ring_theory.tensor_product
⟷
Mathlib.RingTheory.TensorProduct.Basic
The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.
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@@ -322,16 +322,16 @@ begin
{ intros, simp only [linear_map.map_add, *, linear_map.add_apply], },
end
-lemma mul_assoc (x y z : A ⊗[R] B) : mul (mul x y) z = mul x (mul y z) :=
+protected lemma mul_assoc (x y z : A ⊗[R] B) : mul (mul x y) z = mul x (mul y z) :=
mul_assoc' mul (by { intros, simp only [mul_apply, mul_assoc], }) x y z
-lemma one_mul (x : A ⊗[R] B) : mul (1 ⊗ₜ 1) x = x :=
+protected lemma one_mul (x : A ⊗[R] B) : mul (1 ⊗ₜ 1) x = x :=
begin
apply tensor_product.induction_on x;
simp {contextual := tt},
end
-lemma mul_one (x : A ⊗[R] B) : mul x (1 ⊗ₜ 1) = x :=
+protected lemma mul_one (x : A ⊗[R] B) : mul x (1 ⊗ₜ 1) = x :=
begin
apply tensor_product.induction_on x;
simp {contextual := tt},
@@ -347,9 +347,9 @@ instance : semiring (A ⊗[R] B) :=
add := (+),
one := 1,
mul := λ a b, mul a b,
- one_mul := one_mul,
- mul_one := mul_one,
- mul_assoc := mul_assoc,
+ one_mul := algebra.tensor_product.one_mul,
+ mul_one := algebra.tensor_product.mul_one,
+ mul_assoc := algebra.tensor_product.mul_assoc,
zero_mul := by simp,
mul_zero := by simp,
left_distrib := by simp,
@@ -383,22 +383,57 @@ def include_left_ring_hom : A →+* A ⊗[R] B :=
map_one' := rfl,
map_mul' := by simp }
-variables {S : Type*} [comm_semiring S] [algebra S A]
+variables {S : Type*}
+
+-- we want `is_scalar_tower_right` to take priority since it's better for unification elsewhere
+@[priority 100]
+instance is_scalar_tower_right
+ [monoid S] [distrib_mul_action S A] [is_scalar_tower S A A] [smul_comm_class R S A] :
+ is_scalar_tower S (A ⊗[R] B) (A ⊗[R] B) :=
+{ smul_assoc := λ r x y, begin
+ change (r • x) * y = r • (x * y),
+ apply tensor_product.induction_on y,
+ { simp [smul_zero], },
+ { apply tensor_product.induction_on x,
+ { simp [smul_zero] },
+ { intros a b a' b',
+ dsimp,
+ rw [tensor_product.smul_tmul', tensor_product.smul_tmul', tmul_mul_tmul, smul_mul_assoc], },
+ { intros, simp [smul_add, add_mul, *], } },
+ { intros, simp [smul_add, mul_add, *], },
+ end }
+
+-- we want `algebra.to_smul_comm_class` to take priority since it's better for unification elsewhere
+@[priority 100]
+instance smul_comm_class_right
+ [monoid S] [distrib_mul_action S A] [smul_comm_class S A A] [smul_comm_class R S A] :
+ smul_comm_class S (A ⊗[R] B) (A ⊗[R] B) :=
+{ smul_comm := λ r x y, begin
+ change r • (x * y) = x * r • y,
+ apply tensor_product.induction_on y,
+ { simp [smul_zero], },
+ { apply tensor_product.induction_on x,
+ { simp [smul_zero] },
+ { intros a b a' b',
+ dsimp,
+ rw [tensor_product.smul_tmul', tensor_product.smul_tmul', tmul_mul_tmul, mul_smul_comm], },
+ { intros, simp [smul_add, add_mul, *], } },
+ { intros, simp [smul_add, mul_add, *], },
+ end }
+
+variables [comm_semiring S] [algebra S A]
instance left_algebra [smul_comm_class R S A] : algebra S (A ⊗[R] B) :=
{ commutes' := λ r x,
begin
- apply tensor_product.induction_on x,
- { simp, },
- { intros a b, dsimp, rw [algebra.commutes, _root_.mul_one, _root_.one_mul], },
- { intros y y' h h', dsimp at h h' ⊢, simp only [mul_add, add_mul, h, h'], },
+ dsimp only [ring_hom.to_fun_eq_coe, ring_hom.comp_apply, include_left_ring_hom_apply],
+ rw [algebra_map_eq_smul_one, ←smul_tmul', ←one_def, mul_smul_comm, smul_mul_assoc, mul_one,
+ one_mul],
end,
smul_def' := λ r x,
begin
- apply tensor_product.induction_on x,
- { simp [smul_zero], },
- { intros a b, dsimp, rw [tensor_product.smul_tmul', algebra.smul_def r a, _root_.one_mul] },
- { intros, dsimp, simp [smul_add, mul_add, *], },
+ dsimp only [ring_hom.to_fun_eq_coe, ring_hom.comp_apply, include_left_ring_hom_apply],
+ rw [algebra_map_eq_smul_one, ←smul_tmul', smul_mul_assoc, ←one_def, one_mul],
end,
.. tensor_product.include_left_ring_hom.comp (algebra_map S A),
.. (by apply_instance : module S (A ⊗[R] B)) }.
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is_scalar_tower
by smul_comm_class
in left_algebra
(#19118)
With this change, this instance works for both restriction (e.g tensor product over ℂ
of complex algebras is a real algebra) and extension (e.g tensor product over ℝ
of complex algebras is a complex algebra) of scalars.
