.{u} k (AddCommGroupWithOne.toAddGroupWithOne.{u} k (Ring.toAddCommGroupWithOne.{u} k (CommRing.toRing.{u} k _inst_1)))))))) (Fintype.card.{u} G _inst_11))] (v : V), Eq.{succ u} V (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_9 _inst_5) (fun (_x : LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_9 _inst_5) => W -> V) (LinearMap.hasCoeToFun.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_9 _inst_5 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) (LinearMap.equivariantProjection.{u} k _inst_1 G _inst_2 V _inst_3 _inst_4 _inst_5 _inst_6 W _inst_7 _inst_8 _inst_9 _inst_10 π _inst_11 inv) (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9) (fun (_x : LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9) => V -> W) (LinearMap.hasCoeToFun.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v)
 but is expected to have type
-  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] (G : Type.{u}) [_inst_2 : Group.{u} G] {V : Type.{v}} [_inst_3 : AddCommGroup.{v} V] [_inst_4 : Module.{u, v} k V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_5 : Module.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, v} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u, v} k V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} k V (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} k V (Semiring.toMonoidWithZero.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} k V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_4))))] {W : Type.{w}} [_inst_7 : AddCommGroup.{w} W] [_inst_8 : Module.{u, w} k W (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_9 : Module.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, w} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_9)))) (SMulZeroClass.toSMul.{u, w} k W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} k W (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} k W (Semiring.toMonoidWithZero.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} k W (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_8))))] (π : LinearMap.{u, u, w, v} k k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) (i : LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9), (forall (v : V), Eq.{succ v} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : W) => V) (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, 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: V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V) => W) a) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k 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(Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))))) π (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G 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(CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9) V (fun (a : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V) => W) a) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) (FunLike.coe.{max (succ v) (succ w), succ w, succ v} (LinearMap.{u, u, w, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_9 _inst_5) W (fun (_x : W) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : W) => V) _x) (LinearMap.instFunLikeLinearMap.{u, u, w, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_9 _inst_5 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) (LinearMap.equivariantProjection.{u, v, w} k _inst_1 G _inst_2 V _inst_3 _inst_4 _inst_5 _inst_6 W _inst_7 _inst_8 _inst_9 _inst_10 π _inst_11 inv) (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V) => W) _x) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v)
+  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] (G : Type.{u}) [_inst_2 : Group.{u} G] {V : Type.{v}} [_inst_3 : AddCommGroup.{v} V] [_inst_4 : Module.{u, v} k V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_5 : Module.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, v} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u, v} k V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} k V (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} k V (Semiring.toMonoidWithZero.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} k V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_4))))] {W : Type.{w}} [_inst_7 : AddCommGroup.{w} W] [_inst_8 : Module.{u, w} k W (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_9 : Module.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, w} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_9)))) (SMulZeroClass.toSMul.{u, w} k W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} k W (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} k W (Semiring.toMonoidWithZero.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} k W (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_8))))] (π : LinearMap.{u, u, w, v} k k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) (i : LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9), (forall (v : V), Eq.{succ v} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : W) => V) (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, 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_inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) (FunLike.coe.{max (succ v) (succ w), succ w, succ v} (LinearMap.{u, u, w, v} k k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) W (fun (_x : W) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : W) => V) _x) (LinearMap.instFunLikeLinearMap.{u, u, w, v} k k W V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4 (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))))) π (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V) => W) _x) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v) -> (forall [_inst_11 : Fintype.{u} G] [inv : Invertible.{u} k (NonUnitalNonAssocRing.toMul.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))) (Semiring.toOne.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Nat.cast.{u} k (Semiring.toNatCast.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Fintype.card.{u} G _inst_11))] (v : V), Eq.{succ v} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : W) => V) (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k 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(x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V) => W) a) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) 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(DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_9 _inst_5) W (fun (_x : W) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : W) => V) _x) (LinearMap.instFunLikeLinearMap.{u, u, w, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_9 _inst_5 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) (LinearMap.equivariantProjection.{u, v, w} k _inst_1 G _inst_2 V _inst_3 _inst_4 _inst_5 _inst_6 W _inst_7 _inst_8 _inst_9 _inst_10 π _inst_11 inv) (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V) => W) _x) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v)
 Case conversion may be inaccurate. Consider using '#align linear_map.equivariant_projection_condition LinearMap.equivariantProjection_conditionₓ'. -/
 theorem equivariantProjection_condition (v : V) : (π.equivariantProjection G) (i v) = v :=
   by

31ca6f9c

bump to nightly-2023-05-18-03

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

b46e9d53

Diff

@@ -106,7 +106,7 @@ include h
 lean 3 declaration is
   forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] {G : Type.{u}} [_inst_2 : Group.{u} G] {V : Type.{u}} [_inst_3 : AddCommGroup.{u} V] [_inst_4 : Module.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_5 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_5)))) (SMulZeroClass.toHasSmul.{u, u} k V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} k V (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} k V (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_4))))] {W : Type.{u}} [_inst_7 : AddCommGroup.{u} W] [_inst_8 : Module.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_9 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_9)))) (SMulZeroClass.toHasSmul.{u, u} k W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} k W (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} k W (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_8))))] (π : LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) (i : LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9), (forall (v : V), Eq.{succ u} V (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k 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(v : V), Eq.{succ u} V (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) (fun (_x : LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) => W -> V) (LinearMap.hasCoeToFun.{u, u, u, u} k k W V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4 (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))))) (LinearMap.conjugate.{u} k _inst_1 G _inst_2 V _inst_3 _inst_4 _inst_5 _inst_6 W _inst_7 _inst_8 _inst_9 _inst_10 π g) (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9) (fun (_x : LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9) => V -> W) (LinearMap.hasCoeToFun.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v)
 but is expected to have type
-  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] {G : Type.{u}} [_inst_2 : Group.{u} G] {V : Type.{v}} [_inst_3 : AddCommGroup.{v} V] [_inst_4 : Module.{u, v} k V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_5 : Module.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, v} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u, v} k V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} k V (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} k V (Semiring.toMonoidWithZero.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} k V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_4))))] {W : Type.{w}} [_inst_7 : AddCommGroup.{w} W] [_inst_8 : Module.{u, w} k W (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_9 : Module.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, w} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_9)))) (SMulZeroClass.toSMul.{u, w} k W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} k W (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} k W (Semiring.toMonoidWithZero.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} k W (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_8))))] (π : LinearMap.{u, u, w, v} k k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) (i : LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9), (forall (v : V), Eq.{succ v} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : W) => V) (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9) V (fun (a : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => W) a) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) (FunLike.coe.{max (succ v) (succ w), succ w, succ v} (LinearMap.{u, u, w, v} k k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) W (fun (_x : W) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : W) => V) _x) (LinearMap.instFunLikeLinearMap.{u, u, w, v} k k W V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4 (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))))) π (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => W) _x) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v) -> (forall (g : G) (v : V), Eq.{succ v} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : W) => V) (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9) V (fun (a : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => W) a) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) (FunLike.coe.{max (succ v) (succ w), succ w, succ v} (LinearMap.{u, u, w, v} k k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) W (fun (_x : W) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : W) => V) _x) (LinearMap.instFunLikeLinearMap.{u, u, w, v} k k W V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4 (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))))) (LinearMap.conjugate.{u, v, w} k _inst_1 G _inst_2 V _inst_3 _inst_4 _inst_5 _inst_6 W _inst_7 _inst_8 _inst_9 _inst_10 π g) (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => W) _x) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v)
+  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] {G : Type.{u}} [_inst_2 : Group.{u} G] {V : Type.{v}} [_inst_3 : AddCommGroup.{v} V] [_inst_4 : Module.{u, v} k V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_5 : Module.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, v} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u, v} k V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} k V (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} k V (Semiring.toMonoidWithZero.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} k V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_4))))] {W : Type.{w}} [_inst_7 : AddCommGroup.{w} W] [_inst_8 : Module.{u, w} k W (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_9 : Module.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, w} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_9)))) (SMulZeroClass.toSMul.{u, w} k W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} k W (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} k W (Semiring.toMonoidWithZero.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} k W (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_8))))] (π : LinearMap.{u, u, w, v} k k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) (i : LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9), (forall (v : V), Eq.{succ v} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : W) => V) (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9) V (fun (a : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V) => W) a) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) (FunLike.coe.{max (succ v) (succ w), succ w, succ v} (LinearMap.{u, u, w, v} k k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) W (fun (_x : W) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : W) => V) _x) (LinearMap.instFunLikeLinearMap.{u, u, w, v} k k W V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4 (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))))) π (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V) => W) _x) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v) -> (forall (g : G) (v : V), Eq.{succ v} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : W) => V) (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9) V (fun (a : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V) => W) a) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) (FunLike.coe.{max (succ v) (succ w), succ w, succ v} (LinearMap.{u, u, w, v} k k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) W (fun (_x : W) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : W) => V) _x) (LinearMap.instFunLikeLinearMap.{u, u, w, v} k k W V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4 (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))))) (LinearMap.conjugate.{u, v, w} k _inst_1 G _inst_2 V _inst_3 _inst_4 _inst_5 _inst_6 W _inst_7 _inst_8 _inst_9 _inst_10 π g) (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V) => W) _x) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v)
 Case conversion may be inaccurate. Consider using '#align linear_map.conjugate_i LinearMap.conjugate_iₓ'. -/
 theorem conjugate_i (g : G) (v : V) : (conjugate π g) (i v) = v :=
   by
@@ -183,7 +183,7 @@ include h
 lean 3 declaration is
   forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] (G : Type.{u}) [_inst_2 : Group.{u} G] {V : Type.{u}} [_inst_3 : AddCommGroup.{u} V] [_inst_4 : Module.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_5 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_5)))) (SMulZeroClass.toHasSmul.{u, u} k V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} k V (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} k V (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_4))))] {W : Type.{u}} [_inst_7 : AddCommGroup.{u} W] [_inst_8 : Module.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_9 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_9)))) (SMulZeroClass.toHasSmul.{u, u} k W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} k W (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} k W (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_8))))] (π : LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) (i : LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9), (forall (v : V), Eq.{succ u} V (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) (fun (_x : LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) => W -> V) (LinearMap.hasCoeToFun.{u, u, u, u} k k W V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4 (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))))) π (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9) (fun (_x : LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9) => V -> W) (LinearMap.hasCoeToFun.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v) -> (forall [_inst_11 : Fintype.{u} G] [inv : Invertible.{u} k (Distrib.toHasMul.{u} k (Ring.toDistrib.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoidWithOne.toOne.{u} k (AddGroupWithOne.toAddMonoidWithOne.{u} k (AddCommGroupWithOne.toAddGroupWithOne.{u} k (Ring.toAddCommGroupWithOne.{u} k (CommRing.toRing.{u} k _inst_1))))) ((fun (a : Type) (b : Type.{u}) [self : HasLiftT.{1, succ u} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u} Nat k (CoeTCₓ.coe.{1, succ u} Nat k (Nat.castCoe.{u} k (AddMonoidWithOne.toNatCast.{u} k (AddGroupWithOne.toAddMonoidWithOne.{u} k (AddCommGroupWithOne.toAddGroupWithOne.{u} k (Ring.toAddCommGroupWithOne.{u} k (CommRing.toRing.{u} k _inst_1)))))))) (Fintype.card.{u} G _inst_11))] (v : V), Eq.{succ u} V (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_9 _inst_5) (fun (_x : LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_9 _inst_5) => W -> V) (LinearMap.hasCoeToFun.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_9 _inst_5 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) (LinearMap.equivariantProjection.{u} k _inst_1 G _inst_2 V _inst_3 _inst_4 _inst_5 _inst_6 W _inst_7 _inst_8 _inst_9 _inst_10 π _inst_11 inv) (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9) (fun (_x : LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9) => V -> W) (LinearMap.hasCoeToFun.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v)
 but is expected to have type
-  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] (G : Type.{u}) [_inst_2 : Group.{u} G] {V : Type.{v}} [_inst_3 : AddCommGroup.{v} V] [_inst_4 : Module.{u, v} k V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_5 : Module.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, v} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u, v} k V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} k V (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} k V (Semiring.toMonoidWithZero.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} k V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_4))))] {W : Type.{w}} [_inst_7 : AddCommGroup.{w} W] [_inst_8 : Module.{u, w} k W (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_9 : Module.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, w} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_9)))) (SMulZeroClass.toSMul.{u, w} k W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} k W (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} k W (Semiring.toMonoidWithZero.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} k W (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_8))))] (π : LinearMap.{u, u, w, v} k k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) (i : LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k 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(DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => W) _x) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} 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(Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) (FunLike.coe.{max (succ v) (succ w), succ w, succ v} (LinearMap.{u, u, w, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_9 _inst_5) W (fun (_x : W) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : W) => V) _x) (LinearMap.instFunLikeLinearMap.{u, u, w, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_9 _inst_5 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) (LinearMap.equivariantProjection.{u, v, w} k _inst_1 G _inst_2 V _inst_3 _inst_4 _inst_5 _inst_6 W _inst_7 _inst_8 _inst_9 _inst_10 π _inst_11 inv) (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => W) _x) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v)
+  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] (G : Type.{u}) [_inst_2 : Group.{u} G] {V : Type.{v}} [_inst_3 : AddCommGroup.{v} V] [_inst_4 : Module.{u, v} k V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_5 : Module.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, v} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u, v} k V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} k V (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} k V (Semiring.toMonoidWithZero.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} k V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_4))))] {W : Type.{w}} [_inst_7 : AddCommGroup.{w} W] [_inst_8 : Module.{u, w} k W (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_9 : Module.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, w} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_9)))) (SMulZeroClass.toSMul.{u, w} k W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} k W (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} k W (Semiring.toMonoidWithZero.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} k W (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_8))))] (π : LinearMap.{u, u, w, v} k k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) (i : LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9), (forall (v : V), Eq.{succ v} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : W) => V) (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9) V (fun (a : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V) => W) a) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) (FunLike.coe.{max (succ v) (succ w), succ w, succ v} (LinearMap.{u, u, w, v} k k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) W (fun (_x : W) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : W) => V) _x) (LinearMap.instFunLikeLinearMap.{u, u, w, v} k k W V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4 (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))))) π (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V) => W) _x) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v) -> (forall [_inst_11 : Fintype.{u} G] [inv : Invertible.{u} k (NonUnitalNonAssocRing.toMul.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))) (Semiring.toOne.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Nat.cast.{u} k (Semiring.toNatCast.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Fintype.card.{u} G _inst_11))] (v : V), Eq.{succ v} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : W) => V) (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9) V (fun (a : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V) => W) a) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) (FunLike.coe.{max (succ v) (succ w), succ w, succ v} (LinearMap.{u, u, w, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_9 _inst_5) W (fun (_x : W) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : W) => V) _x) (LinearMap.instFunLikeLinearMap.{u, u, w, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_9 _inst_5 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) (LinearMap.equivariantProjection.{u, v, w} k _inst_1 G _inst_2 V _inst_3 _inst_4 _inst_5 _inst_6 W _inst_7 _inst_8 _inst_9 _inst_10 π _inst_11 inv) (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V) => W) _x) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v)
 Case conversion may be inaccurate. Consider using '#align linear_map.equivariant_projection_condition LinearMap.equivariantProjection_conditionₓ'. -/
 theorem equivariantProjection_condition (v : V) : (π.equivariantProjection G) (i v) = v :=
   by
@@ -229,7 +229,7 @@ variable [IsScalarTower k (MonoidAlgebra k G) W]
 lean 3 declaration is
   forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] {G : Type.{u1}} [_inst_2 : Fintype.{u1} G] [_inst_3 : Invertible.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u1} Nat k (CoeTCₓ.coe.{1, succ u1} Nat k (Nat.castCoe.{u1} k (AddMonoidWithOne.toNatCast.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))))) (Fintype.card.{u1} G _inst_2))] [_inst_4 : Group.{u1} G] {V : Type.{u1}} [_inst_5 : AddCommGroup.{u1} V] [_inst_6 : Module.{u1, u1} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_7 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_8 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (SMulZeroClass.toHasSmul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.addCommMonoid.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MonoidAlgebra.smulZeroClass.{u1, u1, u1} k G k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (SMulWithZero.toSmulZeroClass.{u1, u1} k k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MulZeroClass.toSMulWithZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))))))) (SMulZeroClass.toHasSmul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MulZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MulZeroOneClass.toMulZeroClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))) (SMulZeroClass.toHasSmul.{u1, u1} k V (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, u1} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, u1} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (Module.toMulActionWithZero.{u1, u1} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_6))))] {W : Type.{u1}} [_inst_9 : AddCommGroup.{u1} W] [_inst_10 : Module.{u1, u1} k W (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)] [_inst_11 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) W (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)] [_inst_12 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) W (SMulZeroClass.toHasSmul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.addCommMonoid.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MonoidAlgebra.smulZeroClass.{u1, u1, u1} k G k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (SMulWithZero.toSmulZeroClass.{u1, u1} k k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MulZeroClass.toSMulWithZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))))))) (SMulZeroClass.toHasSmul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) W (AddZeroClass.toHasZero.{u1} W (AddMonoid.toAddZeroClass.{u1} W (AddCommMonoid.toAddMonoid.{u1} W (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)))) (SMulWithZero.toSmulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) W (MulZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MulZeroOneClass.toMulZeroClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))))) (AddZeroClass.toHasZero.{u1} W (AddMonoid.toAddZeroClass.{u1} W (AddCommMonoid.toAddMonoid.{u1} W (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) W (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (AddZeroClass.toHasZero.{u1} W (AddMonoid.toAddZeroClass.{u1} W (AddCommMonoid.toAddMonoid.{u1} W (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) W (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_11)))) (SMulZeroClass.toHasSmul.{u1, u1} k W (AddZeroClass.toHasZero.{u1} W (AddMonoid.toAddZeroClass.{u1} W (AddCommMonoid.toAddMonoid.{u1} W (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)))) (SMulWithZero.toSmulZeroClass.{u1, u1} k W (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (AddZeroClass.toHasZero.{u1} W (AddMonoid.toAddZeroClass.{u1} W (AddCommMonoid.toAddMonoid.{u1} W (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)))) (MulActionWithZero.toSMulWithZero.{u1, u1} k W (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} W (AddMonoid.toAddZeroClass.{u1} W (AddCommMonoid.toAddMonoid.{u1} W (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)))) (Module.toMulActionWithZero.{u1, u1} k W (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_10))))] (f : LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) V W (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11), (Eq.{succ u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (LinearMap.ker.{u1, u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V W (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11 (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) V W (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11) (LinearMap.semilinearMapClass.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V W (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11 (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))))) f) (Bot.bot.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.hasBot.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))) -> (Exists.{succ u1} (LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) W V (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_11 _inst_7) (fun (g : LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) W V (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_11 _inst_7) => Eq.{succ u1} (LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) V V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7 _inst_7) (LinearMap.comp.{u1, u1, u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V W V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7 _inst_11 _inst_7 (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (RingHomCompTriple.right_ids.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))))) g f) (LinearMap.id.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))
 but is expected to have type
-  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] {G : Type.{u1}} [_inst_2 : Fintype.{u1} G] [_inst_3 : Invertible.{u1} k (NonUnitalNonAssocRing.toMul.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toOne.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Nat.cast.{u1} k (Semiring.toNatCast.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Fintype.card.{u1} G _inst_2))] [_inst_4 : Group.{u1} G] {V : Type.{u1}} [_inst_5 : AddCommGroup.{u1} V] [_inst_6 : Module.{u1, u1} k V (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_7 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_8 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (Algebra.toSMul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.algebra.{u1, u1, u1} k G k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Algebra.id.{u1} k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (SMulZeroClass.toSMul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidWithZero.toZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))) (SMulZeroClass.toSMul.{u1, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, u1} k V (CommMonoidWithZero.toZero.{u1} k (CommGroupWithZero.toCommMonoidWithZero.{u1} k (Semifield.toCommGroupWithZero.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, u1} k V (Semiring.toMonoidWithZero.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (Module.toMulActionWithZero.{u1, u1} k V (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_6))))] {W : Type.{u1}} [_inst_9 : AddCommGroup.{u1} W] [_inst_10 : Module.{u1, u1} k W (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)] [_inst_11 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)] [_inst_12 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (Algebra.toSMul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.algebra.{u1, u1, u1} k G k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Algebra.id.{u1} k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (SMulZeroClass.toSMul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (NegZeroClass.toZero.{u1} W (SubNegZeroMonoid.toNegZeroClass.{u1} W (SubtractionMonoid.toSubNegZeroMonoid.{u1} W (SubtractionCommMonoid.toSubtractionMonoid.{u1} W (AddCommGroup.toDivisionAddCommMonoid.{u1} W _inst_9))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (MonoidWithZero.toZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (NegZeroClass.toZero.{u1} W (SubNegZeroMonoid.toNegZeroClass.{u1} W (SubtractionMonoid.toSubNegZeroMonoid.{u1} W (SubtractionCommMonoid.toSubtractionMonoid.{u1} W (AddCommGroup.toDivisionAddCommMonoid.{u1} W _inst_9))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (NegZeroClass.toZero.{u1} W (SubNegZeroMonoid.toNegZeroClass.{u1} W (SubtractionMonoid.toSubNegZeroMonoid.{u1} W (SubtractionCommMonoid.toSubtractionMonoid.{u1} W (AddCommGroup.toDivisionAddCommMonoid.{u1} W _inst_9))))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_11)))) (SMulZeroClass.toSMul.{u1, u1} k W (NegZeroClass.toZero.{u1} W (SubNegZeroMonoid.toNegZeroClass.{u1} W (SubtractionMonoid.toSubNegZeroMonoid.{u1} W (SubtractionCommMonoid.toSubtractionMonoid.{u1} W (AddCommGroup.toDivisionAddCommMonoid.{u1} W _inst_9))))) (SMulWithZero.toSMulZeroClass.{u1, u1} k W (CommMonoidWithZero.toZero.{u1} k 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k _inst_1)))) V W (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11 (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (LinearMap.{u1, u1, u1, u1} 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(DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))))) g f) (LinearMap.id.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))
+  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] {G : Type.{u1}} [_inst_2 : Fintype.{u1} G] [_inst_3 : Invertible.{u1} k (NonUnitalNonAssocRing.toMul.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toOne.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Nat.cast.{u1} k (Semiring.toNatCast.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Fintype.card.{u1} G _inst_2))] [_inst_4 : Group.{u1} G] {V : Type.{u1}} [_inst_5 : AddCommGroup.{u1} V] [_inst_6 : Module.{u1, u1} k V (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_7 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_8 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (Algebra.toSMul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.algebra.{u1, u1, u1} k G k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Algebra.id.{u1} k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (SMulZeroClass.toSMul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidWithZero.toZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))) (SMulZeroClass.toSMul.{u1, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, u1} k V (CommMonoidWithZero.toZero.{u1} k (CommGroupWithZero.toCommMonoidWithZero.{u1} k (Semifield.toCommGroupWithZero.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, u1} k V (Semiring.toMonoidWithZero.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (Module.toMulActionWithZero.{u1, u1} k V (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_6))))] {W : Type.{u1}} [_inst_9 : AddCommGroup.{u1} W] [_inst_10 : Module.{u1, u1} k W (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)] [_inst_11 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)] [_inst_12 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (Algebra.toSMul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.algebra.{u1, u1, u1} k G k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Algebra.id.{u1} k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (SMulZeroClass.toSMul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (NegZeroClass.toZero.{u1} W (SubNegZeroMonoid.toNegZeroClass.{u1} W (SubtractionMonoid.toSubNegZeroMonoid.{u1} W (SubtractionCommMonoid.toSubtractionMonoid.{u1} W (AddCommGroup.toDivisionAddCommMonoid.{u1} W _inst_9))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (MonoidWithZero.toZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (NegZeroClass.toZero.{u1} W (SubNegZeroMonoid.toNegZeroClass.{u1} W (SubtractionMonoid.toSubNegZeroMonoid.{u1} W (SubtractionCommMonoid.toSubtractionMonoid.{u1} W (AddCommGroup.toDivisionAddCommMonoid.{u1} W _inst_9))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (NegZeroClass.toZero.{u1} W (SubNegZeroMonoid.toNegZeroClass.{u1} W (SubtractionMonoid.toSubNegZeroMonoid.{u1} W (SubtractionCommMonoid.toSubtractionMonoid.{u1} W (AddCommGroup.toDivisionAddCommMonoid.{u1} W _inst_9))))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_11)))) (SMulZeroClass.toSMul.{u1, u1} k W (NegZeroClass.toZero.{u1} W (SubNegZeroMonoid.toNegZeroClass.{u1} W (SubtractionMonoid.toSubNegZeroMonoid.{u1} W (SubtractionCommMonoid.toSubtractionMonoid.{u1} W (AddCommGroup.toDivisionAddCommMonoid.{u1} W _inst_9))))) (SMulWithZero.toSMulZeroClass.{u1, u1} k W (CommMonoidWithZero.toZero.{u1} k (CommGroupWithZero.toCommMonoidWithZero.{u1} k (Semifield.toCommGroupWithZero.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} W (SubNegZeroMonoid.toNegZeroClass.{u1} W (SubtractionMonoid.toSubNegZeroMonoid.{u1} W (SubtractionCommMonoid.toSubtractionMonoid.{u1} W (AddCommGroup.toDivisionAddCommMonoid.{u1} W _inst_9))))) (MulActionWithZero.toSMulWithZero.{u1, u1} k W (Semiring.toMonoidWithZero.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} W (SubNegZeroMonoid.toNegZeroClass.{u1} W (SubtractionMonoid.toSubNegZeroMonoid.{u1} W (SubtractionCommMonoid.toSubtractionMonoid.{u1} W (AddCommGroup.toDivisionAddCommMonoid.{u1} W _inst_9))))) (Module.toMulActionWithZero.{u1, u1} k W (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_10))))] (f : LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) V W (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11), (Eq.{succ u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (LinearMap.ker.{u1, u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V W (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11 (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) V W (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11) (LinearMap.semilinearMapClass.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V W (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11 (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))))) f) (Bot.bot.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.instBotSubmodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))) -> (Exists.{succ u1} (LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) W V (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_11 _inst_7) (fun (g : LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) W V (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_11 _inst_7) => Eq.{succ u1} (LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) V V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7 _inst_7) (LinearMap.comp.{u1, u1, u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V W V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7 _inst_11 _inst_7 (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (RingHomCompTriple.ids.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))))) g f) (LinearMap.id.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))
 Case conversion may be inaccurate. Consider using '#align monoid_algebra.exists_left_inverse_of_injective MonoidAlgebra.exists_leftInverse_of_injectiveₓ'. -/
 theorem exists_leftInverse_of_injective (f : V →ₗ[MonoidAlgebra k G] W) (hf : f.ker = ⊥) :
     ∃ g : W →ₗ[MonoidAlgebra k G] V, g.comp f = LinearMap.id :=