Zulip
I also removes algebra.tensor_product.tensor_product.is_scalar_tower since it is automatically inferred from tensor_product.is_scalar_tower
Co-authored-by: Antoine Chambert-Loir <antoine.chambert-loir@math.univ-paris-diderot.fr>
@@ -383,9 +383,9 @@ def include_left_ring_hom : A →+* A ⊗[R] B :=
map_one' := rfl,
map_mul' := by simp }
-variables {S : Type*} [comm_semiring S] [algebra R S] [algebra S A] [is_scalar_tower R S A]
+variables {S : Type*} [comm_semiring S] [algebra S A]
-instance left_algebra : algebra S (A ⊗[R] B) :=
+instance left_algebra [smul_comm_class R S A] : algebra S (A ⊗[R] B) :=
{ commutes' := λ r x,
begin
apply tensor_product.induction_on x,
@@ -408,11 +408,9 @@ instance left_algebra : algebra S (A ⊗[R] B) :=
instance : algebra R (A ⊗[R] B) := infer_instance
@[simp]
-lemma algebra_map_apply (r : S) :
+lemma algebra_map_apply [smul_comm_class R S A] (r : S) :
(algebra_map S (A ⊗[R] B)) r = ((algebra_map S A) r) ⊗ₜ 1 := rfl
-instance : is_scalar_tower R S (A ⊗[R] B) := ⟨λ a b c, by simp⟩
-
variables {C : Type v₃} [semiring C] [algebra R C]
@[ext]
@@ -424,6 +422,7 @@ begin
simp [H],
end
+-- TODO: with `smul_comm_class R S A` we can have this as an `S`-algebra morphism
/-- The `R`-algebra morphism `A →ₐ[R] A ⊗[R] B` sending `a` to `a ⊗ₜ 1`. -/
def include_left : A →ₐ[R] A ⊗[R] B :=
{ commutes' := by simp,
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(first ported)
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -499,7 +499,7 @@ theorem tmul_pow (a : A) (b : B) (k : ℕ) : a ⊗ₜ[R] b ^ k = (a ^ k) ⊗ₜ[
by
induction' k with k ih
· simp [one_def]
- · simp [pow_succ, ih]
+ · simp [pow_succ', ih]
#align algebra.tensor_product.tmul_pow Algebra.TensorProduct.tmul_pow
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -817,10 +817,10 @@ def algEquivOfLinearEquivTripleTensorProduct (f : (A ⊗[R] B) ⊗[R] C ≃ₗ[R
· simp only [zero_tmul, map_zero, MulZeroClass.mul_zero]
· intros; simp only [tmul_mul_tmul, w₁]
· intro x₁ x₂ h₁ h₂
- simp only [tmul_mul_tmul] at h₁ h₂
+ simp only [tmul_mul_tmul] at h₁ h₂
simp only [tmul_mul_tmul, mul_add, add_tmul, map_add, h₁, h₂]
· intro x₁ x₂ h₁ h₂
- simp only [tmul_mul_tmul] at h₁ h₂
+ simp only [tmul_mul_tmul] at h₁ h₂
simp only [tmul_mul_tmul, add_mul, add_tmul, map_add, h₁, h₂]
· intro x₁ x₂ h₁ h₂
simp only [tmul_mul_tmul, map_add, mul_add, add_mul, h₁, h₂]
@@ -1333,14 +1333,14 @@ protected def module : Module (A ⊗[R] B) M
simp only [module_aux_apply, mul_smul, smul_comm a₁ b₂, Algebra.TensorProduct.tmul_mul_tmul,
LinearMap.mul_apply]
· intro z w hz hw a b
- simp only at hz hw
+ simp only at hz hw
simp only [mul_add, hz, hw, map_add, LinearMap.add_apply]
· intro z w hz hw; simp only [MulZeroClass.mul_zero, map_zero, LinearMap.zero_apply]
· intro a b z w hz hw
- simp only at hz hw
+ simp only at hz hw
simp only [map_add, add_mul, LinearMap.add_apply, hz, hw]
· intro u v hu hv z w hz hw
- simp only at hz hw
+ simp only at hz hw
simp only [add_mul, hz, hw, map_add, LinearMap.add_apply]
#align tensor_product.algebra.module TensorProduct.Algebra.module
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -374,7 +374,6 @@ variable {B : Type v₂} [Semiring B] [Algebra R B]
-/
-#print Algebra.TensorProduct.mulAux /-
/-- (Implementation detail)
The multiplication map on `A ⊗[R] B`,
for a fixed pure tensor in the first argument,
@@ -383,15 +382,12 @@ as an `R`-linear map.
def mulAux (a₁ : A) (b₁ : B) : A ⊗[R] B →ₗ[R] A ⊗[R] B :=
TensorProduct.map (LinearMap.mulLeft R a₁) (LinearMap.mulLeft R b₁)
#align algebra.tensor_product.mul_aux Algebra.TensorProduct.mulAux
--/
-#print Algebra.TensorProduct.mulAux_apply /-
@[simp]
theorem mulAux_apply (a₁ a₂ : A) (b₁ b₂ : B) :
(mulAux a₁ b₁) (a₂ ⊗ₜ[R] b₂) = (a₁ * a₂) ⊗ₜ[R] (b₁ * b₂) :=
rfl
#align algebra.tensor_product.mul_aux_apply Algebra.TensorProduct.mulAux_apply
--/
#print Algebra.TensorProduct.mul /-
/-- (Implementation detail)
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -935,13 +935,11 @@ theorem assoc_aux_1 (a₁ a₂ : A) (b₁ b₂ : B) (c₁ c₂ : C) :
#align algebra.tensor_product.assoc_aux_1 Algebra.TensorProduct.assoc_aux_1
-/
-#print Algebra.TensorProduct.assoc_aux_2 /-
theorem assoc_aux_2 (r : R) :
(TensorProduct.assoc R A B C) (((algebraMap R A) r ⊗ₜ[R] 1) ⊗ₜ[R] 1) =
(algebraMap R (A ⊗ (B ⊗ C))) r :=
rfl
-#align algebra.tensor_product.assoc_aux_2 Algebra.TensorProduct.assoc_aux_2
--/
+#align algebra.tensor_product.assoc_aux_2 Algebra.TensorProduct.assoc_aux_2ₓ
variable (R A B C)
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -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, Johan Commelin
-/
-import Mathbin.LinearAlgebra.FiniteDimensional
-import Mathbin.RingTheory.Adjoin.Basic
-import Mathbin.LinearAlgebra.DirectSum.Finsupp
+import LinearAlgebra.FiniteDimensional
+import RingTheory.Adjoin.Basic
+import LinearAlgebra.DirectSum.Finsupp
#align_import ring_theory.tensor_product from "leanprover-community/mathlib"@"88fcdc3da43943f5b01925deddaa5bf0c0e85e4e"
mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504
@@ -1328,7 +1328,7 @@ protected def module : Module (A ⊗[R] B) M
smul_add x m₁ m₂ := by simp only [map_add]
add_smul x y m := by simp only [map_add, LinearMap.add_apply]
one_smul m := by simp only [module_aux_apply, Algebra.TensorProduct.one_def, one_smul]
- mul_smul x y m :=
+ hMul_smul x y m :=
by
apply TensorProduct.induction_on x <;> apply TensorProduct.induction_on y
· simp only [MulZeroClass.mul_zero, map_zero, LinearMap.zero_apply]
mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504
@@ -642,14 +642,12 @@ theorem includeRight_apply (b : B) : (includeRight : B →ₐ[R] A ⊗[R] B) b =
#align algebra.tensor_product.include_right_apply Algebra.TensorProduct.includeRight_apply
-/
-#print Algebra.TensorProduct.includeLeft_comp_algebraMap /-
-theorem includeLeft_comp_algebraMap {R S T : Type _} [CommRing R] [CommRing S] [CommRing T]
+theorem includeLeftRingHom_comp_algebraMap {R S T : Type _} [CommRing R] [CommRing S] [CommRing T]
[Algebra R S] [Algebra R T] :
(includeLeft.toRingHom.comp (algebraMap R S) : R →+* S ⊗[R] T) =
includeRight.toRingHom.comp (algebraMap R T) :=
by ext; simp
-#align algebra.tensor_product.include_left_comp_algebra_map Algebra.TensorProduct.includeLeft_comp_algebraMap
--/
+#align algebra.tensor_product.include_left_comp_algebra_map Algebra.TensorProduct.includeLeftRingHom_comp_algebraMapₓ
end Semiring
mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504
@@ -169,7 +169,6 @@ theorem lift_tmul (f : M →ₗ[A] N →ₗ[R] P) (x : M) (y : N) : lift f (x
variable (R A M N P)
-#print TensorProduct.AlgebraTensorModule.uncurry /-
/-- Heterobasic version of `tensor_product.uncurry`:
Linearly constructing a linear map `M ⊗[R] N →[A] P` given a bilinear map `M →[A] N →[R] P`
@@ -181,10 +180,8 @@ def uncurry : (M →ₗ[A] N →ₗ[R] P) →ₗ[A] M ⊗[R] N →ₗ[A] P
toFun := lift
map_add' f g := ext fun x y => by simp only [lift_tmul, add_apply]
map_smul' c f := ext fun x y => by simp only [lift_tmul, smul_apply, RingHom.id_apply]
-#align tensor_product.algebra_tensor_module.uncurry TensorProduct.AlgebraTensorModule.uncurry
--/
+#align tensor_product.algebra_tensor_module.uncurry TensorProduct.AlgebraTensorModule.uncurryₓ
-#print TensorProduct.AlgebraTensorModule.lcurry /-
/-- Heterobasic version of `tensor_product.lcurry`:
Given a linear map `M ⊗[R] N →[A] P`, compose it with the canonical
@@ -195,10 +192,8 @@ def lcurry : (M ⊗[R] N →ₗ[A] P) →ₗ[A] M →ₗ[A] N →ₗ[R] P
toFun := curry
map_add' f g := rfl
map_smul' c f := rfl
-#align tensor_product.algebra_tensor_module.lcurry TensorProduct.AlgebraTensorModule.lcurry
--/
+#align tensor_product.algebra_tensor_module.lcurry TensorProduct.AlgebraTensorModule.lcurryₓ
-#print TensorProduct.AlgebraTensorModule.lift.equiv /-
/-- Heterobasic version of `tensor_product.lift.equiv`:
A linear equivalence constructing a linear map `M ⊗[R] N →[A] P` given a
@@ -208,8 +203,7 @@ def lift.equiv : (M →ₗ[A] N →ₗ[R] P) ≃ₗ[A] M ⊗[R] N →ₗ[A] P :=
LinearEquiv.ofLinear (uncurry R A M N P) (lcurry R A M N P)
(LinearMap.ext fun f => ext fun x y => lift_tmul _ x y)
(LinearMap.ext fun f => LinearMap.ext fun x => LinearMap.ext fun y => lift_tmul f x y)
-#align tensor_product.algebra_tensor_module.lift.equiv TensorProduct.AlgebraTensorModule.lift.equiv
--/
+#align tensor_product.algebra_tensor_module.lift.equiv TensorProduct.AlgebraTensorModule.lift.equivₓ
variable (R A M N P)
@@ -225,7 +219,6 @@ def mk : M →ₗ[A] N →ₗ[R] M ⊗[R] N :=
attribute [local ext] TensorProduct.ext
-#print TensorProduct.AlgebraTensorModule.assoc /-
/-- Heterobasic version of `tensor_product.assoc`:
Linear equivalence between `(M ⊗[A] N) ⊗[R] P` and `M ⊗[A] (N ⊗[R] P)`. -/
@@ -241,8 +234,7 @@ def assoc : (M ⊗[A] P) ⊗[R] N ≃ₗ[A] M ⊗[A] P ⊗[R] N :=
uncurry_apply, TensorProduct.uncurry_apply, id_apply, lift_tmul, compr₂_apply,
restrict_scalars_apply, Function.comp_apply, to_fun_eq_coe, lcurry_apply,
LinearMap.comp_apply])
-#align tensor_product.algebra_tensor_module.assoc TensorProduct.AlgebraTensorModule.assoc
--/
+#align tensor_product.algebra_tensor_module.assoc TensorProduct.AlgebraTensorModule.assocₓ
end CommSemiring
mathlib commit https://github.com/leanprover-community/mathlib/commit/63721b2c3eba6c325ecf8ae8cca27155a4f6306f
@@ -432,7 +432,6 @@ theorem mul_apply (a₁ a₂ : A) (b₁ b₂ : B) :
#align algebra.tensor_product.mul_apply Algebra.TensorProduct.mul_apply
-/
-#print Algebra.TensorProduct.mul_assoc' /-
theorem mul_assoc' (mul : A ⊗[R] B →ₗ[R] A ⊗[R] B →ₗ[R] A ⊗[R] B)
(h :
∀ (a₁ a₂ a₃ : A) (b₁ b₂ b₃ : B),
@@ -452,7 +451,6 @@ theorem mul_assoc' (mul : A ⊗[R] B →ₗ[R] A ⊗[R] B →ₗ[R] A ⊗[R] B)
· intros; simp only [LinearMap.map_add, *, LinearMap.add_apply]
· intros; simp only [LinearMap.map_add, *, LinearMap.add_apply]
#align algebra.tensor_product.mul_assoc' Algebra.TensorProduct.mul_assoc'
--/
#print Algebra.TensorProduct.mul_assoc /-
protected theorem mul_assoc (x y z : A ⊗[R] B) : mul (mul x y) z = mul x (mul y z) :=
@@ -532,6 +530,7 @@ def includeLeftRingHom : A →+* A ⊗[R] B
variable {S : Type _}
+#print Algebra.TensorProduct.isScalarTower_right /-
-- we want `is_scalar_tower_right` to take priority since it's better for unification elsewhere
instance (priority := 100) isScalarTower_right [Monoid S] [DistribMulAction S A]
[IsScalarTower S A A] [SMulCommClass R S A] : IsScalarTower S (A ⊗[R] B) (A ⊗[R] B)
@@ -547,7 +546,9 @@ instance (priority := 100) isScalarTower_right [Monoid S] [DistribMulAction S A]
· intros; simp [smul_add, add_mul, *]
· intros; simp [smul_add, mul_add, *]
#align algebra.tensor_product.is_scalar_tower_right Algebra.TensorProduct.isScalarTower_right
+-/
+#print Algebra.TensorProduct.sMulCommClass_right /-
-- we want `algebra.to_smul_comm_class` to take priority since it's better for unification elsewhere
instance (priority := 100) sMulCommClass_right [Monoid S] [DistribMulAction S A]
[SMulCommClass S A A] [SMulCommClass R S A] : SMulCommClass S (A ⊗[R] B) (A ⊗[R] B)
@@ -563,6 +564,7 @@ instance (priority := 100) sMulCommClass_right [Monoid S] [DistribMulAction S A]
· intros; simp [smul_add, add_mul, *]
· intros; simp [smul_add, mul_add, *]
#align algebra.tensor_product.smul_comm_class_right Algebra.TensorProduct.sMulCommClass_right
+-/
variable [CommSemiring S] [Algebra S A]
mathlib commit https://github.com/leanprover-community/mathlib/commit/88fcdc3da43943f5b01925deddaa5bf0c0e85e4e
@@ -7,7 +7,7 @@ import Mathbin.LinearAlgebra.FiniteDimensional
import Mathbin.RingTheory.Adjoin.Basic
import Mathbin.LinearAlgebra.DirectSum.Finsupp
-#align_import ring_theory.tensor_product from "leanprover-community/mathlib"@"69b2e97a276619372b19cf80fc1e91b05ae2baa4"
+#align_import ring_theory.tensor_product from "leanprover-community/mathlib"@"88fcdc3da43943f5b01925deddaa5bf0c0e85e4e"
/-!