31ca6f9c

bump to nightly-2023-05-08-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/08e1d8d4d989df3a6df86f385e9053ec8a372cc1

63e712c6

Diff

@@ -88,7 +88,7 @@ include π
 lean 3 declaration is
   forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] {G : Type.{u}} [_inst_2 : Group.{u} G] {V : Type.{u}} [_inst_3 : AddCommGroup.{u} V] [_inst_4 : Module.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_5 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_5)))) (SMulZeroClass.toHasSmul.{u, u} k V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} k V (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} k V (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_4))))] {W : Type.{u}} [_inst_7 : AddCommGroup.{u} W] [_inst_8 : Module.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_9 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_9)))) (SMulZeroClass.toHasSmul.{u, u} k W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} k W (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} k W (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_8))))], (LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) -> G -> (LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4)
 but is expected to have type
-  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] {G : Type.{u}} [_inst_2 : Group.{u} G] {V : Type.{v}} [_inst_3 : AddCommGroup.{v} V] [_inst_4 : Module.{u, v} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_5 : Module.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, v} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u, v} k V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} k V (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} k V (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_4))))] {W : Type.{w}} [_inst_7 : AddCommGroup.{w} W] [_inst_8 : Module.{u, w} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_9 : Module.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, w} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_9)))) (SMulZeroClass.toSMul.{u, w} k W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} k W (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} k W (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_8))))], (LinearMap.{u, u, w, v} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (NonAssocRing.toNonAssocSemiring.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) -> G -> (LinearMap.{u, u, w, v} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (NonAssocRing.toNonAssocSemiring.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4)
+  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] {G : Type.{u}} [_inst_2 : Group.{u} G] {V : Type.{v}} [_inst_3 : AddCommGroup.{v} V] [_inst_4 : Module.{u, v} k V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_5 : Module.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, v} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u, v} k V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} k V (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} k V (Semiring.toMonoidWithZero.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} k V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_4))))] {W : Type.{w}} [_inst_7 : AddCommGroup.{w} W] [_inst_8 : Module.{u, w} k W (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_9 : Module.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, w} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_9)))) (SMulZeroClass.toSMul.{u, w} k W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} k W (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} k W (Semiring.toMonoidWithZero.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} k W (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_8))))], (LinearMap.{u, u, w, v} k k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) -> G -> (LinearMap.{u, u, w, v} k k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4)
 Case conversion may be inaccurate. Consider using '#align linear_map.conjugate LinearMap.conjugateₓ'. -/
 /-- We define the conjugate of `π` by `g`, as a `k`-linear map.
 -/
@@ -106,7 +106,7 @@ include h
 lean 3 declaration is
   forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] {G : Type.{u}} [_inst_2 : Group.{u} G] {V : Type.{u}} [_inst_3 : AddCommGroup.{u} V] [_inst_4 : Module.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_5 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_5)))) (SMulZeroClass.toHasSmul.{u, u} k V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} k V (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} k V (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_4))))] {W : Type.{u}} [_inst_7 : AddCommGroup.{u} W] [_inst_8 : Module.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_9 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_9)))) (SMulZeroClass.toHasSmul.{u, u} k W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} k W (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} k W (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_8))))] (π : LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) (i : LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9), (forall (v : V), Eq.{succ u} V (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) (fun (_x : LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) => W -> V) (LinearMap.hasCoeToFun.{u, u, u, u} k k W V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4 (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))))) π (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} 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(MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v)
 but is expected to have type
-  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] {G : Type.{u}} [_inst_2 : Group.{u} G] {V : Type.{v}} [_inst_3 : AddCommGroup.{v} V] [_inst_4 : Module.{u, v} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_5 : Module.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, v} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u, v} k V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} k V (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} k V (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_4))))] {W : Type.{w}} [_inst_7 : AddCommGroup.{w} W] [_inst_8 : Module.{u, w} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_9 : Module.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, w} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_9)))) (SMulZeroClass.toSMul.{u, w} k W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} k W (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} k W (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_8))))] (π : LinearMap.{u, u, w, v} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (NonAssocRing.toNonAssocSemiring.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) (i : LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9), (forall (v : V), Eq.{succ v} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : W) => V) (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9) V (fun (a : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => W) a) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) (FunLike.coe.{max (succ v) (succ w), succ w, succ v} (LinearMap.{u, u, w, v} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (NonAssocRing.toNonAssocSemiring.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) W (fun (_x : W) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : W) => V) _x) (LinearMap.instFunLikeLinearMap.{u, u, w, v} k k W V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) 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(MonoidAlgebra.nonAssocSemiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v) -> (forall (g : G) (v : V), Eq.{succ v} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : W) => V) (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9) V (fun (a : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => W) a) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) (FunLike.coe.{max (succ v) (succ w), succ w, succ v} (LinearMap.{u, u, w, v} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (NonAssocRing.toNonAssocSemiring.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) W (fun (_x : W) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : W) => V) _x) (LinearMap.instFunLikeLinearMap.{u, u, w, v} k k W V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4 (RingHom.id.{u} k (NonAssocRing.toNonAssocSemiring.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))) (LinearMap.conjugate.{u, v, w} k _inst_1 G _inst_2 V _inst_3 _inst_4 _inst_5 _inst_6 W _inst_7 _inst_8 _inst_9 _inst_10 π g) (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => W) _x) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v)
+  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] {G : Type.{u}} [_inst_2 : Group.{u} G] {V : Type.{v}} [_inst_3 : AddCommGroup.{v} V] [_inst_4 : Module.{u, v} k V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_5 : Module.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, v} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u, v} k V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} k V (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} k V (Semiring.toMonoidWithZero.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} k V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_4))))] {W : Type.{w}} [_inst_7 : AddCommGroup.{w} W] [_inst_8 : Module.{u, w} k W (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_9 : Module.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, w} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_9)))) (SMulZeroClass.toSMul.{u, w} k W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} k W (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} k W (Semiring.toMonoidWithZero.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} k W (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_8))))] (π : LinearMap.{u, u, w, v} k k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) (i : LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9), (forall (v : V), Eq.{succ v} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : W) => V) (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9) V (fun (a 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_inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) (FunLike.coe.{max (succ v) (succ w), succ w, succ v} (LinearMap.{u, u, w, v} k k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) W (fun (_x : W) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : W) => V) _x) (LinearMap.instFunLikeLinearMap.{u, u, w, v} k k W V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4 (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))))) π (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => W) _x) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} 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(DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9) V (fun (a : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => W) a) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) (FunLike.coe.{max (succ v) (succ w), succ w, succ v} (LinearMap.{u, u, w, v} k k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) W (fun (_x : W) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : W) => V) _x) (LinearMap.instFunLikeLinearMap.{u, u, w, v} k k W V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4 (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))))) (LinearMap.conjugate.{u, v, w} k _inst_1 G _inst_2 V _inst_3 _inst_4 _inst_5 _inst_6 W _inst_7 _inst_8 _inst_9 _inst_10 π g) (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => W) _x) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v)
 Case conversion may be inaccurate. Consider using '#align linear_map.conjugate_i LinearMap.conjugate_iₓ'. -/
 theorem conjugate_i (g : G) (v : V) : (conjugate π g) (i v) = v :=
   by
@@ -124,7 +124,7 @@ variable (G) [Fintype G]
 lean 3 declaration is
   forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] (G : Type.{u}) [_inst_2 : Group.{u} G] {V : Type.{u}} [_inst_3 : AddCommGroup.{u} V] [_inst_4 : Module.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_5 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_5)))) (SMulZeroClass.toHasSmul.{u, u} k V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} k V (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} k V (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_4))))] {W : Type.{u}} [_inst_7 : AddCommGroup.{u} W] [_inst_8 : Module.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_9 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_9)))) (SMulZeroClass.toHasSmul.{u, u} k W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} k W (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} k W (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_8))))], (LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) -> (forall [_inst_11 : Fintype.{u} G], LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4)
 but is expected to have type
-  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] (G : Type.{u}) [_inst_2 : Group.{u} G] {V : Type.{v}} [_inst_3 : AddCommGroup.{v} V] [_inst_4 : Module.{u, v} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_5 : Module.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, v} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u, v} k V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} k V (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} k V (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_4))))] {W : Type.{w}} [_inst_7 : AddCommGroup.{w} W] [_inst_8 : Module.{u, w} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_9 : Module.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, w} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_9)))) (SMulZeroClass.toSMul.{u, w} k W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} k W (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} k W (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_8))))], (LinearMap.{u, u, w, v} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (NonAssocRing.toNonAssocSemiring.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) -> (forall [_inst_11 : Fintype.{u} G], LinearMap.{u, u, w, v} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (NonAssocRing.toNonAssocSemiring.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4)
+  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] (G : Type.{u}) [_inst_2 : Group.{u} G] {V : Type.{v}} [_inst_3 : AddCommGroup.{v} V] [_inst_4 : Module.{u, v} k V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_5 : Module.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, v} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u, v} k V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} k V (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} k V (Semiring.toMonoidWithZero.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} k V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_4))))] {W : Type.{w}} [_inst_7 : AddCommGroup.{w} W] [_inst_8 : Module.{u, w} k W (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_9 : Module.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, w} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_9)))) (SMulZeroClass.toSMul.{u, w} k W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} k W (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} k W (Semiring.toMonoidWithZero.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} k W (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_8))))], (LinearMap.{u, u, w, v} k k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) -> (forall [_inst_11 : Fintype.{u} G], LinearMap.{u, u, w, v} k k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4)
 Case conversion may be inaccurate. Consider using '#align linear_map.sum_of_conjugates LinearMap.sumOfConjugatesₓ'. -/
 /-- The sum of the conjugates of `π` by each element `g : G`, as a `k`-linear map.
 