# The tensor product of R-algebras
@@ -455,19 +455,19 @@ theorem mul_assoc' (mul : A ⊗[R] B →ₗ[R] A ⊗[R] B →ₗ[R] A ⊗[R] B)
-/
#print Algebra.TensorProduct.mul_assoc /-
-theorem mul_assoc (x y z : A ⊗[R] B) : mul (mul x y) z = mul x (mul y z) :=
+protected theorem mul_assoc (x y z : A ⊗[R] B) : mul (mul x y) z = mul x (mul y z) :=
mul_assoc' mul (by intros; simp only [mul_apply, mul_assoc]) x y z
#align algebra.tensor_product.mul_assoc Algebra.TensorProduct.mul_assoc
-/
#print Algebra.TensorProduct.one_mul /-
-theorem one_mul (x : A ⊗[R] B) : mul (1 ⊗ₜ 1) x = x := by
+protected theorem one_mul (x : A ⊗[R] B) : mul (1 ⊗ₜ 1) x = x := by
apply TensorProduct.induction_on x <;> simp (config := { contextual := true })
#align algebra.tensor_product.one_mul Algebra.TensorProduct.one_mul
-/
#print Algebra.TensorProduct.mul_one /-
-theorem mul_one (x : A ⊗[R] B) : mul x (1 ⊗ₜ 1) = x := by
+protected theorem mul_one (x : A ⊗[R] B) : mul x (1 ⊗ₜ 1) = x := by
apply TensorProduct.induction_on x <;> simp (config := { contextual := true })
#align algebra.tensor_product.mul_one Algebra.TensorProduct.mul_one
-/
@@ -485,9 +485,9 @@ instance : Semiring (A ⊗[R] B) :=
add := (· + ·)
one := 1
mul := fun a b => mul a b
- one_mul := one_mul
- mul_one := mul_one
- mul_assoc := mul_assoc
+ one_mul := Algebra.TensorProduct.one_mul
+ mul_one := Algebra.TensorProduct.mul_one
+ mul_assoc := Algebra.TensorProduct.mul_assoc
zero_mul := by simp
mul_zero := by simp
left_distrib := by simp
@@ -530,7 +530,41 @@ def includeLeftRingHom : A →+* A ⊗[R] B
#align algebra.tensor_product.include_left_ring_hom Algebra.TensorProduct.includeLeftRingHom
-/
-variable {S : Type _} [CommSemiring S] [Algebra S A]
+variable {S : Type _}
+
+-- we want `is_scalar_tower_right` to take priority since it's better for unification elsewhere
+instance (priority := 100) isScalarTower_right [Monoid S] [DistribMulAction S A]
+ [IsScalarTower S A A] [SMulCommClass R S A] : IsScalarTower S (A ⊗[R] B) (A ⊗[R] B)
+ where smul_assoc r x y := by
+ change r • x * y = r • (x * y)
+ apply TensorProduct.induction_on y
+ · simp [smul_zero]
+ · apply TensorProduct.induction_on x
+ · simp [smul_zero]
+ · intro a b a' b'
+ dsimp
+ rw [TensorProduct.smul_tmul', TensorProduct.smul_tmul', tmul_mul_tmul, smul_mul_assoc]
+ · intros; simp [smul_add, add_mul, *]
+ · intros; simp [smul_add, mul_add, *]
+#align algebra.tensor_product.is_scalar_tower_right Algebra.TensorProduct.isScalarTower_right
+
+-- we want `algebra.to_smul_comm_class` to take priority since it's better for unification elsewhere
+instance (priority := 100) sMulCommClass_right [Monoid S] [DistribMulAction S A]
+ [SMulCommClass S A A] [SMulCommClass R S A] : SMulCommClass S (A ⊗[R] B) (A ⊗[R] B)
+ where smul_comm r x y := by
+ change r • (x * y) = x * r • y
+ apply TensorProduct.induction_on y
+ · simp [smul_zero]
+ · apply TensorProduct.induction_on x
+ · simp [smul_zero]
+ · intro a b a' b'
+ dsimp
+ rw [TensorProduct.smul_tmul', TensorProduct.smul_tmul', tmul_mul_tmul, mul_smul_comm]
+ · intros; simp [smul_add, add_mul, *]
+ · intros; simp [smul_add, mul_add, *]
+#align algebra.tensor_product.smul_comm_class_right Algebra.TensorProduct.sMulCommClass_right
+
+variable [CommSemiring S] [Algebra S A]
#print Algebra.TensorProduct.leftAlgebra /-
instance leftAlgebra [SMulCommClass R S A] : Algebra S (A ⊗[R] B) :=
@@ -539,16 +573,15 @@ instance leftAlgebra [SMulCommClass R S A] : Algebra S (A ⊗[R] B) :=
Module S
(A ⊗[R]
B)) with
- commutes' := fun r x => by
- apply TensorProduct.induction_on x
- · simp
- · intro a b; dsimp; rw [Algebra.commutes, _root_.mul_one, _root_.one_mul]
- · intro y y' h h'; dsimp at h h' ⊢; simp only [mul_add, add_mul, h, h']
- smul_def' := fun r x => by
- apply TensorProduct.induction_on x
- · simp [smul_zero]
- · intro a b; dsimp; rw [TensorProduct.smul_tmul', Algebra.smul_def r a, _root_.one_mul]
- · intros; dsimp; simp [smul_add, mul_add, *] }
+ commutes' := fun r x =>
+ by
+ dsimp only [RingHom.toFun_eq_coe, RingHom.comp_apply, include_left_ring_hom_apply]
+ rw [algebra_map_eq_smul_one, ← smul_tmul', ← one_def, mul_smul_comm, smul_mul_assoc, mul_one,
+ one_mul]
+ smul_def' := fun r x =>
+ by
+ dsimp only [RingHom.toFun_eq_coe, RingHom.comp_apply, include_left_ring_hom_apply]
+ rw [algebra_map_eq_smul_one, ← smul_tmul', smul_mul_assoc, ← one_def, one_mul] }
#align algebra.tensor_product.left_algebra Algebra.TensorProduct.leftAlgebra
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -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, Johan Commelin
-
-! This file was ported from Lean 3 source module ring_theory.tensor_product
-! leanprover-community/mathlib commit 69b2e97a276619372b19cf80fc1e91b05ae2baa4
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.LinearAlgebra.FiniteDimensional
import Mathbin.RingTheory.Adjoin.Basic
import Mathbin.LinearAlgebra.DirectSum.Finsupp
+#align_import ring_theory.tensor_product from "leanprover-community/mathlib"@"69b2e97a276619372b19cf80fc1e91b05ae2baa4"
+
/-!