@@ -138,7 +138,7 @@ def sumOfConjugates : W →ₗ[k] V :=
 lean 3 declaration is
   forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] (G : Type.{u}) [_inst_2 : Group.{u} G] {V : Type.{u}} [_inst_3 : AddCommGroup.{u} V] [_inst_4 : Module.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_5 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_5)))) (SMulZeroClass.toHasSmul.{u, u} k V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} k V (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} k V (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_4))))] {W : Type.{u}} [_inst_7 : AddCommGroup.{u} W] [_inst_8 : Module.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_9 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_9)))) (SMulZeroClass.toHasSmul.{u, u} k W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} k W (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} k W (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_8))))], (LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) -> (forall [_inst_11 : Fintype.{u} G], LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_9 _inst_5)
 but is expected to have type
-  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] (G : Type.{u}) [_inst_2 : Group.{u} G] {V : Type.{v}} [_inst_3 : AddCommGroup.{v} V] [_inst_4 : Module.{u, v} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_5 : Module.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, v} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u, v} k V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} k V (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} k V (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_4))))] {W : Type.{w}} [_inst_7 : AddCommGroup.{w} W] [_inst_8 : Module.{u, w} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_9 : Module.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, w} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_9)))) (SMulZeroClass.toSMul.{u, w} k W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} k W (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} k W (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_8))))], (LinearMap.{u, u, w, v} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (NonAssocRing.toNonAssocSemiring.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) -> (forall [_inst_11 : Fintype.{u} G], LinearMap.{u, u, w, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_9 _inst_5)
+  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] (G : Type.{u}) [_inst_2 : Group.{u} G] {V : Type.{v}} [_inst_3 : AddCommGroup.{v} V] [_inst_4 : Module.{u, v} k V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_5 : Module.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, v} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u, v} k V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} k V (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} k V (Semiring.toMonoidWithZero.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} k V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_4))))] {W : Type.{w}} [_inst_7 : AddCommGroup.{w} W] [_inst_8 : Module.{u, w} k W (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_9 : Module.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, w} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_9)))) (SMulZeroClass.toSMul.{u, w} k W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} k W (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} k W (Semiring.toMonoidWithZero.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} k W (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_8))))], (LinearMap.{u, u, w, v} k k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) -> (forall [_inst_11 : Fintype.{u} G], LinearMap.{u, u, w, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_9 _inst_5)
 Case conversion may be inaccurate. Consider using '#align linear_map.sum_of_conjugates_equivariant LinearMap.sumOfConjugatesEquivariantₓ'. -/
 /-- In fact, the sum over `g : G` of the conjugate of `π` by `g` is a `k[G]`-linear map.
 -/
@@ -168,7 +168,7 @@ include inv
 lean 3 declaration is
   forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] (G : Type.{u}) [_inst_2 : Group.{u} G] {V : Type.{u}} [_inst_3 : AddCommGroup.{u} V] [_inst_4 : Module.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_5 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_5)))) (SMulZeroClass.toHasSmul.{u, u} k V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} k V (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} k V (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_4))))] {W : Type.{u}} [_inst_7 : AddCommGroup.{u} W] [_inst_8 : Module.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_9 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_9)))) (SMulZeroClass.toHasSmul.{u, u} k W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} k W (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} k W (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_8))))], (LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) -> (forall [_inst_11 : Fintype.{u} G] [inv : Invertible.{u} k (Distrib.toHasMul.{u} k (Ring.toDistrib.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoidWithOne.toOne.{u} k (AddGroupWithOne.toAddMonoidWithOne.{u} k (AddCommGroupWithOne.toAddGroupWithOne.{u} k (Ring.toAddCommGroupWithOne.{u} k (CommRing.toRing.{u} k _inst_1))))) ((fun (a : Type) (b : Type.{u}) [self : HasLiftT.{1, succ u} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u} Nat k (CoeTCₓ.coe.{1, succ u} Nat k (Nat.castCoe.{u} k (AddMonoidWithOne.toNatCast.{u} k (AddGroupWithOne.toAddMonoidWithOne.{u} k (AddCommGroupWithOne.toAddGroupWithOne.{u} k (Ring.toAddCommGroupWithOne.{u} k (CommRing.toRing.{u} k _inst_1)))))))) (Fintype.card.{u} G _inst_11))], LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_9 _inst_5)
 but is expected to have type
-  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] (G : Type.{u}) [_inst_2 : Group.{u} G] {V : Type.{v}} [_inst_3 : AddCommGroup.{v} V] [_inst_4 : Module.{u, v} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_5 : Module.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, v} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u, v} k V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} k V (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} k V (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_4))))] {W : Type.{w}} [_inst_7 : AddCommGroup.{w} W] [_inst_8 : Module.{u, w} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_9 : Module.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, w} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_9)))) (SMulZeroClass.toSMul.{u, w} k W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} k W (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} k W (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_8))))], (LinearMap.{u, u, w, v} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (NonAssocRing.toNonAssocSemiring.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) -> (forall [_inst_11 : Fintype.{u} G] [inv : Invertible.{u} k (NonUnitalNonAssocRing.toMul.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))) (NonAssocRing.toOne.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))) (Nat.cast.{u} k (NonAssocRing.toNatCast.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))) (Fintype.card.{u} G _inst_11))], LinearMap.{u, u, w, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_9 _inst_5)
+  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] (G : Type.{u}) [_inst_2 : Group.{u} G] {V : Type.{v}} [_inst_3 : AddCommGroup.{v} V] [_inst_4 : Module.{u, v} k V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_5 : Module.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, v} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u, v} k V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} k V (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} k V (Semiring.toMonoidWithZero.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} k V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_4))))] {W : Type.{w}} [_inst_7 : AddCommGroup.{w} W] [_inst_8 : Module.{u, w} k W (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_9 : Module.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, w} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_9)))) (SMulZeroClass.toSMul.{u, w} k W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} k W (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} k W (Semiring.toMonoidWithZero.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} k W (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_8))))], (LinearMap.{u, u, w, v} k k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) -> (forall [_inst_11 : Fintype.{u} G] [inv : Invertible.{u} k (NonUnitalNonAssocRing.toMul.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))) (Semiring.toOne.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Nat.cast.{u} k (Semiring.toNatCast.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Fintype.card.{u} G _inst_11))], LinearMap.{u, u, w, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_9 _inst_5)
 Case conversion may be inaccurate. Consider using '#align linear_map.equivariant_projection LinearMap.equivariantProjectionₓ'. -/
 /-- We construct our `k[G]`-linear retraction of `i` as
 $$ \frac{1}{|G|} \sum_{g \in G} g⁻¹ • π(g • -). $$
@@ -183,7 +183,7 @@ include h
 lean 3 declaration is
   forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] (G : Type.{u}) [_inst_2 : Group.{u} G] {V : Type.{u}} [_inst_3 : AddCommGroup.{u} V] [_inst_4 : Module.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_5 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_5)))) (SMulZeroClass.toHasSmul.{u, u} k V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} k V (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} k V (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_4))))] {W : Type.{u}} [_inst_7 : AddCommGroup.{u} W] [_inst_8 : Module.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_9 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_9)))) (SMulZeroClass.toHasSmul.{u, u} k W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} k W (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} k W (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_8))))] (π : LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) (i : LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9), (forall (v : V), Eq.{succ u} V (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k 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(Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9) => V -> W) (LinearMap.hasCoeToFun.{u, u, u, u} 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: Fintype.{u} G] [inv : Invertible.{u} k (Distrib.toHasMul.{u} k (Ring.toDistrib.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoidWithOne.toOne.{u} k (AddGroupWithOne.toAddMonoidWithOne.{u} k (AddCommGroupWithOne.toAddGroupWithOne.{u} k (Ring.toAddCommGroupWithOne.{u} k (CommRing.toRing.{u} k _inst_1))))) ((fun (a : Type) (b : Type.{u}) [self : HasLiftT.{1, succ u} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u} Nat k (CoeTCₓ.coe.{1, succ u} Nat k (Nat.castCoe.{u} k (AddMonoidWithOne.toNatCast.{u} k (AddGroupWithOne.toAddMonoidWithOne.{u} k (AddCommGroupWithOne.toAddGroupWithOne.{u} k (Ring.toAddCommGroupWithOne.{u} k (CommRing.toRing.{u} k _inst_1)))))))) (Fintype.card.{u} G _inst_11))] (v : V), Eq.{succ u} V (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_9 _inst_5) (fun (_x : LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_9 _inst_5) => W -> V) (LinearMap.hasCoeToFun.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_9 _inst_5 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) (LinearMap.equivariantProjection.{u} k _inst_1 G _inst_2 V _inst_3 _inst_4 _inst_5 _inst_6 W _inst_7 _inst_8 _inst_9 _inst_10 π _inst_11 inv) (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9) (fun (_x : LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9) => V -> W) (LinearMap.hasCoeToFun.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v)
 but is expected to have type
-  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] (G : Type.{u}) [_inst_2 : Group.{u} G] {V : Type.{v}} [_inst_3 : AddCommGroup.{v} V] [_inst_4 : Module.{u, v} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_5 : Module.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, v} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u, v} k V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} k V (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} k V (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_4))))] {W : Type.{w}} [_inst_7 : AddCommGroup.{w} W] [_inst_8 : Module.{u, w} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_9 : Module.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, w} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_9)))) (SMulZeroClass.toSMul.{u, w} k W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} k W (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} k W (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_8))))] (π : LinearMap.{u, u, w, v} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (NonAssocRing.toNonAssocSemiring.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) (i : LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9), (forall (v : V), Eq.{succ v} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : W) => V) (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k 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(AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4 (RingHom.id.{u} k (NonAssocRing.toNonAssocSemiring.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))) π (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => W) _x) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v) -> (forall [_inst_11 : Fintype.{u} G] [inv : Invertible.{u} k (NonUnitalNonAssocRing.toMul.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))) (NonAssocRing.toOne.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))) (Nat.cast.{u} k (NonAssocRing.toNatCast.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))) (Fintype.card.{u} G _inst_11))] (v : V), Eq.{succ v} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : W) => V) (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9) V (fun (a : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => W) a) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) (FunLike.coe.{max (succ v) (succ w), succ w, succ v} (LinearMap.{u, u, w, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_9 _inst_5) W (fun (_x : W) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : W) => V) _x) (LinearMap.instFunLikeLinearMap.{u, u, w, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_9 _inst_5 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) (LinearMap.equivariantProjection.{u, v, w} k _inst_1 G _inst_2 V _inst_3 _inst_4 _inst_5 _inst_6 W _inst_7 _inst_8 _inst_9 _inst_10 π _inst_11 inv) (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => W) _x) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v)
+  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] (G : Type.{u}) [_inst_2 : Group.{u} G] {V : Type.{v}} [_inst_3 : AddCommGroup.{v} V] [_inst_4 : Module.{u, v} k V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_5 : Module.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, v} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u, v} k V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} k V (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} k V (Semiring.toMonoidWithZero.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} k V (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_4))))] {W : Type.{w}} [_inst_7 : AddCommGroup.{w} W] [_inst_8 : Module.{u, w} k W (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_9 : Module.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, w} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_9)))) (SMulZeroClass.toSMul.{u, w} k W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} k W (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} k W (Semiring.toMonoidWithZero.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} k W (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_8))))] (π : LinearMap.{u, u, w, v} k k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) (i : LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9), (forall (v : V), Eq.{succ v} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : W) => V) (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, 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: V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => W) a) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k 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(Semiring.toNonAssocSemiring.{u} k (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))))) π (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G 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(CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9) V (fun (a : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => W) a) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) (FunLike.coe.{max (succ v) (succ w), succ w, succ v} (LinearMap.{u, u, w, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_9 _inst_5) W (fun (_x : W) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : W) => V) _x) (LinearMap.instFunLikeLinearMap.{u, u, w, v} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) W V (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_9 _inst_5 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) (LinearMap.equivariantProjection.{u, v, w} k _inst_1 G _inst_2 V _inst_3 _inst_4 _inst_5 _inst_6 W _inst_7 _inst_8 _inst_9 _inst_10 π _inst_11 inv) (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => W) _x) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (CommSemiring.toSemiring.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v)
 Case conversion may be inaccurate. Consider using '#align linear_map.equivariant_projection_condition LinearMap.equivariantProjection_conditionₓ'. -/
 theorem equivariantProjection_condition (v : V) : (π.equivariantProjection G) (i v) = v :=
   by
@@ -229,7 +229,7 @@ variable [IsScalarTower k (MonoidAlgebra k G) W]
 lean 3 declaration is
   forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] {G : Type.{u1}} [_inst_2 : Fintype.{u1} G] [_inst_3 : Invertible.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u1} Nat k (CoeTCₓ.coe.{1, succ u1} Nat k (Nat.castCoe.{u1} k (AddMonoidWithOne.toNatCast.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))))) (Fintype.card.{u1} G _inst_2))] [_inst_4 : Group.{u1} G] {V : Type.{u1}} [_inst_5 : AddCommGroup.{u1} V] [_inst_6 : Module.{u1, u1} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_7 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_8 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (SMulZeroClass.toHasSmul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.addCommMonoid.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MonoidAlgebra.smulZeroClass.{u1, u1, u1} k G k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (SMulWithZero.toSmulZeroClass.{u1, u1} k k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MulZeroClass.toSMulWithZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))))))) (SMulZeroClass.toHasSmul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MulZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MulZeroOneClass.toMulZeroClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))) (SMulZeroClass.toHasSmul.{u1, u1} k V (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, u1} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, u1} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (Module.toMulActionWithZero.{u1, u1} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_6))))] {W : Type.{u1}} [_inst_9 : AddCommGroup.{u1} W] [_inst_10 : Module.{u1, u1} k W (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)] [_inst_11 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) W (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)] [_inst_12 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) W (SMulZeroClass.toHasSmul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.addCommMonoid.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MonoidAlgebra.smulZeroClass.{u1, u1, u1} k G k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (SMulWithZero.toSmulZeroClass.{u1, u1} k k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MulZeroClass.toSMulWithZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))))))) (SMulZeroClass.toHasSmul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) W (AddZeroClass.toHasZero.{u1} W (AddMonoid.toAddZeroClass.{u1} W (AddCommMonoid.toAddMonoid.{u1} W (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)))) (SMulWithZero.toSmulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) W (MulZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MulZeroOneClass.toMulZeroClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))))) (AddZeroClass.toHasZero.{u1} W (AddMonoid.toAddZeroClass.{u1} W (AddCommMonoid.toAddMonoid.{u1} W (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) W (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (AddZeroClass.toHasZero.{u1} W (AddMonoid.toAddZeroClass.{u1} W (AddCommMonoid.toAddMonoid.{u1} W (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) W (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_11)))) (SMulZeroClass.toHasSmul.{u1, u1} k W (AddZeroClass.toHasZero.{u1} W (AddMonoid.toAddZeroClass.{u1} W (AddCommMonoid.toAddMonoid.{u1} W (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)))) (SMulWithZero.toSmulZeroClass.{u1, u1} k W (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (AddZeroClass.toHasZero.{u1} W (AddMonoid.toAddZeroClass.{u1} W (AddCommMonoid.toAddMonoid.{u1} W (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)))) (MulActionWithZero.toSMulWithZero.{u1, u1} k W (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} W (AddMonoid.toAddZeroClass.{u1} W (AddCommMonoid.toAddMonoid.{u1} W (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)))) (Module.toMulActionWithZero.{u1, u1} k W (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_10))))] (f : LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) V W (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11), (Eq.{succ u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (LinearMap.ker.{u1, u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V W (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11 (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) V W (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11) (LinearMap.semilinearMapClass.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V W (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11 (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))))) f) (Bot.bot.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.hasBot.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))) -> (Exists.{succ u1} (LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k 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_inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) W V (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_11 _inst_7) (fun (g : LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) W V (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_11 _inst_7) => Eq.{succ u1} (LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) V V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7 _inst_7) (LinearMap.comp.{u1, u1, u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V W V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7 _inst_11 _inst_7 (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (RingHomCompTriple.right_ids.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))))) g f) (LinearMap.id.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))
 but is expected to have type
-  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] {G : Type.{u1}} [_inst_2 : Fintype.{u1} G] [_inst_3 : Invertible.{u1} k (NonUnitalNonAssocRing.toMul.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (NonAssocRing.toOne.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Nat.cast.{u1} k (NonAssocRing.toNatCast.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Fintype.card.{u1} G _inst_2))] [_inst_4 : Group.{u1} G] {V : Type.{u1}} [_inst_5 : AddCommGroup.{u1} V] [_inst_6 : Module.{u1, u1} k V (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_7 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_8 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (Algebra.toSMul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.algebra.{u1, u1, u1} k G k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Algebra.id.{u1} k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (SMulZeroClass.toSMul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidWithZero.toZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))) (SMulZeroClass.toSMul.{u1, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, u1} k V (CommMonoidWithZero.toZero.{u1} k (CommGroupWithZero.toCommMonoidWithZero.{u1} k (Semifield.toCommGroupWithZero.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, u1} k V (Semiring.toMonoidWithZero.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (Module.toMulActionWithZero.{u1, u1} k V (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_6))))] {W : Type.{u1}} [_inst_9 : AddCommGroup.{u1} W] [_inst_10 : Module.{u1, u1} k W (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)] [_inst_11 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)] [_inst_12 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (Algebra.toSMul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.algebra.{u1, u1, u1} k G k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Algebra.id.{u1} k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (SMulZeroClass.toSMul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (NegZeroClass.toZero.{u1} W (SubNegZeroMonoid.toNegZeroClass.{u1} W (SubtractionMonoid.toSubNegZeroMonoid.{u1} W (SubtractionCommMonoid.toSubtractionMonoid.{u1} W (AddCommGroup.toDivisionAddCommMonoid.{u1} W _inst_9))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (MonoidWithZero.toZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (NegZeroClass.toZero.{u1} W (SubNegZeroMonoid.toNegZeroClass.{u1} W (SubtractionMonoid.toSubNegZeroMonoid.{u1} W (SubtractionCommMonoid.toSubtractionMonoid.{u1} W (AddCommGroup.toDivisionAddCommMonoid.{u1} W _inst_9))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (NegZeroClass.toZero.{u1} W (SubNegZeroMonoid.toNegZeroClass.{u1} W (SubtractionMonoid.toSubNegZeroMonoid.{u1} W (SubtractionCommMonoid.toSubtractionMonoid.{u1} W (AddCommGroup.toDivisionAddCommMonoid.{u1} W _inst_9))))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_11)))) (SMulZeroClass.toSMul.{u1, u1} k W (NegZeroClass.toZero.{u1} W (SubNegZeroMonoid.toNegZeroClass.{u1} W (SubtractionMonoid.toSubNegZeroMonoid.{u1} W (SubtractionCommMonoid.toSubtractionMonoid.{u1} W (AddCommGroup.toDivisionAddCommMonoid.{u1} W _inst_9))))) (SMulWithZero.toSMulZeroClass.{u1, u1} k W (CommMonoidWithZero.toZero.{u1} k (CommGroupWithZero.toCommMonoidWithZero.{u1} k (Semifield.toCommGroupWithZero.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} W (SubNegZeroMonoid.toNegZeroClass.{u1} W (SubtractionMonoid.toSubNegZeroMonoid.{u1} W (SubtractionCommMonoid.toSubtractionMonoid.{u1} W (AddCommGroup.toDivisionAddCommMonoid.{u1} W _inst_9))))) (MulActionWithZero.toSMulWithZero.{u1, u1} k W (Semiring.toMonoidWithZero.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} W (SubNegZeroMonoid.toNegZeroClass.{u1} W (SubtractionMonoid.toSubNegZeroMonoid.{u1} W (SubtractionCommMonoid.toSubtractionMonoid.{u1} W (AddCommGroup.toDivisionAddCommMonoid.{u1} W _inst_9))))) (Module.toMulActionWithZero.{u1, u1} k W (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_10))))] (f : LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) V W (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11), (Eq.{succ u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (LinearMap.ker.{u1, u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V W (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11 (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (LinearMap.{u1, u1, u1, u1} 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(Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) V W (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V W (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11 (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))))) f) (Bot.bot.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.instBotSubmodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))) -> (Exists.{succ u1} (LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) W V (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_11 _inst_7) (fun (g : LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) W V (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_11 _inst_7) => Eq.{succ u1} (LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) 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(DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7 _inst_11 _inst_7 (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (RingHomCompTriple.ids.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))))) g f) (LinearMap.id.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))
+  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] {G : Type.{u1}} [_inst_2 : Fintype.{u1} G] [_inst_3 : Invertible.{u1} k (NonUnitalNonAssocRing.toMul.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toOne.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Nat.cast.{u1} k (Semiring.toNatCast.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Fintype.card.{u1} G _inst_2))] [_inst_4 : Group.{u1} G] {V : Type.{u1}} [_inst_5 : AddCommGroup.{u1} V] [_inst_6 : Module.{u1, u1} k V (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_7 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_8 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (Algebra.toSMul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.algebra.{u1, u1, u1} k G k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Algebra.id.{u1} k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (SMulZeroClass.toSMul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidWithZero.toZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))) (SMulZeroClass.toSMul.{u1, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, u1} k V (CommMonoidWithZero.toZero.{u1} k (CommGroupWithZero.toCommMonoidWithZero.{u1} k (Semifield.toCommGroupWithZero.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, u1} k V (Semiring.toMonoidWithZero.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (Module.toMulActionWithZero.{u1, u1} k V (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_6))))] {W : Type.{u1}} [_inst_9 : AddCommGroup.{u1} W] [_inst_10 : Module.{u1, u1} k W (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)] [_inst_11 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)] [_inst_12 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (Algebra.toSMul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.algebra.{u1, u1, u1} k G k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Algebra.id.{u1} k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (SMulZeroClass.toSMul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (NegZeroClass.toZero.{u1} W (SubNegZeroMonoid.toNegZeroClass.{u1} W (SubtractionMonoid.toSubNegZeroMonoid.{u1} W (SubtractionCommMonoid.toSubtractionMonoid.{u1} W (AddCommGroup.toDivisionAddCommMonoid.{u1} W _inst_9))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (MonoidWithZero.toZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (NegZeroClass.toZero.{u1} W (SubNegZeroMonoid.toNegZeroClass.{u1} W (SubtractionMonoid.toSubNegZeroMonoid.{u1} W (SubtractionCommMonoid.toSubtractionMonoid.{u1} W (AddCommGroup.toDivisionAddCommMonoid.{u1} W _inst_9))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (NegZeroClass.toZero.{u1} W (SubNegZeroMonoid.toNegZeroClass.{u1} W (SubtractionMonoid.toSubNegZeroMonoid.{u1} W (SubtractionCommMonoid.toSubtractionMonoid.{u1} W (AddCommGroup.toDivisionAddCommMonoid.{u1} W _inst_9))))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_11)))) (SMulZeroClass.toSMul.{u1, u1} k W (NegZeroClass.toZero.{u1} W (SubNegZeroMonoid.toNegZeroClass.{u1} W (SubtractionMonoid.toSubNegZeroMonoid.{u1} W (SubtractionCommMonoid.toSubtractionMonoid.{u1} W (AddCommGroup.toDivisionAddCommMonoid.{u1} W _inst_9))))) (SMulWithZero.toSMulZeroClass.{u1, u1} k W (CommMonoidWithZero.toZero.{u1} k (CommGroupWithZero.toCommMonoidWithZero.{u1} k (Semifield.toCommGroupWithZero.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} W (SubNegZeroMonoid.toNegZeroClass.{u1} W (SubtractionMonoid.toSubNegZeroMonoid.{u1} W (SubtractionCommMonoid.toSubtractionMonoid.{u1} W (AddCommGroup.toDivisionAddCommMonoid.{u1} W _inst_9))))) (MulActionWithZero.toSMulWithZero.{u1, u1} k W (Semiring.toMonoidWithZero.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} W (SubNegZeroMonoid.toNegZeroClass.{u1} W (SubtractionMonoid.toSubNegZeroMonoid.{u1} W (SubtractionCommMonoid.toSubtractionMonoid.{u1} W (AddCommGroup.toDivisionAddCommMonoid.{u1} W _inst_9))))) (Module.toMulActionWithZero.{u1, u1} k W (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_10))))] (f : LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) V W (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11), (Eq.{succ u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (LinearMap.ker.{u1, u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V W (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11 (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) V W (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V W (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11 (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))))) f) (Bot.bot.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.instBotSubmodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))) -> (Exists.{succ u1} (LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) W V (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_11 _inst_7) (fun (g : LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) W V (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_11 _inst_7) => Eq.{succ u1} (LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) V V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7 _inst_7) (LinearMap.comp.{u1, u1, u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V W V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7 _inst_11 _inst_7 (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (RingHomCompTriple.ids.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))))) g f) (LinearMap.id.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))
 Case conversion may be inaccurate. Consider using '#align monoid_algebra.exists_left_inverse_of_injective MonoidAlgebra.exists_leftInverse_of_injectiveₓ'. -/
 theorem exists_leftInverse_of_injective (f : V →ₗ[MonoidAlgebra k G] W) (hf : f.ker = ⊥) :
     ∃ g : W →ₗ[MonoidAlgebra k G] V, g.comp f = LinearMap.id :=
@@ -253,7 +253,7 @@ namespace Submodule
 lean 3 declaration is
   forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] {G : Type.{u1}} [_inst_2 : Fintype.{u1} G] [_inst_3 : Invertible.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u1} Nat k (CoeTCₓ.coe.{1, succ u1} Nat k (Nat.castCoe.{u1} k (AddMonoidWithOne.toNatCast.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))))) (Fintype.card.{u1} G _inst_2))] [_inst_4 : Group.{u1} G] {V : Type.{u1}} [_inst_5 : AddCommGroup.{u1} V] [_inst_6 : Module.{u1, u1} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_7 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_8 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (SMulZeroClass.toHasSmul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.addCommMonoid.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MonoidAlgebra.smulZeroClass.{u1, u1, u1} k G k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (SMulWithZero.toSmulZeroClass.{u1, u1} k k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MulZeroClass.toSMulWithZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))))))) (SMulZeroClass.toHasSmul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MulZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MulZeroOneClass.toMulZeroClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))) (SMulZeroClass.toHasSmul.{u1, u1} k V (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, u1} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, u1} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (Module.toMulActionWithZero.{u1, u1} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_6))))] (p : Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7), Exists.{succ u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (fun (q : Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) => IsCompl.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.completeLattice.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))) (CompleteLattice.toBoundedOrder.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.completeLattice.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)) p q)
 but is expected to have type
-  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] {G : Type.{u1}} [_inst_2 : Fintype.{u1} G] [_inst_3 : Invertible.{u1} k (NonUnitalNonAssocRing.toMul.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (NonAssocRing.toOne.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Nat.cast.{u1} k (NonAssocRing.toNatCast.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Fintype.card.{u1} G _inst_2))] [_inst_4 : Group.{u1} G] {V : Type.{u1}} [_inst_5 : AddCommGroup.{u1} V] [_inst_6 : Module.{u1, u1} k V (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_7 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_8 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (Algebra.toSMul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.algebra.{u1, u1, u1} k G k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Algebra.id.{u1} k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (SMulZeroClass.toSMul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidWithZero.toZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))) (SMulZeroClass.toSMul.{u1, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, u1} k V (CommMonoidWithZero.toZero.{u1} k (CommGroupWithZero.toCommMonoidWithZero.{u1} k (Semifield.toCommGroupWithZero.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, u1} k V (Semiring.toMonoidWithZero.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (Module.toMulActionWithZero.{u1, u1} k V (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_6))))] (p : Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7), Exists.{succ u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (fun (q : Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) => IsCompl.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.completeLattice.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))) (CompleteLattice.toBoundedOrder.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.completeLattice.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)) p q)
+  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] {G : Type.{u1}} [_inst_2 : Fintype.{u1} G] [_inst_3 : Invertible.{u1} k (NonUnitalNonAssocRing.toMul.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toOne.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Nat.cast.{u1} k (Semiring.toNatCast.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Fintype.card.{u1} G _inst_2))] [_inst_4 : Group.{u1} G] {V : Type.{u1}} [_inst_5 : AddCommGroup.{u1} V] [_inst_6 : Module.{u1, u1} k V (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_7 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_8 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (Algebra.toSMul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.algebra.{u1, u1, u1} k G k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Algebra.id.{u1} k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (SMulZeroClass.toSMul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidWithZero.toZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))) (SMulZeroClass.toSMul.{u1, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, u1} k V (CommMonoidWithZero.toZero.{u1} k (CommGroupWithZero.toCommMonoidWithZero.{u1} k (Semifield.toCommGroupWithZero.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, u1} k V (Semiring.toMonoidWithZero.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (Module.toMulActionWithZero.{u1, u1} k V (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_6))))] (p : Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7), Exists.{succ u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (fun (q : Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) => IsCompl.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.completeLattice.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))) (CompleteLattice.toBoundedOrder.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.completeLattice.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)) p q)
 Case conversion may be inaccurate. Consider using '#align monoid_algebra.submodule.exists_is_compl MonoidAlgebra.Submodule.exists_isComplₓ'. -/
 theorem exists_isCompl (p : Submodule (MonoidAlgebra k G) V) :
     ∃ q : Submodule (MonoidAlgebra k G) V, IsCompl p q :=
@@ -265,7 +265,7 @@ theorem exists_isCompl (p : Submodule (MonoidAlgebra k G) V) :
 lean 3 declaration is
   forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] {G : Type.{u1}} [_inst_2 : Fintype.{u1} G] [_inst_3 : Invertible.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u1} Nat k (CoeTCₓ.coe.{1, succ u1} Nat k (Nat.castCoe.{u1} k (AddMonoidWithOne.toNatCast.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))))) (Fintype.card.{u1} G _inst_2))] [_inst_4 : Group.{u1} G] {V : Type.{u1}} [_inst_5 : AddCommGroup.{u1} V] [_inst_6 : Module.{u1, u1} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_7 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_8 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (SMulZeroClass.toHasSmul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.addCommMonoid.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MonoidAlgebra.smulZeroClass.{u1, u1, u1} k G k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (SMulWithZero.toSmulZeroClass.{u1, u1} k k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MulZeroClass.toSMulWithZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))))))) (SMulZeroClass.toHasSmul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MulZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MulZeroOneClass.toMulZeroClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))) (SMulZeroClass.toHasSmul.{u1, u1} k V (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, u1} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, u1} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (Module.toMulActionWithZero.{u1, u1} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_6))))], ComplementedLattice.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (ConditionallyCompleteLattice.toLattice.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.completeLattice.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))) (CompleteLattice.toBoundedOrder.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.completeLattice.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))
 but is expected to have type
-  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] {G : Type.{u1}} [_inst_2 : Fintype.{u1} G] [_inst_3 : Invertible.{u1} k (NonUnitalNonAssocRing.toMul.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (NonAssocRing.toOne.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Nat.cast.{u1} k (NonAssocRing.toNatCast.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Fintype.card.{u1} G _inst_2))] [_inst_4 : Group.{u1} G] {V : Type.{u1}} [_inst_5 : AddCommGroup.{u1} V] [_inst_6 : Module.{u1, u1} k V (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_7 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_8 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (Algebra.toSMul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.algebra.{u1, u1, u1} k G k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Algebra.id.{u1} k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (SMulZeroClass.toSMul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidWithZero.toZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))) (SMulZeroClass.toSMul.{u1, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, u1} k V (CommMonoidWithZero.toZero.{u1} k (CommGroupWithZero.toCommMonoidWithZero.{u1} k (Semifield.toCommGroupWithZero.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, u1} k V (Semiring.toMonoidWithZero.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (Module.toMulActionWithZero.{u1, u1} k V (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_6))))], ComplementedLattice.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (ConditionallyCompleteLattice.toLattice.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.completeLattice.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))) (CompleteLattice.toBoundedOrder.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.completeLattice.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))
+  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] {G : Type.{u1}} [_inst_2 : Fintype.{u1} G] [_inst_3 : Invertible.{u1} k (NonUnitalNonAssocRing.toMul.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (Semiring.toOne.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Nat.cast.{u1} k (Semiring.toNatCast.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Fintype.card.{u1} G _inst_2))] [_inst_4 : Group.{u1} G] {V : Type.{u1}} [_inst_5 : AddCommGroup.{u1} V] [_inst_6 : Module.{u1, u1} k V (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_7 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_8 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (Algebra.toSMul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.algebra.{u1, u1, u1} k G k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Algebra.id.{u1} k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (SMulZeroClass.toSMul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidWithZero.toZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))) (SMulZeroClass.toSMul.{u1, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, u1} k V (CommMonoidWithZero.toZero.{u1} k (CommGroupWithZero.toCommMonoidWithZero.{u1} k (Semifield.toCommGroupWithZero.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, u1} k V (Semiring.toMonoidWithZero.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (Module.toMulActionWithZero.{u1, u1} k V (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_6))))], ComplementedLattice.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (ConditionallyCompleteLattice.toLattice.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.completeLattice.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))) (CompleteLattice.toBoundedOrder.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.completeLattice.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))
 Case conversion may be inaccurate. Consider using '#align monoid_algebra.submodule.complemented_lattice MonoidAlgebra.Submodule.complementedLatticeₓ'. -/
 /-- This also implies an instance `is_semisimple_module (monoid_algebra k G) V`. -/
 instance complementedLattice : ComplementedLattice (Submodule (MonoidAlgebra k G) V) :=

31ca6f9c

bump to nightly-2023-04-04-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/3cacc945118c8c637d89950af01da78307f59325

2ee17135

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 
 ! This file was ported from Lean 3 source module representation_theory.maschke
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! leanprover-community/mathlib commit 31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.LinearAlgebra.Basis
 /-!
 # Maschke's theorem
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We prove **Maschke's theorem** for finite groups,
 in the formulation that every submodule of a `k[G]` module has a complement,
 when `k` is a field with `invertible (fintype.card G : k)`.

70fd9563

bump to nightly-2023-03-27-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce86f4e05e9a9b8da5e316b22c76ce76440c56a1

0e4ebd8c

Diff

@@ -163,7 +163,7 @@ include inv
 
 /- warning: linear_map.equivariant_projection -> LinearMap.equivariantProjection is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] (G : Type.{u}) [_inst_2 : Group.{u} G] {V : Type.{u}} [_inst_3 : AddCommGroup.{u} V] [_inst_4 : Module.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_5 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_5)))) (SMulZeroClass.toHasSmul.{u, u} k V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} k V (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} k V (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_4))))] {W : Type.{u}} [_inst_7 : AddCommGroup.{u} W] [_inst_8 : Module.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_9 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_9)))) (SMulZeroClass.toHasSmul.{u, u} k W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} k W (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} k W (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_8))))], (LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) -> (forall [_inst_11 : Fintype.{u} G] [inv : Invertible.{u} k (Distrib.toHasMul.{u} k (Ring.toDistrib.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoidWithOne.toOne.{u} k (AddGroupWithOne.toAddMonoidWithOne.{u} k (NonAssocRing.toAddGroupWithOne.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))) ((fun (a : Type) (b : Type.{u}) [self : HasLiftT.{1, succ u} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u} Nat k (CoeTCₓ.coe.{1, succ u} Nat k (Nat.castCoe.{u} k (AddMonoidWithOne.toNatCast.{u} k (AddGroupWithOne.toAddMonoidWithOne.{u} k (NonAssocRing.toAddGroupWithOne.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))))) (Fintype.card.{u} G _inst_11))], LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_9 _inst_5)
+  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] (G : Type.{u}) [_inst_2 : Group.{u} G] {V : Type.{u}} [_inst_3 : AddCommGroup.{u} V] [_inst_4 : Module.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_5 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_5)))) (SMulZeroClass.toHasSmul.{u, u} k V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} k V (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} k V (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_4))))] {W : Type.{u}} [_inst_7 : AddCommGroup.{u} W] [_inst_8 : Module.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_9 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_9)))) (SMulZeroClass.toHasSmul.{u, u} k W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} k W (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} k W (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_8))))], (LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) -> (forall [_inst_11 : Fintype.{u} G] [inv : Invertible.{u} k (Distrib.toHasMul.{u} k (Ring.toDistrib.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoidWithOne.toOne.{u} k (AddGroupWithOne.toAddMonoidWithOne.{u} k (AddCommGroupWithOne.toAddGroupWithOne.{u} k (Ring.toAddCommGroupWithOne.{u} k (CommRing.toRing.{u} k _inst_1))))) ((fun (a : Type) (b : Type.{u}) [self : HasLiftT.{1, succ u} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u} Nat k (CoeTCₓ.coe.{1, succ u} Nat k (Nat.castCoe.{u} k (AddMonoidWithOne.toNatCast.{u} k (AddGroupWithOne.toAddMonoidWithOne.{u} k (AddCommGroupWithOne.toAddGroupWithOne.{u} k (Ring.toAddCommGroupWithOne.{u} k (CommRing.toRing.{u} k _inst_1)))))))) (Fintype.card.{u} G _inst_11))], LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_9 _inst_5)
 but is expected to have type
   forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] (G : Type.{u}) [_inst_2 : Group.{u} G] {V : Type.{v}} [_inst_3 : AddCommGroup.{v} V] [_inst_4 : Module.{u, v} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_5 : Module.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, v} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u, v} k V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} k V (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} k V (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_4))))] {W : Type.{w}} [_inst_7 : AddCommGroup.{w} W] [_inst_8 : Module.{u, w} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_9 : Module.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, w} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_9)))) (SMulZeroClass.toSMul.{u, w} k W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} k W (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} k W (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_8))))], (LinearMap.{u, u, w, v} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (NonAssocRing.toNonAssocSemiring.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) -> (forall [_inst_11 : Fintype.{u} G] [inv : Invertible.{u} k (NonUnitalNonAssocRing.toMul.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))) (NonAssocRing.toOne.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))) (Nat.cast.{u} k (NonAssocRing.toNatCast.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))) (Fintype.card.{u} G _inst_11))], LinearMap.{u, u, w, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_9 _inst_5)
 Case conversion may be inaccurate. Consider using '#align linear_map.equivariant_projection LinearMap.equivariantProjectionₓ'. -/
@@ -178,7 +178,7 @@ include h
 