# The tensor product of R-algebras
mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303
@@ -1227,7 +1227,7 @@ def endTensorEndAlgHom : End R M ⊗[R] End R N →ₐ[R] End R (M ⊗[R] N) :=
simp only [hom_tensor_hom_map_apply, TensorProduct.map_mul]
· intro r
simp only [hom_tensor_hom_map_apply]
- ext (m n); simp [smul_tmul]
+ ext m n; simp [smul_tmul]
#align module.End_tensor_End_alg_hom Module.endTensorEndAlgHom
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -82,9 +82,11 @@ variable [AddCommMonoid N] [Module R N]
variable [AddCommMonoid P] [Module R P] [Module A P] [IsScalarTower R A P]
+#print TensorProduct.AlgebraTensorModule.smul_eq_lsmul_rTensor /-
theorem smul_eq_lsmul_rTensor (a : A) (x : M ⊗[R] N) : a • x = (lsmul R M a).rTensor N x :=
rfl
#align tensor_product.algebra_tensor_module.smul_eq_lsmul_rtensor TensorProduct.AlgebraTensorModule.smul_eq_lsmul_rTensor
+-/
#print TensorProduct.AlgebraTensorModule.curry /-
/-- Heterobasic version of `tensor_product.curry`:
@@ -101,11 +103,14 @@ def curry (f : M ⊗[R] N →ₗ[A] P) : M →ₗ[A] N →ₗ[R] P :=
#align tensor_product.algebra_tensor_module.curry TensorProduct.AlgebraTensorModule.curry
-/
+#print TensorProduct.AlgebraTensorModule.restrictScalars_curry /-
theorem restrictScalars_curry (f : M ⊗[R] N →ₗ[A] P) :
RestrictScalars R (curry f) = curry (f.restrictScalars R) :=
rfl
#align tensor_product.algebra_tensor_module.restrict_scalars_curry TensorProduct.AlgebraTensorModule.restrictScalars_curry
+-/
+#print TensorProduct.AlgebraTensorModule.curry_injective /-
/-- Just as `tensor_product.ext` is marked `ext` instead of `tensor_product.ext'`, this is
a better `ext` lemma than `tensor_product.algebra_tensor_module.ext` below.
@@ -116,10 +121,13 @@ theorem curry_injective : Function.Injective (curry : (M ⊗ N →ₗ[A] P) →
LinearMap.restrictScalars_injective R <|
curry_injective <| (congr_arg (LinearMap.restrictScalars R) h : _)
#align tensor_product.algebra_tensor_module.curry_injective TensorProduct.AlgebraTensorModule.curry_injective
+-/
+#print TensorProduct.AlgebraTensorModule.ext /-
theorem ext {g h : M ⊗[R] N →ₗ[A] P} (H : ∀ x y, g (x ⊗ₜ y) = h (x ⊗ₜ y)) : g = h :=
curry_injective <| LinearMap.ext₂ H
#align tensor_product.algebra_tensor_module.ext TensorProduct.AlgebraTensorModule.ext
+-/
end Semiring
@@ -155,10 +163,12 @@ def lift (f : M →ₗ[A] N →ₗ[R] P) : M ⊗[R] N →ₗ[A] P :=
#align tensor_product.algebra_tensor_module.lift TensorProduct.AlgebraTensorModule.lift
-/
+#print TensorProduct.AlgebraTensorModule.lift_tmul /-
@[simp]
theorem lift_tmul (f : M →ₗ[A] N →ₗ[R] P) (x : M) (y : N) : lift f (x ⊗ₜ y) = f x y :=
rfl
#align tensor_product.algebra_tensor_module.lift_tmul TensorProduct.AlgebraTensorModule.lift_tmul
+-/
variable (R A M N P)
@@ -206,6 +216,7 @@ def lift.equiv : (M →ₗ[A] N →ₗ[R] P) ≃ₗ[A] M ⊗[R] N →ₗ[A] P :=
variable (R A M N P)
+#print TensorProduct.AlgebraTensorModule.mk /-
/-- Heterobasic version of `tensor_product.mk`:
The canonical bilinear map `M →[A] N →[R] M ⊗[R] N`. -/
@@ -213,6 +224,7 @@ The canonical bilinear map `M →[A] N →[R] M ⊗[R] N`. -/
def mk : M →ₗ[A] N →ₗ[R] M ⊗[R] N :=
{ mk R M N with map_smul' := fun c x => rfl }
#align tensor_product.algebra_tensor_module.mk TensorProduct.AlgebraTensorModule.mk
+-/
attribute [local ext] TensorProduct.ext
@@ -280,28 +292,38 @@ def baseChange (f : M →ₗ[R] N) : A ⊗[R] M →ₗ[A] A ⊗[R] N
variable {A}
+#print LinearMap.baseChange_tmul /-
@[simp]
theorem baseChange_tmul (a : A) (x : M) : f.base_change A (a ⊗ₜ x) = a ⊗ₜ f x :=
rfl
#align linear_map.base_change_tmul LinearMap.baseChange_tmul
+-/
+#print LinearMap.baseChange_eq_ltensor /-
theorem baseChange_eq_ltensor : (f.base_change A : A ⊗ M → A ⊗ N) = f.lTensor A :=
rfl
#align linear_map.base_change_eq_ltensor LinearMap.baseChange_eq_ltensor
+-/
+#print LinearMap.baseChange_add /-
@[simp]
theorem baseChange_add : (f + g).base_change A = f.base_change A + g.base_change A := by ext;
simp [base_change_eq_ltensor]
#align linear_map.base_change_add LinearMap.baseChange_add
+-/
+#print LinearMap.baseChange_zero /-
@[simp]
theorem baseChange_zero : baseChange A (0 : M →ₗ[R] N) = 0 := by ext; simp [base_change_eq_ltensor]
#align linear_map.base_change_zero LinearMap.baseChange_zero
+-/
+#print LinearMap.baseChange_smul /-
@[simp]
theorem baseChange_smul : (r • f).base_change A = r • f.base_change A := by ext;
simp [base_change_tmul]
#align linear_map.base_change_smul LinearMap.baseChange_smul
+-/
variable (R A M N)
@@ -328,15 +350,19 @@ variable [AddCommGroup M] [Module R M] [AddCommGroup N] [Module R N]
variable (f g : M →ₗ[R] N)
+#print LinearMap.baseChange_sub /-
@[simp]
theorem baseChange_sub : (f - g).base_change A = f.base_change A - g.base_change A := by ext;
simp [base_change_eq_ltensor]
#align linear_map.base_change_sub LinearMap.baseChange_sub
+-/
+#print LinearMap.baseChange_neg /-
@[simp]
theorem baseChange_neg : (-f).base_change A = -f.base_change A := by ext;
simp [base_change_eq_ltensor]
#align linear_map.base_change_neg LinearMap.baseChange_neg
+-/
end Ring
@@ -359,6 +385,7 @@ variable {B : Type v₂} [Semiring B] [Algebra R B]
-/
+#print Algebra.TensorProduct.mulAux /-
/-- (Implementation detail)
The multiplication map on `A ⊗[R] B`,
for a fixed pure tensor in the first argument,
@@ -367,13 +394,17 @@ as an `R`-linear map.