 /- warning: linear_map.equivariant_projection_condition -> LinearMap.equivariantProjection_condition is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] (G : Type.{u}) [_inst_2 : Group.{u} G] {V : Type.{u}} [_inst_3 : AddCommGroup.{u} V] [_inst_4 : Module.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_5 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_5)))) (SMulZeroClass.toHasSmul.{u, u} k V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} k V (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} k V (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_4))))] {W : Type.{u}} [_inst_7 : AddCommGroup.{u} W] [_inst_8 : Module.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_9 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_9)))) (SMulZeroClass.toHasSmul.{u, u} k W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} k W (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} k W (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_8))))] (π : LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) (i : LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9), (forall (v : V), Eq.{succ u} V (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) (fun (_x : LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) => W -> V) (LinearMap.hasCoeToFun.{u, u, u, u} k k W V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4 (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))))) π (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} 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(Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9) => V -> W) (LinearMap.hasCoeToFun.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v) -> (forall [_inst_11 : Fintype.{u} G] [inv : Invertible.{u} k (Distrib.toHasMul.{u} k (Ring.toDistrib.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoidWithOne.toOne.{u} k (AddGroupWithOne.toAddMonoidWithOne.{u} k (NonAssocRing.toAddGroupWithOne.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))) ((fun (a : Type) (b : Type.{u}) [self : HasLiftT.{1, succ u} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u} Nat k (CoeTCₓ.coe.{1, succ u} Nat k (Nat.castCoe.{u} k (AddMonoidWithOne.toNatCast.{u} k (AddGroupWithOne.toAddMonoidWithOne.{u} k (NonAssocRing.toAddGroupWithOne.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))))) (Fintype.card.{u} G _inst_11))] (v : V), Eq.{succ u} V (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_9 _inst_5) (fun (_x : LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_9 _inst_5) => W -> V) (LinearMap.hasCoeToFun.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_9 _inst_5 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) (LinearMap.equivariantProjection.{u} k _inst_1 G _inst_2 V _inst_3 _inst_4 _inst_5 _inst_6 W _inst_7 _inst_8 _inst_9 _inst_10 π _inst_11 inv) (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9) (fun (_x : LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9) => V -> W) (LinearMap.hasCoeToFun.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v)
+  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] (G : Type.{u}) [_inst_2 : Group.{u} G] {V : Type.{u}} [_inst_3 : AddCommGroup.{u} V] [_inst_4 : Module.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_5 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_5)))) (SMulZeroClass.toHasSmul.{u, u} k V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} k V (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} k V (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_4))))] {W : Type.{u}} [_inst_7 : AddCommGroup.{u} W] [_inst_8 : Module.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_9 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_9)))) (SMulZeroClass.toHasSmul.{u, u} k W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} k W (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} k W (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_8))))] (π : LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) (i : LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9), (forall (v : V), Eq.{succ u} V (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) (fun (_x : LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) => W -> V) (LinearMap.hasCoeToFun.{u, u, u, u} k k W V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4 (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))))) π (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9) (fun (_x : LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9) => V -> W) (LinearMap.hasCoeToFun.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v) -> (forall [_inst_11 : Fintype.{u} G] [inv : Invertible.{u} k (Distrib.toHasMul.{u} k (Ring.toDistrib.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoidWithOne.toOne.{u} k (AddGroupWithOne.toAddMonoidWithOne.{u} k (AddCommGroupWithOne.toAddGroupWithOne.{u} k (Ring.toAddCommGroupWithOne.{u} k (CommRing.toRing.{u} k _inst_1))))) ((fun (a : Type) (b : Type.{u}) [self : HasLiftT.{1, succ u} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u} Nat k (CoeTCₓ.coe.{1, succ u} Nat k (Nat.castCoe.{u} k (AddMonoidWithOne.toNatCast.{u} k (AddGroupWithOne.toAddMonoidWithOne.{u} k (AddCommGroupWithOne.toAddGroupWithOne.{u} k (Ring.toAddCommGroupWithOne.{u} k (CommRing.toRing.{u} k _inst_1)))))))) (Fintype.card.{u} G _inst_11))] (v : V), Eq.{succ u} V (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_9 _inst_5) (fun (_x : LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G 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(MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_9 _inst_5 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) (LinearMap.equivariantProjection.{u} k _inst_1 G _inst_2 V _inst_3 _inst_4 _inst_5 _inst_6 W _inst_7 _inst_8 _inst_9 _inst_10 π _inst_11 inv) (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9) (fun (_x : LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9) => V -> W) (LinearMap.hasCoeToFun.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v)
 but is expected to have type
   forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] (G : Type.{u}) [_inst_2 : Group.{u} G] {V : Type.{v}} [_inst_3 : AddCommGroup.{v} V] [_inst_4 : Module.{u, v} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_5 : Module.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, v} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u, v} k V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} k V (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} k V (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_4))))] {W : Type.{w}} [_inst_7 : AddCommGroup.{w} W] [_inst_8 : Module.{u, w} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_9 : Module.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, w} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_9)))) (SMulZeroClass.toSMul.{u, w} k W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} k W (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} k W (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_8))))] (π : LinearMap.{u, u, w, v} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (NonAssocRing.toNonAssocSemiring.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) (i : LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9), (forall (v : V), Eq.{succ v} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : W) => V) (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9) V (fun (a : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => W) a) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) (FunLike.coe.{max (succ v) (succ w), succ w, succ v} (LinearMap.{u, u, w, v} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (NonAssocRing.toNonAssocSemiring.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) W (fun (_x : W) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : W) => V) _x) (LinearMap.instFunLikeLinearMap.{u, u, w, v} k k W V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4 (RingHom.id.{u} k (NonAssocRing.toNonAssocSemiring.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))) π (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => W) _x) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) 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(Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9) V (fun (a : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => W) a) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V W 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k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_9 _inst_5) W (fun (_x : W) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : W) => V) _x) (LinearMap.instFunLikeLinearMap.{u, u, w, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_9 _inst_5 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) (LinearMap.equivariantProjection.{u, v, w} k _inst_1 G _inst_2 V _inst_3 _inst_4 _inst_5 _inst_6 W _inst_7 _inst_8 _inst_9 _inst_10 π _inst_11 inv) (FunLike.coe.{max (succ v) (succ w), succ v, succ w} (LinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => W) _x) (LinearMap.instFunLikeLinearMap.{u, u, v, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v)
 Case conversion may be inaccurate. Consider using '#align linear_map.equivariant_projection_condition LinearMap.equivariantProjection_conditionₓ'. -/
@@ -224,7 +224,7 @@ variable [IsScalarTower k (MonoidAlgebra k G) W]
 
 /- warning: monoid_algebra.exists_left_inverse_of_injective -> MonoidAlgebra.exists_leftInverse_of_injective is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] {G : Type.{u1}} [_inst_2 : Fintype.{u1} G] [_inst_3 : Invertible.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (NonAssocRing.toAddGroupWithOne.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u1} Nat k (CoeTCₓ.coe.{1, succ u1} Nat k (Nat.castCoe.{u1} k (AddMonoidWithOne.toNatCast.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (NonAssocRing.toAddGroupWithOne.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))))) (Fintype.card.{u1} G _inst_2))] [_inst_4 : Group.{u1} G] {V : Type.{u1}} [_inst_5 : AddCommGroup.{u1} V] [_inst_6 : Module.{u1, u1} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_7 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_8 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (SMulZeroClass.toHasSmul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.addCommMonoid.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MonoidAlgebra.smulZeroClass.{u1, u1, u1} k G k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (SMulWithZero.toSmulZeroClass.{u1, u1} k k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MulZeroClass.toSMulWithZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))))))) (SMulZeroClass.toHasSmul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MulZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MulZeroOneClass.toMulZeroClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))) (SMulZeroClass.toHasSmul.{u1, u1} k V (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, u1} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, u1} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (Module.toMulActionWithZero.{u1, u1} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_6))))] {W : Type.{u1}} [_inst_9 : AddCommGroup.{u1} W] [_inst_10 : Module.{u1, u1} k W (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)] [_inst_11 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) W (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)] [_inst_12 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) W (SMulZeroClass.toHasSmul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.addCommMonoid.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MonoidAlgebra.smulZeroClass.{u1, u1, u1} k G k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (SMulWithZero.toSmulZeroClass.{u1, u1} k k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MulZeroClass.toSMulWithZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))))))) (SMulZeroClass.toHasSmul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) W (AddZeroClass.toHasZero.{u1} W (AddMonoid.toAddZeroClass.{u1} W (AddCommMonoid.toAddMonoid.{u1} W (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)))) (SMulWithZero.toSmulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) W (MulZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MulZeroOneClass.toMulZeroClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))))) (AddZeroClass.toHasZero.{u1} W (AddMonoid.toAddZeroClass.{u1} W (AddCommMonoid.toAddMonoid.{u1} W (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) W (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (AddZeroClass.toHasZero.{u1} W (AddMonoid.toAddZeroClass.{u1} W (AddCommMonoid.toAddMonoid.{u1} W (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) W (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_11)))) (SMulZeroClass.toHasSmul.{u1, u1} k W (AddZeroClass.toHasZero.{u1} W (AddMonoid.toAddZeroClass.{u1} W (AddCommMonoid.toAddMonoid.{u1} W (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)))) (SMulWithZero.toSmulZeroClass.{u1, u1} k W (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (AddZeroClass.toHasZero.{u1} W (AddMonoid.toAddZeroClass.{u1} W (AddCommMonoid.toAddMonoid.{u1} W (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)))) (MulActionWithZero.toSMulWithZero.{u1, u1} k W (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} W (AddMonoid.toAddZeroClass.{u1} W (AddCommMonoid.toAddMonoid.{u1} W (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)))) (Module.toMulActionWithZero.{u1, u1} k W (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_10))))] (f : LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) V W (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11), (Eq.{succ u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (LinearMap.ker.{u1, u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V W (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11 (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) V W (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11) (LinearMap.semilinearMapClass.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V W (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11 (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))))) f) (Bot.bot.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.hasBot.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))) -> (Exists.{succ u1} (LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k 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_inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) W V (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_11 _inst_7) (fun (g : LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) W V (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_11 _inst_7) => Eq.{succ u1} (LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) V V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7 _inst_7) (LinearMap.comp.{u1, u1, u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V W V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7 _inst_11 _inst_7 (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (RingHomCompTriple.right_ids.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))))) g f) (LinearMap.id.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))
+  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] {G : Type.{u1}} [_inst_2 : Fintype.{u1} G] [_inst_3 : Invertible.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u1} Nat k (CoeTCₓ.coe.{1, succ u1} Nat k (Nat.castCoe.{u1} k (AddMonoidWithOne.toNatCast.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))))) (Fintype.card.{u1} G _inst_2))] [_inst_4 : Group.{u1} G] {V : Type.{u1}} [_inst_5 : AddCommGroup.{u1} V] [_inst_6 : Module.{u1, u1} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_7 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_8 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (SMulZeroClass.toHasSmul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.addCommMonoid.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MonoidAlgebra.smulZeroClass.{u1, u1, u1} k G k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (SMulWithZero.toSmulZeroClass.{u1, u1} k k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MulZeroClass.toSMulWithZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))))))) (SMulZeroClass.toHasSmul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MulZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MulZeroOneClass.toMulZeroClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))) (SMulZeroClass.toHasSmul.{u1, u1} k V (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, u1} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, u1} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (Module.toMulActionWithZero.{u1, u1} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_6))))] {W : Type.{u1}} [_inst_9 : AddCommGroup.{u1} W] [_inst_10 : Module.{u1, u1} k W (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)] [_inst_11 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) W (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)] [_inst_12 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) W (SMulZeroClass.toHasSmul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.addCommMonoid.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MonoidAlgebra.smulZeroClass.{u1, u1, u1} k G k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (SMulWithZero.toSmulZeroClass.{u1, u1} k k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MulZeroClass.toSMulWithZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))))))) (SMulZeroClass.toHasSmul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) W (AddZeroClass.toHasZero.{u1} W (AddMonoid.toAddZeroClass.{u1} W (AddCommMonoid.toAddMonoid.{u1} W (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)))) (SMulWithZero.toSmulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) W (MulZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MulZeroOneClass.toMulZeroClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))))) (AddZeroClass.toHasZero.{u1} W (AddMonoid.toAddZeroClass.{u1} W (AddCommMonoid.toAddMonoid.{u1} W (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) W (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (AddZeroClass.toHasZero.{u1} W (AddMonoid.toAddZeroClass.{u1} W (AddCommMonoid.toAddMonoid.{u1} W (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k 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(Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} W (AddMonoid.toAddZeroClass.{u1} W (AddCommMonoid.toAddMonoid.{u1} W (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)))) (Module.toMulActionWithZero.{u1, u1} k W (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_10))))] (f : LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) V W (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11), (Eq.{succ u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (LinearMap.ker.{u1, u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V W (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11 (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) V W (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11) (LinearMap.semilinearMapClass.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V W (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11 (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))))) f) (Bot.bot.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.hasBot.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))) -> (Exists.{succ u1} (LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k 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_inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) W V (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_11 _inst_7) (fun (g : LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) W V (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_11 _inst_7) => Eq.{succ u1} (LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) V V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7 _inst_7) (LinearMap.comp.{u1, u1, u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V W V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7 _inst_11 _inst_7 (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (RingHomCompTriple.right_ids.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))))) g f) (LinearMap.id.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))
 but is expected to have type
   forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] {G : Type.{u1}} [_inst_2 : Fintype.{u1} G] [_inst_3 : Invertible.{u1} k (NonUnitalNonAssocRing.toMul.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (NonAssocRing.toOne.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Nat.cast.{u1} k (NonAssocRing.toNatCast.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Fintype.card.{u1} G _inst_2))] [_inst_4 : Group.{u1} G] {V : Type.{u1}} [_inst_5 : AddCommGroup.{u1} V] [_inst_6 : Module.{u1, u1} k V (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_7 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_8 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (Algebra.toSMul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.algebra.{u1, u1, u1} k G k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Algebra.id.{u1} k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (SMulZeroClass.toSMul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidWithZero.toZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))) (SMulZeroClass.toSMul.{u1, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, u1} k V (CommMonoidWithZero.toZero.{u1} k (CommGroupWithZero.toCommMonoidWithZero.{u1} k (Semifield.toCommGroupWithZero.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, u1} k V (Semiring.toMonoidWithZero.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (Module.toMulActionWithZero.{u1, u1} k V (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_6))))] {W : Type.{u1}} [_inst_9 : AddCommGroup.{u1} W] [_inst_10 : Module.{u1, u1} k W (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)] [_inst_11 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)] [_inst_12 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (Algebra.toSMul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.algebra.{u1, u1, u1} k G k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Algebra.id.{u1} k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (SMulZeroClass.toSMul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (NegZeroClass.toZero.{u1} W (SubNegZeroMonoid.toNegZeroClass.{u1} W (SubtractionMonoid.toSubNegZeroMonoid.{u1} W (SubtractionCommMonoid.toSubtractionMonoid.{u1} W (AddCommGroup.toDivisionAddCommMonoid.{u1} W _inst_9))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (MonoidWithZero.toZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (NegZeroClass.toZero.{u1} W (SubNegZeroMonoid.toNegZeroClass.{u1} W (SubtractionMonoid.toSubNegZeroMonoid.{u1} W (SubtractionCommMonoid.toSubtractionMonoid.{u1} W (AddCommGroup.toDivisionAddCommMonoid.{u1} W _inst_9))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (NegZeroClass.toZero.{u1} W (SubNegZeroMonoid.toNegZeroClass.{u1} W (SubtractionMonoid.toSubNegZeroMonoid.{u1} W (SubtractionCommMonoid.toSubtractionMonoid.{u1} W (AddCommGroup.toDivisionAddCommMonoid.{u1} W _inst_9))))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_11)))) (SMulZeroClass.toSMul.{u1, u1} k W (NegZeroClass.toZero.{u1} W (SubNegZeroMonoid.toNegZeroClass.{u1} W (SubtractionMonoid.toSubNegZeroMonoid.{u1} W (SubtractionCommMonoid.toSubtractionMonoid.{u1} W (AddCommGroup.toDivisionAddCommMonoid.{u1} W _inst_9))))) (SMulWithZero.toSMulZeroClass.{u1, u1} k W (CommMonoidWithZero.toZero.{u1} k (CommGroupWithZero.toCommMonoidWithZero.{u1} k (Semifield.toCommGroupWithZero.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} W (SubNegZeroMonoid.toNegZeroClass.{u1} W (SubtractionMonoid.toSubNegZeroMonoid.{u1} W (SubtractionCommMonoid.toSubtractionMonoid.{u1} W (AddCommGroup.toDivisionAddCommMonoid.{u1} W _inst_9))))) (MulActionWithZero.toSMulWithZero.{u1, u1} k W (Semiring.toMonoidWithZero.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} W (SubNegZeroMonoid.toNegZeroClass.{u1} W (SubtractionMonoid.toSubNegZeroMonoid.{u1} W (SubtractionCommMonoid.toSubtractionMonoid.{u1} W (AddCommGroup.toDivisionAddCommMonoid.{u1} W _inst_9))))) (Module.toMulActionWithZero.{u1, u1} k W (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_10))))] (f : LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) V W (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11), (Eq.{succ u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (LinearMap.ker.{u1, u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V W 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(Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11 (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))))) f) (Bot.bot.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.instBotSubmodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))) -> (Exists.{succ u1} (LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) W V (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_11 _inst_7) (fun (g : LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k 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(AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_11 _inst_7) => Eq.{succ u1} (LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) 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(Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (RingHomCompTriple.ids.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))))) g f) (LinearMap.id.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))
 Case conversion may be inaccurate. Consider using '#align monoid_algebra.exists_left_inverse_of_injective MonoidAlgebra.exists_leftInverse_of_injectiveₓ'. -/
@@ -248,7 +248,7 @@ namespace Submodule
 
 /- warning: monoid_algebra.submodule.exists_is_compl -> MonoidAlgebra.Submodule.exists_isCompl is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] {G : Type.{u1}} [_inst_2 : Fintype.{u1} G] [_inst_3 : Invertible.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (NonAssocRing.toAddGroupWithOne.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u1} Nat k (CoeTCₓ.coe.{1, succ u1} Nat k (Nat.castCoe.{u1} k (AddMonoidWithOne.toNatCast.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (NonAssocRing.toAddGroupWithOne.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))))) (Fintype.card.{u1} G _inst_2))] [_inst_4 : Group.{u1} G] {V : Type.{u1}} [_inst_5 : AddCommGroup.{u1} V] [_inst_6 : Module.{u1, u1} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_7 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_8 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (SMulZeroClass.toHasSmul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.addCommMonoid.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MonoidAlgebra.smulZeroClass.{u1, u1, u1} k G k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (SMulWithZero.toSmulZeroClass.{u1, u1} k k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MulZeroClass.toSMulWithZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))))))) (SMulZeroClass.toHasSmul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MulZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MulZeroOneClass.toMulZeroClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))) (SMulZeroClass.toHasSmul.{u1, u1} k V (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, u1} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, u1} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (Module.toMulActionWithZero.{u1, u1} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_6))))] (p : Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7), Exists.{succ u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (fun (q : Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) => IsCompl.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.completeLattice.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))) (CompleteLattice.toBoundedOrder.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.completeLattice.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)) p q)
+  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] {G : Type.{u1}} [_inst_2 : Fintype.{u1} G] [_inst_3 : Invertible.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u1} Nat k (CoeTCₓ.coe.{1, succ u1} Nat k (Nat.castCoe.{u1} k (AddMonoidWithOne.toNatCast.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))))) (Fintype.card.{u1} G _inst_2))] [_inst_4 : Group.{u1} G] {V : Type.{u1}} [_inst_5 : AddCommGroup.{u1} V] [_inst_6 : Module.{u1, u1} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_7 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_8 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (SMulZeroClass.toHasSmul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.addCommMonoid.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MonoidAlgebra.smulZeroClass.{u1, u1, u1} k G k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (SMulWithZero.toSmulZeroClass.{u1, u1} k k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MulZeroClass.toSMulWithZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))))))) (SMulZeroClass.toHasSmul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MulZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MulZeroOneClass.toMulZeroClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))) (SMulZeroClass.toHasSmul.{u1, u1} k V (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, u1} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, u1} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (Module.toMulActionWithZero.{u1, u1} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_6))))] (p : Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7), Exists.{succ u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (fun (q : Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) => IsCompl.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.completeLattice.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))) (CompleteLattice.toBoundedOrder.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.completeLattice.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)) p q)
 but is expected to have type
   forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] {G : Type.{u1}} [_inst_2 : Fintype.{u1} G] [_inst_3 : Invertible.{u1} k (NonUnitalNonAssocRing.toMul.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (NonAssocRing.toOne.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Nat.cast.{u1} k (NonAssocRing.toNatCast.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Fintype.card.{u1} G _inst_2))] [_inst_4 : Group.{u1} G] {V : Type.{u1}} [_inst_5 : AddCommGroup.{u1} V] [_inst_6 : Module.{u1, u1} k V (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_7 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_8 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (Algebra.toSMul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.algebra.{u1, u1, u1} k G k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Algebra.id.{u1} k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (SMulZeroClass.toSMul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidWithZero.toZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))) (SMulZeroClass.toSMul.{u1, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, u1} k V (CommMonoidWithZero.toZero.{u1} k (CommGroupWithZero.toCommMonoidWithZero.{u1} k (Semifield.toCommGroupWithZero.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, u1} k V (Semiring.toMonoidWithZero.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (Module.toMulActionWithZero.{u1, u1} k V (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_6))))] (p : Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7), Exists.{succ u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (fun (q : Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) => IsCompl.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.completeLattice.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))) (CompleteLattice.toBoundedOrder.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.completeLattice.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)) p q)
 Case conversion may be inaccurate. Consider using '#align monoid_algebra.submodule.exists_is_compl MonoidAlgebra.Submodule.exists_isComplₓ'. -/
@@ -260,7 +260,7 @@ theorem exists_isCompl (p : Submodule (MonoidAlgebra k G) V) :
 
 /- warning: monoid_algebra.submodule.complemented_lattice -> MonoidAlgebra.Submodule.complementedLattice is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] {G : Type.{u1}} [_inst_2 : Fintype.{u1} G] [_inst_3 : Invertible.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (NonAssocRing.toAddGroupWithOne.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u1} Nat k (CoeTCₓ.coe.{1, succ u1} Nat k (Nat.castCoe.{u1} k (AddMonoidWithOne.toNatCast.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (NonAssocRing.toAddGroupWithOne.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))))) (Fintype.card.{u1} G _inst_2))] [_inst_4 : Group.{u1} G] {V : Type.{u1}} [_inst_5 : AddCommGroup.{u1} V] [_inst_6 : Module.{u1, u1} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_7 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_8 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (SMulZeroClass.toHasSmul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.addCommMonoid.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MonoidAlgebra.smulZeroClass.{u1, u1, u1} k G k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (SMulWithZero.toSmulZeroClass.{u1, u1} k k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MulZeroClass.toSMulWithZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))))))) (SMulZeroClass.toHasSmul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MulZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MulZeroOneClass.toMulZeroClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))) (SMulZeroClass.toHasSmul.{u1, u1} k V (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, u1} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, u1} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (Module.toMulActionWithZero.{u1, u1} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_6))))], ComplementedLattice.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (ConditionallyCompleteLattice.toLattice.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.completeLattice.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))) (CompleteLattice.toBoundedOrder.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.completeLattice.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))
+  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] {G : Type.{u1}} [_inst_2 : Fintype.{u1} G] [_inst_3 : Invertible.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u1} Nat k (CoeTCₓ.coe.{1, succ u1} Nat k (Nat.castCoe.{u1} k (AddMonoidWithOne.toNatCast.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))))) (Fintype.card.{u1} G _inst_2))] [_inst_4 : Group.{u1} G] {V : Type.{u1}} [_inst_5 : AddCommGroup.{u1} V] [_inst_6 : Module.{u1, u1} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_7 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_8 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (SMulZeroClass.toHasSmul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.addCommMonoid.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MonoidAlgebra.smulZeroClass.{u1, u1, u1} k G k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (SMulWithZero.toSmulZeroClass.{u1, u1} k k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MulZeroClass.toSMulWithZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))))))) (SMulZeroClass.toHasSmul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MulZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MulZeroOneClass.toMulZeroClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))) (SMulZeroClass.toHasSmul.{u1, u1} k V (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, u1} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, u1} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (Module.toMulActionWithZero.{u1, u1} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_6))))], ComplementedLattice.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (ConditionallyCompleteLattice.toLattice.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.completeLattice.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))) (CompleteLattice.toBoundedOrder.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.completeLattice.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))
 but is expected to have type
   forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] {G : Type.{u1}} [_inst_2 : Fintype.{u1} G] [_inst_3 : Invertible.{u1} k (NonUnitalNonAssocRing.toMul.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (NonAssocRing.toOne.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Nat.cast.{u1} k (NonAssocRing.toNatCast.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Fintype.card.{u1} G _inst_2))] [_inst_4 : Group.{u1} G] {V : Type.{u1}} [_inst_5 : AddCommGroup.{u1} V] [_inst_6 : Module.{u1, u1} k V (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_7 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_8 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (Algebra.toSMul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.algebra.{u1, u1, u1} k G k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Algebra.id.{u1} k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (SMulZeroClass.toSMul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidWithZero.toZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))) (SMulZeroClass.toSMul.{u1, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, u1} k V (CommMonoidWithZero.toZero.{u1} k (CommGroupWithZero.toCommMonoidWithZero.{u1} k (Semifield.toCommGroupWithZero.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, u1} k V (Semiring.toMonoidWithZero.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (Module.toMulActionWithZero.{u1, u1} k V (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_6))))], ComplementedLattice.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (ConditionallyCompleteLattice.toLattice.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.completeLattice.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))) (CompleteLattice.toBoundedOrder.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.completeLattice.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))
 Case conversion may be inaccurate. Consider using '#align monoid_algebra.submodule.complemented_lattice MonoidAlgebra.Submodule.complementedLatticeₓ'. -/

70fd9563

bump to nightly-2023-03-26-10

mathlib commit https://github.com/leanprover-community/mathlib/commit/55d771df074d0dd020139ee1cd4b95521422df9f

bd810858

Diff

@@ -81,6 +81,12 @@ variable (π : W →ₗ[k] V)
 
 include π
 
+/- warning: linear_map.conjugate -> LinearMap.conjugate is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] {G : Type.{u}} [_inst_2 : Group.{u} G] {V : Type.{u}} [_inst_3 : AddCommGroup.{u} V] [_inst_4 : Module.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_5 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_5)))) (SMulZeroClass.toHasSmul.{u, u} k V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} k V (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} k V (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_4))))] {W : Type.{u}} [_inst_7 : AddCommGroup.{u} W] [_inst_8 : Module.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_9 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_9)))) (SMulZeroClass.toHasSmul.{u, u} k W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} k W (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} k W (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_8))))], (LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) -> G -> (LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4)
+but is expected to have type
+  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] {G : Type.{u}} [_inst_2 : Group.{u} G] {V : Type.{v}} [_inst_3 : AddCommGroup.{v} V] [_inst_4 : Module.{u, v} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_5 : Module.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, v} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u, v} k V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} k V (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} k V (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_4))))] {W : Type.{w}} [_inst_7 : AddCommGroup.{w} W] [_inst_8 : Module.{u, w} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_9 : Module.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, w} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_9)))) (SMulZeroClass.toSMul.{u, w} k W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} k W (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} k W (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_8))))], (LinearMap.{u, u, w, v} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (NonAssocRing.toNonAssocSemiring.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) -> G -> (LinearMap.{u, u, w, v} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (NonAssocRing.toNonAssocSemiring.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4)
+Case conversion may be inaccurate. Consider using '#align linear_map.conjugate LinearMap.conjugateₓ'. -/
 /-- We define the conjugate of `π` by `g`, as a `k`-linear map.
 -/
 def conjugate (g : G) : W →ₗ[k] V :=
@@ -93,6 +99,12 @@ section
 
 include h
 
+/- warning: linear_map.conjugate_i -> LinearMap.conjugate_i is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] {G : Type.{u}} [_inst_2 : Group.{u} G] {V : Type.{u}} [_inst_3 : AddCommGroup.{u} V] [_inst_4 : Module.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_5 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_5)))) (SMulZeroClass.toHasSmul.{u, u} k V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} k V (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} k V (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_4))))] {W : Type.{u}} [_inst_7 : AddCommGroup.{u} W] [_inst_8 : Module.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_9 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_9)))) (SMulZeroClass.toHasSmul.{u, u} k W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} k W (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} k W (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_8))))] (π : LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) (i : LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9), (forall (v : V), Eq.{succ u} V (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) (fun (_x : LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) => W -> V) (LinearMap.hasCoeToFun.{u, u, u, u} k k W V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4 (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))))) π (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9) (fun (_x : LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9) => V -> W) (LinearMap.hasCoeToFun.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v) -> (forall (g : G) (v : V), Eq.{succ u} V (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) (fun (_x : LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) => W -> V) (LinearMap.hasCoeToFun.{u, u, u, u} k k W V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4 (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))))) (LinearMap.conjugate.{u} k _inst_1 G _inst_2 V _inst_3 _inst_4 _inst_5 _inst_6 W _inst_7 _inst_8 _inst_9 _inst_10 π g) (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9) (fun (_x : LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9) => V -> W) (LinearMap.hasCoeToFun.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v)
+but is expected to have type
+  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] {G : Type.{u}} [_inst_2 : Group.{u} G] {V : Type.{v}} [_inst_3 : AddCommGroup.{v} V] [_inst_4 : Module.{u, v} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_5 : Module.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, v} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u, v} k V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} k V (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} k V (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_4))))] {W : Type.{w}} [_inst_7 : AddCommGroup.{w} W] [_inst_8 : Module.{u, w} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_9 : Module.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, w} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_9)))) (SMulZeroClass.toSMul.{u, w} k W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} k W (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} k W (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_8))))] (π : LinearMap.{u, u, w, v} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k 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_inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v)
+Case conversion may be inaccurate. Consider using '#align linear_map.conjugate_i LinearMap.conjugate_iₓ'. -/
 theorem conjugate_i (g : G) (v : V) : (conjugate π g) (i v) = v :=
   by
   dsimp [conjugate]
@@ -105,6 +117,12 @@ end
 
 variable (G) [Fintype G]
 
+/- warning: linear_map.sum_of_conjugates -> LinearMap.sumOfConjugates is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] (G : Type.{u}) [_inst_2 : Group.{u} G] {V : Type.{u}} [_inst_3 : AddCommGroup.{u} V] [_inst_4 : Module.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_5 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_5)))) (SMulZeroClass.toHasSmul.{u, u} k V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} k V (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} k V (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_4))))] {W : Type.{u}} [_inst_7 : AddCommGroup.{u} W] [_inst_8 : Module.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_9 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_9)))) (SMulZeroClass.toHasSmul.{u, u} k W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} k W (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} k W (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_8))))], (LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) -> (forall [_inst_11 : Fintype.{u} G], LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4)
+but is expected to have type
+  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] (G : Type.{u}) [_inst_2 : Group.{u} G] {V : Type.{v}} [_inst_3 : AddCommGroup.{v} V] [_inst_4 : Module.{u, v} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_5 : Module.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, v} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u, v} k V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} k V (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} k V (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_4))))] {W : Type.{w}} [_inst_7 : AddCommGroup.{w} W] [_inst_8 : Module.{u, w} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_9 : Module.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, w} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_9)))) (SMulZeroClass.toSMul.{u, w} k W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} k W (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} k W (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_8))))], (LinearMap.{u, u, w, v} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (NonAssocRing.toNonAssocSemiring.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) -> (forall [_inst_11 : Fintype.{u} G], LinearMap.{u, u, w, v} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (NonAssocRing.toNonAssocSemiring.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4)
+Case conversion may be inaccurate. Consider using '#align linear_map.sum_of_conjugates LinearMap.sumOfConjugatesₓ'. -/
 /-- The sum of the conjugates of `π` by each element `g : G`, as a `k`-linear map.
 
 (We postpone dividing by the size of the group as long as possible.)
@@ -113,6 +131,12 @@ def sumOfConjugates : W →ₗ[k] V :=
   ∑ g : G, π.conjugate g
 #align linear_map.sum_of_conjugates LinearMap.sumOfConjugates
 
+/- warning: linear_map.sum_of_conjugates_equivariant -> LinearMap.sumOfConjugatesEquivariant is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] (G : Type.{u}) [_inst_2 : Group.{u} G] {V : Type.{u}} [_inst_3 : AddCommGroup.{u} V] [_inst_4 : Module.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_5 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_5)))) (SMulZeroClass.toHasSmul.{u, u} k V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} k V (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} k V (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_4))))] {W : Type.{u}} [_inst_7 : AddCommGroup.{u} W] [_inst_8 : Module.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_9 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_9)))) (SMulZeroClass.toHasSmul.{u, u} k W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} k W (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} k W (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_8))))], (LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) -> (forall [_inst_11 : Fintype.{u} G], LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_9 _inst_5)
+but is expected to have type
+  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] (G : Type.{u}) [_inst_2 : Group.{u} G] {V : Type.{v}} [_inst_3 : AddCommGroup.{v} V] [_inst_4 : Module.{u, v} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_5 : Module.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, v} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u, v} k V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} k V (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} k V (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_4))))] {W : Type.{w}} [_inst_7 : AddCommGroup.{w} W] [_inst_8 : Module.{u, w} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_9 : Module.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, w} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_9)))) (SMulZeroClass.toSMul.{u, w} k W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} k W (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} k W (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_8))))], (LinearMap.{u, u, w, v} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (NonAssocRing.toNonAssocSemiring.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) -> (forall [_inst_11 : Fintype.{u} G], LinearMap.{u, u, w, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_9 _inst_5)
+Case conversion may be inaccurate. Consider using '#align linear_map.sum_of_conjugates_equivariant LinearMap.sumOfConjugatesEquivariantₓ'. -/
 /-- In fact, the sum over `g : G` of the conjugate of `π` by `g` is a `k[G]`-linear map.
 -/
 def sumOfConjugatesEquivariant : W →ₗ[MonoidAlgebra k G] V :=
@@ -137,6 +161,12 @@ variable [inv : Invertible (Fintype.card G : k)]
 
 include inv
 
+/- warning: linear_map.equivariant_projection -> LinearMap.equivariantProjection is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] (G : Type.{u}) [_inst_2 : Group.{u} G] {V : Type.{u}} [_inst_3 : AddCommGroup.{u} V] [_inst_4 : Module.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_5 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_5)))) (SMulZeroClass.toHasSmul.{u, u} k V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} k V (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} k V (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_4))))] {W : Type.{u}} [_inst_7 : AddCommGroup.{u} W] [_inst_8 : Module.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_9 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_9)))) (SMulZeroClass.toHasSmul.{u, u} k W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} k W (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} k W (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_8))))], (LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) -> (forall [_inst_11 : Fintype.{u} G] [inv : Invertible.{u} k (Distrib.toHasMul.{u} k (Ring.toDistrib.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoidWithOne.toOne.{u} k (AddGroupWithOne.toAddMonoidWithOne.{u} k (NonAssocRing.toAddGroupWithOne.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))) ((fun (a : Type) (b : Type.{u}) [self : HasLiftT.{1, succ u} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u} Nat k (CoeTCₓ.coe.{1, succ u} Nat k (Nat.castCoe.{u} k (AddMonoidWithOne.toNatCast.{u} k (AddGroupWithOne.toAddMonoidWithOne.{u} k (NonAssocRing.toAddGroupWithOne.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))))) (Fintype.card.{u} G _inst_11))], LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_9 _inst_5)
+but is expected to have type
+  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] (G : Type.{u}) [_inst_2 : Group.{u} G] {V : Type.{v}} [_inst_3 : AddCommGroup.{v} V] [_inst_4 : Module.{u, v} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_5 : Module.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, v} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u, v} k V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} k V (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} k V (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_4))))] {W : Type.{w}} [_inst_7 : AddCommGroup.{w} W] [_inst_8 : Module.{u, w} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_9 : Module.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, w} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_9)))) (SMulZeroClass.toSMul.{u, w} k W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} k W (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} k W (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (Module.toMulActionWithZero.{u, w} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7) _inst_8))))], (LinearMap.{u, u, w, v} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (NonAssocRing.toNonAssocSemiring.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_8 _inst_4) -> (forall [_inst_11 : Fintype.{u} G] [inv : Invertible.{u} k (NonUnitalNonAssocRing.toMul.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))) (NonAssocRing.toOne.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))) (Nat.cast.{u} k (NonAssocRing.toNatCast.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))) (Fintype.card.{u} G _inst_11))], LinearMap.{u, u, w, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.nonAssocSemiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Monoid.toMulOneClass.{u} G (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) W V (AddCommGroup.toAddCommMonoid.{w} W _inst_7) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_9 _inst_5)
+Case conversion may be inaccurate. Consider using '#align linear_map.equivariant_projection LinearMap.equivariantProjectionₓ'. -/
 /-- We construct our `k[G]`-linear retraction of `i` as
 $$ \frac{1}{|G|} \sum_{g \in G} g⁻¹ • π(g • -). $$
 -/
@@ -146,6 +176,12 @@ def equivariantProjection : W →ₗ[MonoidAlgebra k G] V :=
 