def mulAux (a₁ : A) (b₁ : B) : A ⊗[R] B →ₗ[R] A ⊗[R] B :=
TensorProduct.map (LinearMap.mulLeft R a₁) (LinearMap.mulLeft R b₁)
#align algebra.tensor_product.mul_aux Algebra.TensorProduct.mulAux
+-/
+#print Algebra.TensorProduct.mulAux_apply /-
@[simp]
theorem mulAux_apply (a₁ a₂ : A) (b₁ b₂ : B) :
(mulAux a₁ b₁) (a₂ ⊗ₜ[R] b₂) = (a₁ * a₂) ⊗ₜ[R] (b₁ * b₂) :=
rfl
#align algebra.tensor_product.mul_aux_apply Algebra.TensorProduct.mulAux_apply
+-/
+#print Algebra.TensorProduct.mul /-
/-- (Implementation detail)
The multiplication map on `A ⊗[R] B`,
as an `R`-bilinear map.
@@ -394,13 +425,17 @@ def mul : A ⊗[R] B →ₗ[R] A ⊗[R] B →ₗ[R] A ⊗[R] B :=
TensorProduct.ext' fun x' y' => by
simp only [mul_aux_apply, LinearMap.smul_apply, smul_tmul, smul_tmul', smul_mul_assoc]
#align algebra.tensor_product.mul Algebra.TensorProduct.mul
+-/
+#print Algebra.TensorProduct.mul_apply /-
@[simp]
theorem mul_apply (a₁ a₂ : A) (b₁ b₂ : B) :
mul (a₁ ⊗ₜ[R] b₁) (a₂ ⊗ₜ[R] b₂) = (a₁ * a₂) ⊗ₜ[R] (b₁ * b₂) :=
rfl
#align algebra.tensor_product.mul_apply Algebra.TensorProduct.mul_apply
+-/
+#print Algebra.TensorProduct.mul_assoc' /-
theorem mul_assoc' (mul : A ⊗[R] B →ₗ[R] A ⊗[R] B →ₗ[R] A ⊗[R] B)
(h :
∀ (a₁ a₂ a₃ : A) (b₁ b₂ b₃ : B),
@@ -420,18 +455,25 @@ theorem mul_assoc' (mul : A ⊗[R] B →ₗ[R] A ⊗[R] B →ₗ[R] A ⊗[R] B)
· intros; simp only [LinearMap.map_add, *, LinearMap.add_apply]
· intros; simp only [LinearMap.map_add, *, LinearMap.add_apply]
#align algebra.tensor_product.mul_assoc' Algebra.TensorProduct.mul_assoc'
+-/
+#print Algebra.TensorProduct.mul_assoc /-
theorem mul_assoc (x y z : A ⊗[R] B) : mul (mul x y) z = mul x (mul y z) :=
mul_assoc' mul (by intros; simp only [mul_apply, mul_assoc]) x y z
#align algebra.tensor_product.mul_assoc Algebra.TensorProduct.mul_assoc
+-/
+#print Algebra.TensorProduct.one_mul /-
theorem one_mul (x : A ⊗[R] B) : mul (1 ⊗ₜ 1) x = x := by
apply TensorProduct.induction_on x <;> simp (config := { contextual := true })
#align algebra.tensor_product.one_mul Algebra.TensorProduct.one_mul
+-/
+#print Algebra.TensorProduct.mul_one /-
theorem mul_one (x : A ⊗[R] B) : mul x (1 ⊗ₜ 1) = x := by
apply TensorProduct.induction_on x <;> simp (config := { contextual := true })
#align algebra.tensor_product.mul_one Algebra.TensorProduct.mul_one
+-/
instance : One (A ⊗[R] B) where one := 1 ⊗ₜ 1
@@ -460,12 +502,15 @@ theorem one_def : (1 : A ⊗[R] B) = (1 : A) ⊗ₜ (1 : B) :=
#align algebra.tensor_product.one_def Algebra.TensorProduct.one_def
-/
+#print Algebra.TensorProduct.tmul_mul_tmul /-
@[simp]
theorem tmul_mul_tmul (a₁ a₂ : A) (b₁ b₂ : B) :
a₁ ⊗ₜ[R] b₁ * a₂ ⊗ₜ[R] b₂ = (a₁ * a₂) ⊗ₜ[R] (b₁ * b₂) :=
rfl
#align algebra.tensor_product.tmul_mul_tmul Algebra.TensorProduct.tmul_mul_tmul
+-/
+#print Algebra.TensorProduct.tmul_pow /-
@[simp]
theorem tmul_pow (a : A) (b : B) (k : ℕ) : a ⊗ₜ[R] b ^ k = (a ^ k) ⊗ₜ[R] (b ^ k) :=
by
@@ -473,7 +518,9 @@ theorem tmul_pow (a : A) (b : B) (k : ℕ) : a ⊗ₜ[R] b ^ k = (a ^ k) ⊗ₜ[
· simp [one_def]
· simp [pow_succ, ih]
#align algebra.tensor_product.tmul_pow Algebra.TensorProduct.tmul_pow
+-/
+#print Algebra.TensorProduct.includeLeftRingHom /-
/-- The ring morphism `A →+* A ⊗[R] B` sending `a` to `a ⊗ₜ 1`. -/
@[simps]
def includeLeftRingHom : A →+* A ⊗[R] B
@@ -484,9 +531,11 @@ def includeLeftRingHom : A →+* A ⊗[R] B
map_one' := rfl
map_mul' := by simp
#align algebra.tensor_product.include_left_ring_hom Algebra.TensorProduct.includeLeftRingHom
+-/
variable {S : Type _} [CommSemiring S] [Algebra S A]
+#print Algebra.TensorProduct.leftAlgebra /-
instance leftAlgebra [SMulCommClass R S A] : Algebra S (A ⊗[R] B) :=
{ TensorProduct.includeLeftRingHom.comp (algebraMap S A),
(by infer_instance :
@@ -504,20 +553,24 @@ instance leftAlgebra [SMulCommClass R S A] : Algebra S (A ⊗[R] B) :=
· intro a b; dsimp; rw [TensorProduct.smul_tmul', Algebra.smul_def r a, _root_.one_mul]
· intros; dsimp; simp [smul_add, mul_add, *] }
#align algebra.tensor_product.left_algebra Algebra.TensorProduct.leftAlgebra
+-/
-- This is for the `undergrad.yaml` list.