 include h
 
+/- warning: linear_map.equivariant_projection_condition -> LinearMap.equivariantProjection_condition is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] (G : Type.{u}) [_inst_2 : Group.{u} G] {V : Type.{u}} [_inst_3 : AddCommGroup.{u} V] [_inst_4 : Module.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_5 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_5)))) (SMulZeroClass.toHasSmul.{u, u} k V (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (SMulWithZero.toSmulZeroClass.{u, u} k V (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (MulActionWithZero.toSMulWithZero.{u, u} k V (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} V (AddMonoid.toAddZeroClass.{u} V (AddCommMonoid.toAddMonoid.{u} V (AddCommGroup.toAddCommMonoid.{u} V _inst_3)))) (Module.toMulActionWithZero.{u, u} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_4))))] {W : Type.{u}} [_inst_7 : AddCommGroup.{u} W] [_inst_8 : Module.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_9 : Module.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (SMulZeroClass.toHasSmul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoid.toAddZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddCommMonoid.toAddMonoid.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.addCommMonoid.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MonoidAlgebra.smulZeroClass.{u, u, u} k G k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (SMulWithZero.toSmulZeroClass.{u, u} k k (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toHasZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (MulZeroClass.toSMulWithZero.{u} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} k (NonAssocRing.toNonUnitalNonAssocRing.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))))))) (SMulZeroClass.toHasSmul.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MulZeroClass.toHasZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MulZeroOneClass.toMulZeroClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_9)))) (SMulZeroClass.toHasSmul.{u, u} k W (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (SMulWithZero.toSmulZeroClass.{u, u} k W (MulZeroClass.toHasZero.{u} k (MulZeroOneClass.toMulZeroClass.{u} k (MonoidWithZero.toMulZeroOneClass.{u} k (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (MulActionWithZero.toSMulWithZero.{u, u} k W (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (AddZeroClass.toHasZero.{u} W (AddMonoid.toAddZeroClass.{u} W (AddCommMonoid.toAddMonoid.{u} W (AddCommGroup.toAddCommMonoid.{u} W _inst_7)))) (Module.toMulActionWithZero.{u, u} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_8))))] (π : LinearMap.{u, u, u, u} k k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (RingHom.id.{u} k (Semiring.toNonAssocSemiring.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_8 _inst_4) (i : LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) 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k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9) (fun (_x : LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9) => V -> W) (LinearMap.hasCoeToFun.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v) -> (forall [_inst_11 : Fintype.{u} G] [inv : Invertible.{u} k (Distrib.toHasMul.{u} k (Ring.toDistrib.{u} k (CommRing.toRing.{u} k _inst_1))) (AddMonoidWithOne.toOne.{u} k (AddGroupWithOne.toAddMonoidWithOne.{u} k (NonAssocRing.toAddGroupWithOne.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1))))) ((fun (a : Type) (b : Type.{u}) [self : HasLiftT.{1, succ u} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u} Nat k (CoeTCₓ.coe.{1, succ u} Nat k (Nat.castCoe.{u} k (AddMonoidWithOne.toNatCast.{u} k (AddGroupWithOne.toAddMonoidWithOne.{u} k (NonAssocRing.toAddGroupWithOne.{u} k (Ring.toNonAssocRing.{u} k (CommRing.toRing.{u} k _inst_1)))))))) (Fintype.card.{u} G _inst_11))] (v : V), Eq.{succ u} V (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_9 _inst_5) (fun (_x : LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) W V (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_9 _inst_5) => W -> V) (LinearMap.hasCoeToFun.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) _inst_9 _inst_5 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) (LinearMap.equivariantProjection.{u} k _inst_1 G _inst_2 V _inst_3 _inst_4 _inst_5 _inst_6 W _inst_7 _inst_8 _inst_9 _inst_10 π _inst_11 inv) (coeFn.{succ u, succ u} (LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9) (fun (_x : LinearMap.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) V W (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9) => V -> W) (LinearMap.hasCoeToFun.{u, u, u, u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{u} V _inst_3) (AddCommGroup.toAddCommMonoid.{u} W _inst_7) _inst_5 _inst_9 (RingHom.id.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toNonAssocSemiring.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))))) i v)) v)
+but is expected to have type
+  forall {k : Type.{u}} [_inst_1 : CommRing.{u} k] (G : Type.{u}) [_inst_2 : Group.{u} G] {V : Type.{v}} [_inst_3 : AddCommGroup.{v} V] [_inst_4 : Module.{u, v} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_5 : Module.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3)] [_inst_6 : IsScalarTower.{u, u, v} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) V (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u, v} k V (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (SMulWithZero.toSMulZeroClass.{u, v} k V (CommMonoidWithZero.toZero.{u} k (CommSemiring.toCommMonoidWithZero.{u} k (CommRing.toCommSemiring.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (MulActionWithZero.toSMulWithZero.{u, v} k V (Semiring.toMonoidWithZero.{u} k (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (NegZeroClass.toZero.{v} V (SubNegZeroMonoid.toNegZeroClass.{v} V (SubtractionMonoid.toSubNegZeroMonoid.{v} V (SubtractionCommMonoid.toSubtractionMonoid.{v} V (AddCommGroup.toDivisionAddCommMonoid.{v} V _inst_3))))) (Module.toMulActionWithZero.{u, v} k V (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{v} V _inst_3) _inst_4))))] {W : Type.{w}} [_inst_7 : AddCommGroup.{w} W] [_inst_8 : Module.{u, w} k W (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_9 : Module.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (AddCommGroup.toAddCommMonoid.{w} W _inst_7)] [_inst_10 : IsScalarTower.{u, u, w} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Algebra.toSMul.{u, u} k (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (CommRing.toCommSemiring.{u} k _inst_1) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))) (MonoidAlgebra.algebra.{u, u, u} k G k (CommRing.toCommSemiring.{u} k _inst_1) (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (Algebra.id.{u} k (CommRing.toCommSemiring.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2)))) (SMulZeroClass.toSMul.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (SMulWithZero.toSMulZeroClass.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (MonoidWithZero.toZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1)) (DivInvMonoid.toMonoid.{u} G (Group.toDivInvMonoid.{u} G _inst_2))))) (NegZeroClass.toZero.{w} W (SubNegZeroMonoid.toNegZeroClass.{w} W (SubtractionMonoid.toSubNegZeroMonoid.{w} W (SubtractionCommMonoid.toSubtractionMonoid.{w} W (AddCommGroup.toDivisionAddCommMonoid.{w} W _inst_7))))) (MulActionWithZero.toSMulWithZero.{u, w} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) W (Semiring.toMonoidWithZero.{u} (MonoidAlgebra.{u, u} k G (Ring.toSemiring.{u} k (CommRing.toRing.{u} k _inst_1))) (MonoidAlgebra.semiring.{u, u} k G (Ring.toSemiring.{u} k 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+Case conversion may be inaccurate. Consider using '#align linear_map.equivariant_projection_condition LinearMap.equivariantProjection_conditionₓ'. -/
 theorem equivariantProjection_condition (v : V) : (π.equivariantProjection G) (i v) = v :=
   by
   rw [equivariant_projection, smul_apply, sum_of_conjugates_equivariant,
@@ -186,7 +222,13 @@ variable {W : Type u} [AddCommGroup W] [Module k W] [Module (MonoidAlgebra k G)
 
 variable [IsScalarTower k (MonoidAlgebra k G) W]
 
-theorem exists_left_inverse_of_injective (f : V →ₗ[MonoidAlgebra k G] W) (hf : f.ker = ⊥) :
+/- warning: monoid_algebra.exists_left_inverse_of_injective -> MonoidAlgebra.exists_leftInverse_of_injective is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] {G : Type.{u1}} [_inst_2 : Fintype.{u1} G] [_inst_3 : Invertible.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (NonAssocRing.toAddGroupWithOne.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u1} Nat k (CoeTCₓ.coe.{1, succ u1} Nat k (Nat.castCoe.{u1} k (AddMonoidWithOne.toNatCast.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (NonAssocRing.toAddGroupWithOne.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))))) (Fintype.card.{u1} G _inst_2))] [_inst_4 : Group.{u1} G] {V : Type.{u1}} [_inst_5 : AddCommGroup.{u1} V] [_inst_6 : Module.{u1, u1} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_7 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_8 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (SMulZeroClass.toHasSmul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.addCommMonoid.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MonoidAlgebra.smulZeroClass.{u1, u1, u1} k G k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (SMulWithZero.toSmulZeroClass.{u1, u1} k k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MulZeroClass.toSMulWithZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))))))) (SMulZeroClass.toHasSmul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MulZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MulZeroOneClass.toMulZeroClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))) (SMulZeroClass.toHasSmul.{u1, u1} k V (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, u1} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, u1} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (Module.toMulActionWithZero.{u1, u1} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_6))))] {W : Type.{u1}} [_inst_9 : AddCommGroup.{u1} W] [_inst_10 : Module.{u1, u1} k W (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)] [_inst_11 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) W (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)] [_inst_12 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) W (SMulZeroClass.toHasSmul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.addCommMonoid.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MonoidAlgebra.smulZeroClass.{u1, u1, u1} k G k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (SMulWithZero.toSmulZeroClass.{u1, u1} k k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MulZeroClass.toSMulWithZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))))))) (SMulZeroClass.toHasSmul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) W (AddZeroClass.toHasZero.{u1} W (AddMonoid.toAddZeroClass.{u1} W (AddCommMonoid.toAddMonoid.{u1} W (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)))) (SMulWithZero.toSmulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) W (MulZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MulZeroOneClass.toMulZeroClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))))) (AddZeroClass.toHasZero.{u1} W (AddMonoid.toAddZeroClass.{u1} W (AddCommMonoid.toAddMonoid.{u1} W (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) W (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (AddZeroClass.toHasZero.{u1} W (AddMonoid.toAddZeroClass.{u1} W (AddCommMonoid.toAddMonoid.{u1} W (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) W (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_11)))) (SMulZeroClass.toHasSmul.{u1, u1} k W (AddZeroClass.toHasZero.{u1} W (AddMonoid.toAddZeroClass.{u1} W (AddCommMonoid.toAddMonoid.{u1} W (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)))) (SMulWithZero.toSmulZeroClass.{u1, u1} k W (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (AddZeroClass.toHasZero.{u1} W (AddMonoid.toAddZeroClass.{u1} W (AddCommMonoid.toAddMonoid.{u1} W (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)))) (MulActionWithZero.toSMulWithZero.{u1, u1} k W (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} W (AddMonoid.toAddZeroClass.{u1} W (AddCommMonoid.toAddMonoid.{u1} W (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)))) (Module.toMulActionWithZero.{u1, u1} k W (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_10))))] (f : LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k 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(Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (LinearMap.ker.{u1, u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V W (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11 (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) V W (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11) (LinearMap.semilinearMapClass.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V W (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11 (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))))) f) (Bot.bot.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.hasBot.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))) -> (Exists.{succ u1} (LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) W V (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_11 _inst_7) (fun (g : LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) W V (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_11 _inst_7) => Eq.{succ u1} (LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) V V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7 _inst_7) (LinearMap.comp.{u1, u1, u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V W V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7 _inst_11 _inst_7 (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (RingHomCompTriple.right_ids.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))))) g f) (LinearMap.id.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))
+but is expected to have type
+  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] {G : Type.{u1}} [_inst_2 : Fintype.{u1} G] [_inst_3 : Invertible.{u1} k (NonUnitalNonAssocRing.toMul.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (NonAssocRing.toOne.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Nat.cast.{u1} k (NonAssocRing.toNatCast.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Fintype.card.{u1} G _inst_2))] [_inst_4 : Group.{u1} G] {V : Type.{u1}} [_inst_5 : AddCommGroup.{u1} V] [_inst_6 : Module.{u1, u1} k V (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_7 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_8 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (Algebra.toSMul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.algebra.{u1, u1, u1} k G k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Algebra.id.{u1} k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (SMulZeroClass.toSMul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidWithZero.toZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))) (SMulZeroClass.toSMul.{u1, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, u1} k V (CommMonoidWithZero.toZero.{u1} k (CommGroupWithZero.toCommMonoidWithZero.{u1} k (Semifield.toCommGroupWithZero.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, u1} k V (Semiring.toMonoidWithZero.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (Module.toMulActionWithZero.{u1, u1} k V (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_6))))] {W : Type.{u1}} [_inst_9 : AddCommGroup.{u1} W] [_inst_10 : Module.{u1, u1} k W (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)] [_inst_11 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9)] [_inst_12 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (Algebra.toSMul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.algebra.{u1, u1, u1} k G k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Algebra.id.{u1} k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (SMulZeroClass.toSMul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (NegZeroClass.toZero.{u1} W (SubNegZeroMonoid.toNegZeroClass.{u1} W (SubtractionMonoid.toSubNegZeroMonoid.{u1} W (SubtractionCommMonoid.toSubtractionMonoid.{u1} W (AddCommGroup.toDivisionAddCommMonoid.{u1} W _inst_9))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (MonoidWithZero.toZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (NegZeroClass.toZero.{u1} W (SubNegZeroMonoid.toNegZeroClass.{u1} W (SubtractionMonoid.toSubNegZeroMonoid.{u1} W (SubtractionCommMonoid.toSubtractionMonoid.{u1} W (AddCommGroup.toDivisionAddCommMonoid.{u1} W _inst_9))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (NegZeroClass.toZero.{u1} W (SubNegZeroMonoid.toNegZeroClass.{u1} W (SubtractionMonoid.toSubNegZeroMonoid.{u1} W (SubtractionCommMonoid.toSubtractionMonoid.{u1} W (AddCommGroup.toDivisionAddCommMonoid.{u1} W _inst_9))))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) W (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_11)))) (SMulZeroClass.toSMul.{u1, u1} k W (NegZeroClass.toZero.{u1} W (SubNegZeroMonoid.toNegZeroClass.{u1} W (SubtractionMonoid.toSubNegZeroMonoid.{u1} W (SubtractionCommMonoid.toSubtractionMonoid.{u1} W (AddCommGroup.toDivisionAddCommMonoid.{u1} W _inst_9))))) (SMulWithZero.toSMulZeroClass.{u1, u1} k W (CommMonoidWithZero.toZero.{u1} k (CommGroupWithZero.toCommMonoidWithZero.{u1} k (Semifield.toCommGroupWithZero.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} W (SubNegZeroMonoid.toNegZeroClass.{u1} W (SubtractionMonoid.toSubNegZeroMonoid.{u1} W (SubtractionCommMonoid.toSubtractionMonoid.{u1} W (AddCommGroup.toDivisionAddCommMonoid.{u1} W _inst_9))))) (MulActionWithZero.toSMulWithZero.{u1, u1} k W (Semiring.toMonoidWithZero.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} W (SubNegZeroMonoid.toNegZeroClass.{u1} W (SubtractionMonoid.toSubNegZeroMonoid.{u1} W (SubtractionCommMonoid.toSubtractionMonoid.{u1} W (AddCommGroup.toDivisionAddCommMonoid.{u1} W _inst_9))))) (Module.toMulActionWithZero.{u1, u1} k W (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_10))))] (f : LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) V W (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11), (Eq.{succ u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (LinearMap.ker.{u1, u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V W (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11 (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) V W (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V W (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) _inst_7 _inst_11 (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))))) f) (Bot.bot.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.instBotSubmodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))) -> (Exists.{succ u1} (LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) W V (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_11 _inst_7) (fun (g : LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k 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(AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_11 _inst_7) => Eq.{succ u1} (LinearMap.{u1, u1, u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) 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(DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) (AddCommGroup.toAddCommMonoid.{u1} W _inst_9) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7 _inst_11 _inst_7 (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (RingHomCompTriple.ids.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (RingHom.id.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.nonAssocSemiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))))) g f) (LinearMap.id.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))
+Case conversion may be inaccurate. Consider using '#align monoid_algebra.exists_left_inverse_of_injective MonoidAlgebra.exists_leftInverse_of_injectiveₓ'. -/
+theorem exists_leftInverse_of_injective (f : V →ₗ[MonoidAlgebra k G] W) (hf : f.ker = ⊥) :
     ∃ g : W →ₗ[MonoidAlgebra k G] V, g.comp f = LinearMap.id :=
   by
   obtain ⟨φ, hφ⟩ :=
@@ -200,16 +242,28 @@ theorem exists_left_inverse_of_injective (f : V →ₗ[MonoidAlgebra k G] W) (hf
   intro v
   have := congr_arg LinearMap.toFun hφ
   exact congr_fun this v
-#align monoid_algebra.exists_left_inverse_of_injective MonoidAlgebra.exists_left_inverse_of_injective
+#align monoid_algebra.exists_left_inverse_of_injective MonoidAlgebra.exists_leftInverse_of_injective
 
 namespace Submodule
 
+/- warning: monoid_algebra.submodule.exists_is_compl -> MonoidAlgebra.Submodule.exists_isCompl is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] {G : Type.{u1}} [_inst_2 : Fintype.{u1} G] [_inst_3 : Invertible.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (NonAssocRing.toAddGroupWithOne.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u1} Nat k (CoeTCₓ.coe.{1, succ u1} Nat k (Nat.castCoe.{u1} k (AddMonoidWithOne.toNatCast.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (NonAssocRing.toAddGroupWithOne.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))))) (Fintype.card.{u1} G _inst_2))] [_inst_4 : Group.{u1} G] {V : Type.{u1}} [_inst_5 : AddCommGroup.{u1} V] [_inst_6 : Module.{u1, u1} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_7 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_8 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (SMulZeroClass.toHasSmul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) 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(Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))) (SMulZeroClass.toHasSmul.{u1, u1} k V (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, u1} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, u1} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (Module.toMulActionWithZero.{u1, u1} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_6))))] (p : Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7), Exists.{succ u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (fun (q : Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) => IsCompl.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.completeLattice.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))) (CompleteLattice.toBoundedOrder.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.completeLattice.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)) p q)
+but is expected to have type
+  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] {G : Type.{u1}} [_inst_2 : Fintype.{u1} G] [_inst_3 : Invertible.{u1} k (NonUnitalNonAssocRing.toMul.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (NonAssocRing.toOne.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Nat.cast.{u1} k (NonAssocRing.toNatCast.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Fintype.card.{u1} G _inst_2))] [_inst_4 : Group.{u1} G] {V : Type.{u1}} [_inst_5 : AddCommGroup.{u1} V] [_inst_6 : Module.{u1, u1} k V (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_7 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_8 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (Algebra.toSMul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.algebra.{u1, u1, u1} k G k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Algebra.id.{u1} k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (SMulZeroClass.toSMul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidWithZero.toZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))) (SMulZeroClass.toSMul.{u1, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, u1} k V (CommMonoidWithZero.toZero.{u1} k (CommGroupWithZero.toCommMonoidWithZero.{u1} k (Semifield.toCommGroupWithZero.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, u1} k V (Semiring.toMonoidWithZero.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (Module.toMulActionWithZero.{u1, u1} k V (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_6))))] (p : Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7), Exists.{succ u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (fun (q : Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) => IsCompl.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.completeLattice.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))) (CompleteLattice.toBoundedOrder.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.completeLattice.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)) p q)
+Case conversion may be inaccurate. Consider using '#align monoid_algebra.submodule.exists_is_compl MonoidAlgebra.Submodule.exists_isComplₓ'. -/
 theorem exists_isCompl (p : Submodule (MonoidAlgebra k G) V) :
     ∃ q : Submodule (MonoidAlgebra k G) V, IsCompl p q :=
-  let ⟨f, hf⟩ := MonoidAlgebra.exists_left_inverse_of_injective p.Subtype p.ker_subtype
+  let ⟨f, hf⟩ := MonoidAlgebra.exists_leftInverse_of_injective p.Subtype p.ker_subtype
   ⟨f.ker, LinearMap.isCompl_of_proj <| LinearMap.ext_iff.1 hf⟩
 #align monoid_algebra.submodule.exists_is_compl MonoidAlgebra.Submodule.exists_isCompl
 