/-- The tensor product of two `R`-algebras is an `R`-algebra. -/
instance : Algebra R (A ⊗[R] B) :=
inferInstance
+#print Algebra.TensorProduct.algebraMap_apply /-
@[simp]
theorem algebraMap_apply [SMulCommClass R S A] (r : S) :
(algebraMap S (A ⊗[R] B)) r = (algebraMap S A) r ⊗ₜ 1 :=
rfl
#align algebra.tensor_product.algebra_map_apply Algebra.TensorProduct.algebraMap_apply
+-/
variable {C : Type v₃} [Semiring C] [Algebra R C]
+#print Algebra.TensorProduct.ext /-
@[ext]
theorem ext {g h : A ⊗[R] B →ₐ[R] C} (H : ∀ a b, g (a ⊗ₜ b) = h (a ⊗ₜ b)) : g = h :=
by
@@ -525,18 +578,24 @@ theorem ext {g h : A ⊗[R] B →ₐ[R] C} (H : ∀ a b, g (a ⊗ₜ b) = h (a
ext
simp [H]
#align algebra.tensor_product.ext Algebra.TensorProduct.ext
+-/
+#print Algebra.TensorProduct.includeLeft /-
-- TODO: with `smul_comm_class R S A` we can have this as an `S`-algebra morphism
/-- The `R`-algebra morphism `A →ₐ[R] A ⊗[R] B` sending `a` to `a ⊗ₜ 1`. -/
def includeLeft : A →ₐ[R] A ⊗[R] B :=
{ includeLeftRingHom with commutes' := by simp }
#align algebra.tensor_product.include_left Algebra.TensorProduct.includeLeft
+-/
+#print Algebra.TensorProduct.includeLeft_apply /-
@[simp]
theorem includeLeft_apply (a : A) : (includeLeft : A →ₐ[R] A ⊗[R] B) a = a ⊗ₜ 1 :=
rfl
#align algebra.tensor_product.include_left_apply Algebra.TensorProduct.includeLeft_apply
+-/
+#print Algebra.TensorProduct.includeRight /-
/-- The algebra morphism `B →ₐ[R] A ⊗[R] B` sending `b` to `1 ⊗ₜ b`. -/
def includeRight : B →ₐ[R] A ⊗[R] B where
toFun b := 1 ⊗ₜ b
@@ -550,18 +609,23 @@ def includeRight : B →ₐ[R] A ⊗[R] B where
· rw [← tmul_smul, Algebra.smul_def]; simp
· simp [Algebra.smul_def]
#align algebra.tensor_product.include_right Algebra.TensorProduct.includeRight
+-/
+#print Algebra.TensorProduct.includeRight_apply /-
@[simp]
theorem includeRight_apply (b : B) : (includeRight : B →ₐ[R] A ⊗[R] B) b = 1 ⊗ₜ b :=
rfl
#align algebra.tensor_product.include_right_apply Algebra.TensorProduct.includeRight_apply
+-/
+#print Algebra.TensorProduct.includeLeft_comp_algebraMap /-
theorem includeLeft_comp_algebraMap {R S T : Type _} [CommRing R] [CommRing S] [CommRing T]
[Algebra R S] [Algebra R T] :
(includeLeft.toRingHom.comp (algebraMap R S) : R →+* S ⊗[R] T) =
includeRight.toRingHom.comp (algebraMap R T) :=
by ext; simp
#align algebra.tensor_product.include_left_comp_algebra_map Algebra.TensorProduct.includeLeft_comp_algebraMap
+-/
end Semiring
@@ -603,18 +667,22 @@ instance : CommRing (A ⊗[R] B) :=
section RightAlgebra
+#print Algebra.TensorProduct.rightAlgebra /-
/-- `S ⊗[R] T` has a `T`-algebra structure. This is not a global instance or else the action of
`S` on `S ⊗[R] S` would be ambiguous. -/
@[reducible]
def rightAlgebra : Algebra B (A ⊗[R] B) :=
(Algebra.TensorProduct.includeRight.toRingHom : B →+* A ⊗[R] B).toAlgebra
#align algebra.tensor_product.right_algebra Algebra.TensorProduct.rightAlgebra
+-/
attribute [local instance] tensor_product.right_algebra
+#print Algebra.TensorProduct.right_isScalarTower /-
instance right_isScalarTower : IsScalarTower R B (A ⊗[R] B) :=
IsScalarTower.of_algebraMap_eq fun r => (Algebra.TensorProduct.includeRight.commutes r).symm
#align algebra.tensor_product.right_is_scalar_tower Algebra.TensorProduct.right_isScalarTower
+-/
end RightAlgebra
@@ -650,6 +718,7 @@ variable {C : Type v₃} [Semiring C] [Algebra R C]
variable {D : Type v₄} [Semiring D] [Algebra R D]
+#print Algebra.TensorProduct.algHomOfLinearMapTensorProduct /-
/-- Build an algebra morphism from a linear map out of a tensor product,
and evidence of multiplicativity on pure tensors.
-/
@@ -675,13 +744,17 @@ def algHomOfLinearMapTensorProduct (f : A ⊗[R] B →ₗ[R] C)
rw [add_mul, map_add, map_add, add_mul, h₁, h₂]
commutes' := fun r => by rw [LinearMap.toFun_eq_coe, algebraMap_apply, w₂] }
#align algebra.tensor_product.alg_hom_of_linear_map_tensor_product Algebra.TensorProduct.algHomOfLinearMapTensorProduct
+-/
+#print Algebra.TensorProduct.algHomOfLinearMapTensorProduct_apply /-
@[simp]
theorem algHomOfLinearMapTensorProduct_apply (f w₁ w₂ x) :
(algHomOfLinearMapTensorProduct f w₁ w₂ : A ⊗[R] B →ₐ[R] C) x = f x :=
rfl
#align algebra.tensor_product.alg_hom_of_linear_map_tensor_product_apply Algebra.TensorProduct.algHomOfLinearMapTensorProduct_apply
+-/
+#print Algebra.TensorProduct.algEquivOfLinearEquivTensorProduct /-
/-- Build an algebra equivalence from a linear equivalence out of a tensor product,
and evidence of multiplicativity on pure tensors.