+/- warning: monoid_algebra.submodule.complemented_lattice -> MonoidAlgebra.Submodule.complementedLattice is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] {G : Type.{u1}} [_inst_2 : Fintype.{u1} G] [_inst_3 : Invertible.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (NonAssocRing.toAddGroupWithOne.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u1} Nat k (CoeTCₓ.coe.{1, succ u1} Nat k (Nat.castCoe.{u1} k (AddMonoidWithOne.toNatCast.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (NonAssocRing.toAddGroupWithOne.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))))) (Fintype.card.{u1} G _inst_2))] [_inst_4 : Group.{u1} G] {V : Type.{u1}} [_inst_5 : AddCommGroup.{u1} V] [_inst_6 : Module.{u1, u1} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_7 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_8 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (SMulZeroClass.toHasSmul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.addCommMonoid.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MonoidAlgebra.smulZeroClass.{u1, u1, u1} k G k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (SMulWithZero.toSmulZeroClass.{u1, u1} k k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (MulZeroClass.toSMulWithZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))))))) (SMulZeroClass.toHasSmul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MulZeroClass.toHasZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MulZeroOneClass.toMulZeroClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))) (SMulZeroClass.toHasSmul.{u1, u1} k V (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, u1} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, u1} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (AddCommMonoid.toAddMonoid.{u1} V (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)))) (Module.toMulActionWithZero.{u1, u1} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_6))))], ComplementedLattice.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (ConditionallyCompleteLattice.toLattice.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.completeLattice.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))) (CompleteLattice.toBoundedOrder.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.completeLattice.{u1, u1} (MonoidAlgebra.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))
+but is expected to have type
+  forall {k : Type.{u1}} [_inst_1 : Field.{u1} k] {G : Type.{u1}} [_inst_2 : Fintype.{u1} G] [_inst_3 : Invertible.{u1} k (NonUnitalNonAssocRing.toMul.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))) (NonAssocRing.toOne.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Nat.cast.{u1} k (NonAssocRing.toNatCast.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (Fintype.card.{u1} G _inst_2))] [_inst_4 : Group.{u1} G] {V : Type.{u1}} [_inst_5 : AddCommGroup.{u1} V] [_inst_6 : Module.{u1, u1} k V (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_7 : Module.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5)] [_inst_8 : IsScalarTower.{u1, u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (Algebra.toSMul.{u1, u1} k (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (MonoidAlgebra.algebra.{u1, u1, u1} k G k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)) (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (Algebra.id.{u1} k (Semifield.toCommSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (SMulZeroClass.toSMul.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidWithZero.toZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (Semiring.toMonoidWithZero.{u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (Module.toMulActionWithZero.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7)))) (SMulZeroClass.toSMul.{u1, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, u1} k V (CommMonoidWithZero.toZero.{u1} k (CommGroupWithZero.toCommMonoidWithZero.{u1} k (Semifield.toCommGroupWithZero.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, u1} k V (Semiring.toMonoidWithZero.{u1} k (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_5))))) (Module.toMulActionWithZero.{u1, u1} k V (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_6))))], ComplementedLattice.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (ConditionallyCompleteLattice.toLattice.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.completeLattice.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))) (CompleteLattice.toBoundedOrder.{u1} (Submodule.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7) (Submodule.completeLattice.{u1, u1} (MonoidAlgebra.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1)))) V (MonoidAlgebra.semiring.{u1, u1} k G (DivisionSemiring.toSemiring.{u1} k (Semifield.toDivisionSemiring.{u1} k (Field.toSemifield.{u1} k _inst_1))) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_5) _inst_7))
+Case conversion may be inaccurate. Consider using '#align monoid_algebra.submodule.complemented_lattice MonoidAlgebra.Submodule.complementedLatticeₓ'. -/
 /-- This also implies an instance `is_semisimple_module (monoid_algebra k G) V`. -/
 instance complementedLattice : ComplementedLattice (Submodule (MonoidAlgebra k G) V) :=
   ⟨exists_isCompl⟩

70fd9563

bump to nightly-2023-02-28-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211

9e3889e2

Diff

@@ -190,7 +190,7 @@ theorem exists_left_inverse_of_injective (f : V →ₗ[MonoidAlgebra k G] W) (hf
     ∃ g : W →ₗ[MonoidAlgebra k G] V, g.comp f = LinearMap.id :=
   by
   obtain ⟨φ, hφ⟩ :=
-    (f.restrict_scalars k).exists_left_inverse_of_injective
+    (f.restrict_scalars k).exists_leftInverse_of_injective
       (by simp only [hf, Submodule.restrictScalars_bot, LinearMap.ker_restrictScalars])
   refine' ⟨φ.equivariant_projection G, _⟩
   apply LinearMap.ext

70fd9563

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

70fd9563

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

Empty lines were removed by executing the following Python script twice

import os
import re


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

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

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

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

75c86f04

Diff

@@ -63,7 +63,6 @@ variable {V : Type v} [AddCommGroup V] [Module k V] [Module (MonoidAlgebra k G)
 variable [IsScalarTower k (MonoidAlgebra k G) V]
 variable {W : Type w} [AddCommGroup W] [Module k W] [Module (MonoidAlgebra k G) W]
 variable [IsScalarTower k (MonoidAlgebra k G) W]
-
 variable (π : W →ₗ[k] V)
 
 /-- We define the conjugate of `π` by `g`, as a `k`-linear map. -/

70fd9563

feat: sum and product of commuting semisimple endomorphisms (#10808)

Prove isSemisimple_of_mem_adjoin: if two commuting endomorphisms of a finite-dimensional vector space over a perfect field are both semisimple, then every endomorphism in the algebra generated by them (in particular their product and sum) is semisimple.
In the same file LinearAlgebra/Semisimple.lean, eq_zero_of_isNilpotent_isSemisimple and isSemisimple_of_squarefree_aeval_eq_zero are golfed, and IsSemisimple.minpoly_squarefree is proved

RingTheory/SimpleModule.lean:

Define IsSemisimpleRing R to mean that R is a semisimple R-module. add properties of simple modules and a characterization (they are exactly the quotients of the ring by maximal left ideals).
The annihilator of a semisimple module is a radical ideal.
Any module over a semisimple ring is semisimple.
A finite product of semisimple rings is semisimple.
Any quotient of a semisimple ring is semisimple.
Add Artin--Wedderburn as a TODO (proof_wanted).
Order/Atoms.lean: add the instance from IsSimpleOrder to ComplementedLattice, so that IsSimpleModule → IsSemisimpleModule is automatically inferred.

Prerequisites for showing a product of semisimple rings is semisimple:

Algebra/Module/Submodule/Map.lean: generalize orderIsoMapComap so that it only requires RingHomSurjective rather than RingHomInvPair
Algebra/Ring/CompTypeclasses.lean, Mathlib/Algebra/Ring/Pi.lean, Algebra/Ring/Prod.lean: add RingHomSurjective instances

RingTheory/Artinian.lean:

quotNilradicalEquivPi: the quotient of a commutative Artinian ring R by its nilradical is isomorphic to the (finite) product of its quotients by maximal ideals (therefore a product of fields). equivPi: if the ring is moreover reduced, then the ring itself is a product of fields. Deduce that R is a semisimple ring and both R and R[X] are decomposition monoids. Requires RingEquiv.quotientBot in RingTheory/Ideal/QuotientOperations.lean.
Data/Polynomial/Eval.lean: the polynomial ring over a finite product of rings is isomorphic to the product of polynomial rings over individual rings. (Used to show R[X] is a decomposition monoid.)

Other necessary results:

FieldTheory/Minpoly/Field.lean: the minimal polynomial of an element in a reduced algebra over a field is radical.
RingTheory/PowerBasis.lean: generalize PowerBasis.finiteDimensional and rename it to .finite.

Annihilator stuff, some of which do not end up being used:

RingTheory/Ideal/Operations.lean: define Module.annihilator and redefine Submodule.annihilator in terms of it; add lemmas, including one that says an arbitrary intersection of radical ideals is radical. The new lemma Ideal.isRadical_iff_pow_one_lt depends on pow_imp_self_of_one_lt in Mathlib/Data/Nat/Interval.lean, which is also used to golf the proof of isRadical_iff_pow_one_lt.
Algebra/Module/Torsion.lean: add a lemma and an instance (unused)
Data/Polynomial/Module/Basic.lean: add a def (unused) and a lemma
LinearAlgebra/AnnihilatingPolynomial.lean: add lemma span_minpoly_eq_annihilator

Some results about idempotent linear maps (projections) and idempotent elements, used to show that any (left) ideal in a semisimple ring is spanned by an idempotent element (unused):

LinearAlgebra/Projection.lean: add def isIdempotentElemEquiv
LinearAlgebra/Span.lean: add two lemmas

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

0b52a6a5

Diff

@@ -5,6 +5,7 @@ Authors: Scott Morrison
 -/
 import Mathlib.Algebra.MonoidAlgebra.Basic
 import Mathlib.LinearAlgebra.Basis.VectorSpace
+import Mathlib.RingTheory.SimpleModule
 
 #align_import representation_theory.maschke from "leanprover-community/mathlib"@"70fd9563a21e7b963887c9360bd29b2393e6225a"
 
@@ -144,14 +145,17 @@ namespace MonoidAlgebra
 -- Now we work over a `[Field k]`.
 variable {k : Type u} [Field k] {G : Type u} [Fintype G] [Invertible (Fintype.card G : k)]
 variable [Group G]
-variable {V : Type u} [AddCommGroup V] [Module k V] [Module (MonoidAlgebra k G) V]
-variable [IsScalarTower k (MonoidAlgebra k G) V]
-variable {W : Type u} [AddCommGroup W] [Module k W] [Module (MonoidAlgebra k G) W]
-variable [IsScalarTower k (MonoidAlgebra k G) W]
+variable {V : Type u} [AddCommGroup V] [Module (MonoidAlgebra k G) V]
+variable {W : Type u} [AddCommGroup W] [Module (MonoidAlgebra k G) W]
 
 theorem exists_leftInverse_of_injective (f : V →ₗ[MonoidAlgebra k G] W)
     (hf : LinearMap.ker f = ⊥) :
     ∃ g : W →ₗ[MonoidAlgebra k G] V, g.comp f = LinearMap.id := by
+  let A := MonoidAlgebra k G
+  letI : Module k W := .compHom W (algebraMap k A)
+  letI : Module k V := .compHom V (algebraMap k A)
+  have := IsScalarTower.of_compHom k A W
+  have := IsScalarTower.of_compHom k A V
   obtain ⟨φ, hφ⟩ := (f.restrictScalars k).exists_leftInverse_of_injective <| by
     simp only [hf, Submodule.restrictScalars_bot, LinearMap.ker_restrictScalars]
   refine ⟨φ.equivariantProjection G, DFunLike.ext _ _ ?_⟩
@@ -162,17 +166,21 @@ namespace Submodule
 
 theorem exists_isCompl (p : Submodule (MonoidAlgebra k G) V) :
     ∃ q : Submodule (MonoidAlgebra k G) V, IsCompl p q := by
-  have : IsScalarTower k (MonoidAlgebra k G) p := p.isScalarTower'
   rcases MonoidAlgebra.exists_leftInverse_of_injective p.subtype p.ker_subtype with ⟨f, hf⟩
-  refine ⟨LinearMap.ker f, LinearMap.isCompl_of_proj ?_⟩
-  exact DFunLike.congr_fun hf
+  exact ⟨LinearMap.ker f, LinearMap.isCompl_of_proj <| DFunLike.congr_fun hf⟩
 #align monoid_algebra.submodule.exists_is_compl MonoidAlgebra.Submodule.exists_isCompl
 
-/-- This also implies an instance `IsSemisimpleModule (MonoidAlgebra k G) V`. -/
+/-- This also implies instances `IsSemisimpleModule (MonoidAlgebra k G) V` and
+`IsSemisimpleRing (MonoidAlgebra k G)`. -/
 instance complementedLattice : ComplementedLattice (Submodule (MonoidAlgebra k G) V) :=
   ⟨exists_isCompl⟩
 #align monoid_algebra.submodule.complemented_lattice MonoidAlgebra.Submodule.complementedLattice
 
+instance [AddGroup G] : IsSemisimpleRing (AddMonoidAlgebra k G) :=
+  letI : Invertible (Fintype.card (Multiplicative G) : k) := by
+    rwa [Fintype.card_congr Multiplicative.toAdd]
+  (AddMonoidAlgebra.toMultiplicativeAlgEquiv k G (R := ℕ)).toRingEquiv.symm.isSemisimpleRing
+
 end Submodule
 
 end MonoidAlgebra

70fd9563

chore: reduce imports (#9830)

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

f4c4ca61

Diff

@@ -4,7 +4,6 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 -/
 import Mathlib.Algebra.MonoidAlgebra.Basic
-import Mathlib.Algebra.CharP.Invertible
 import Mathlib.LinearAlgebra.Basis.VectorSpace
 
 #align_import representation_theory.maschke from "leanprover-community/mathlib"@"70fd9563a21e7b963887c9360bd29b2393e6225a"

70fd9563

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

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

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

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

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

82656743

Diff

@@ -155,8 +155,8 @@ theorem exists_leftInverse_of_injective (f : V →ₗ[MonoidAlgebra k G] W)
     ∃ g : W →ₗ[MonoidAlgebra k G] V, g.comp f = LinearMap.id := by
   obtain ⟨φ, hφ⟩ := (f.restrictScalars k).exists_leftInverse_of_injective <| by
     simp only [hf, Submodule.restrictScalars_bot, LinearMap.ker_restrictScalars]
-  refine ⟨φ.equivariantProjection G, FunLike.ext _ _ ?_⟩
-  exact φ.equivariantProjection_condition G _ <| FunLike.congr_fun hφ
+  refine ⟨φ.equivariantProjection G, DFunLike.ext _ _ ?_⟩
+  exact φ.equivariantProjection_condition G _ <| DFunLike.congr_fun hφ
 #align monoid_algebra.exists_left_inverse_of_injective MonoidAlgebra.exists_leftInverse_of_injective
 
 namespace Submodule
@@ -166,7 +166,7 @@ theorem exists_isCompl (p : Submodule (MonoidAlgebra k G) V) :
   have : IsScalarTower k (MonoidAlgebra k G) p := p.isScalarTower'
   rcases MonoidAlgebra.exists_leftInverse_of_injective p.subtype p.ker_subtype with ⟨f, hf⟩
   refine ⟨LinearMap.ker f, LinearMap.isCompl_of_proj ?_⟩
-  exact FunLike.congr_fun hf
+  exact DFunLike.congr_fun hf
 #align monoid_algebra.submodule.exists_is_compl MonoidAlgebra.Submodule.exists_isCompl
 
 /-- This also implies an instance `IsSemisimpleModule (MonoidAlgebra k G) V`. -/

70fd9563

chore: Nsmul -> NSMul, Zpow -> ZPow, etc (#9067)

Normalising to naming convention rule number 6.

9b2f0dca

Diff

@@ -68,7 +68,7 @@ variable (π : W →ₗ[k] V)
 
 /-- We define the conjugate of `π` by `g`, as a `k`-linear map. -/
 def conjugate (g : G) : W →ₗ[k] V :=
-  .comp (.comp (GroupSmul.linearMap k V g⁻¹) π) (GroupSmul.linearMap k W g)
+  .comp (.comp (GroupSMul.linearMap k V g⁻¹) π) (GroupSMul.linearMap k W g)
 #align linear_map.conjugate LinearMap.conjugate
 
 theorem conjugate_apply (g : G) (v : W) :

70fd9563

chore(Mathlib/LinearAlgebra/Basis): Move results about vector spaces to a new file (#6321)

This breaks a dependency cycle with Module.Free, which means we can immediately show that all vector spaces are free modules.

The lemmas are moved without modification in this PR. A subsequent PR can use the Module.Free results to golf the vector space ones, and deduplicate the API.

Co-authored-by: Oliver Nash <github@olivernash.org>

4412853e

Diff

@@ -5,7 +5,7 @@ Authors: Scott Morrison
 -/
 import Mathlib.Algebra.MonoidAlgebra.Basic
 import Mathlib.Algebra.CharP.Invertible
-import Mathlib.LinearAlgebra.Basis
+import Mathlib.LinearAlgebra.Basis.VectorSpace
 
 #align_import representation_theory.maschke from "leanprover-community/mathlib"@"70fd9563a21e7b963887c9360bd29b2393e6225a"

70fd9563

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

depends on: #5966

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

89aa3a3b

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module representation_theory.maschke
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.MonoidAlgebra.Basic
 import Mathlib.Algebra.CharP.Invertible
 import Mathlib.LinearAlgebra.Basis
 
+#align_import representation_theory.maschke from "leanprover-community/mathlib"@"70fd9563a21e7b963887c9360bd29b2393e6225a"
+
 /-!
 # Maschke's theorem

70fd9563

chore: cleanup whitespace (#5988)

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

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

12343aa5

Diff

@@ -20,7 +20,7 @@ in the formulation that every submodule of a `k[G]` module has a complement,
 when `k` is a field with `Invertible (Fintype.card G : k)`.
 
 We do the core computation in greater generality.
-For any `[CommRing k]` in which  `[Invertible (Fintype.card G : k)]`,
+For any `[CommRing k]` in which `[Invertible (Fintype.card G : k)]`,
 and a `k[G]`-linear map `i : V → W` which admits a `k`-linear retraction `π`,
 we produce a `k[G]`-linear retraction by
 taking the average over `G` of the conjugates of `π`.

70fd9563

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

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

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

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

a6e1045f

Diff

@@ -58,7 +58,6 @@ $$ \frac{1}{|G|} \sum_{g \in G} g⁻¹ • π(g • -). $$
 
 namespace LinearMap
 
-set_option synthInstance.etaExperiment true
 
 -- At first we work with any `[CommRing k]`, and add the assumption that
 -- `[Invertible (Fintype.card G : k)]` when it is required.

70fd9563

feat: port RepresentationTheory.Maschke (#2986)

fa5d1a15

`representation_theory.maschke` ⟷ `Mathlib.RepresentationTheory.Maschke`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 481

representation_theory.maschke ⟷ Mathlib.RepresentationTheory.Maschke

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 481

`representation_theory.maschke` ⟷ `Mathlib.RepresentationTheory.Maschke`