-/
@@ -690,13 +763,17 @@ def algEquivOfLinearEquivTensorProduct (f : A ⊗[R] B ≃ₗ[R] C)
(w₂ : ∀ r, f ((algebraMap R A) r ⊗ₜ[R] 1) = (algebraMap R C) r) : A ⊗[R] B ≃ₐ[R] C :=
{ algHomOfLinearMapTensorProduct (f : A ⊗[R] B →ₗ[R] C) w₁ w₂, f with }
#align algebra.tensor_product.alg_equiv_of_linear_equiv_tensor_product Algebra.TensorProduct.algEquivOfLinearEquivTensorProduct
+-/
+#print Algebra.TensorProduct.algEquivOfLinearEquivTensorProduct_apply /-
@[simp]
theorem algEquivOfLinearEquivTensorProduct_apply (f w₁ w₂ x) :
(algEquivOfLinearEquivTensorProduct f w₁ w₂ : A ⊗[R] B ≃ₐ[R] C) x = f x :=
rfl
#align algebra.tensor_product.alg_equiv_of_linear_equiv_tensor_product_apply Algebra.TensorProduct.algEquivOfLinearEquivTensorProduct_apply
+-/
+#print Algebra.TensorProduct.algEquivOfLinearEquivTripleTensorProduct /-
/-- Build an algebra equivalence from a linear equivalence out of a triple tensor product,
and evidence of multiplicativity on pure tensors.
-/
@@ -733,12 +810,15 @@ def algEquivOfLinearEquivTripleTensorProduct (f : (A ⊗[R] B) ⊗[R] C ≃ₗ[R
simp only [tmul_mul_tmul, map_add, mul_add, add_mul, h₁, h₂]
commutes' := fun r => by simp [w₂] }
#align algebra.tensor_product.alg_equiv_of_linear_equiv_triple_tensor_product Algebra.TensorProduct.algEquivOfLinearEquivTripleTensorProduct
+-/
+#print Algebra.TensorProduct.algEquivOfLinearEquivTripleTensorProduct_apply /-
@[simp]
theorem algEquivOfLinearEquivTripleTensorProduct_apply (f w₁ w₂ x) :
(algEquivOfLinearEquivTripleTensorProduct f w₁ w₂ : (A ⊗[R] B) ⊗[R] C ≃ₐ[R] D) x = f x :=
rfl
#align algebra.tensor_product.alg_equiv_of_linear_equiv_triple_tensor_product_apply Algebra.TensorProduct.algEquivOfLinearEquivTripleTensorProduct_apply
+-/
end
@@ -756,34 +836,43 @@ section
variable (R A)
+#print Algebra.TensorProduct.lid /-
/-- The base ring is a left identity for the tensor product of algebra, up to algebra isomorphism.
-/
protected def lid : R ⊗[R] A ≃ₐ[R] A :=
algEquivOfLinearEquivTensorProduct (TensorProduct.lid R A) (by simp [mul_smul])
(by simp [Algebra.smul_def])
#align algebra.tensor_product.lid Algebra.TensorProduct.lid
+-/
+#print Algebra.TensorProduct.lid_tmul /-
@[simp]
theorem lid_tmul (r : R) (a : A) : (TensorProduct.lid R A : R ⊗ A → A) (r ⊗ₜ a) = r • a := by
simp [TensorProduct.lid]
#align algebra.tensor_product.lid_tmul Algebra.TensorProduct.lid_tmul
+-/
+#print Algebra.TensorProduct.rid /-
/-- The base ring is a right identity for the tensor product of algebra, up to algebra isomorphism.
-/
protected def rid : A ⊗[R] R ≃ₐ[R] A :=
algEquivOfLinearEquivTensorProduct (TensorProduct.rid R A) (by simp [mul_smul])
(by simp [Algebra.smul_def])
#align algebra.tensor_product.rid Algebra.TensorProduct.rid
+-/
+#print Algebra.TensorProduct.rid_tmul /-
@[simp]
theorem rid_tmul (r : R) (a : A) : (TensorProduct.rid R A : A ⊗ R → A) (a ⊗ₜ r) = r • a := by
simp [TensorProduct.rid]
#align algebra.tensor_product.rid_tmul Algebra.TensorProduct.rid_tmul
+-/
section
variable (R A B)
+#print Algebra.TensorProduct.comm /-
/-- The tensor product of R-algebras is commutative, up to algebra isomorphism.
-/
protected def comm : A ⊗[R] B ≃ₐ[R] B ⊗[R] A :=
@@ -793,16 +882,21 @@ protected def comm : A ⊗[R] B ≃ₐ[R] B ⊗[R] A :=
· rw [← tmul_smul, Algebra.smul_def]; simp
· simp [Algebra.smul_def]
#align algebra.tensor_product.comm Algebra.TensorProduct.comm
+-/
+#print Algebra.TensorProduct.comm_tmul /-
@[simp]
theorem comm_tmul (a : A) (b : B) :
(TensorProduct.comm R A B : A ⊗[R] B → B ⊗[R] A) (a ⊗ₜ b) = b ⊗ₜ a := by
simp [TensorProduct.comm]
#align algebra.tensor_product.comm_tmul Algebra.TensorProduct.comm_tmul
+-/
+#print Algebra.TensorProduct.adjoin_tmul_eq_top /-
theorem adjoin_tmul_eq_top : adjoin R {t : A ⊗[R] B | ∃ a b, a ⊗ₜ[R] b = t} = ⊤ :=
top_le_iff.mp <| (top_le_iff.mpr <| span_tmul_eq_top R A B).trans (span_le_adjoin R _)
#align algebra.tensor_product.adjoin_tmul_eq_top Algebra.TensorProduct.adjoin_tmul_eq_top
+-/
end
@@ -810,21 +904,26 @@ section
variable {R A B C}
+#print Algebra.TensorProduct.assoc_aux_1 /-
theorem assoc_aux_1 (a₁ a₂ : A) (b₁ b₂ : B) (c₁ c₂ : C) :
(TensorProduct.assoc R A B C) (((a₁ * a₂) ⊗ₜ[R] (b₁ * b₂)) ⊗ₜ[R] (c₁ * c₂)) =
(TensorProduct.assoc R A B C) ((a₁ ⊗ₜ[R] b₁) ⊗ₜ[R] c₁) *
(TensorProduct.assoc R A B C) ((a₂ ⊗ₜ[R] b₂) ⊗ₜ[R] c₂) :=
rfl
#align algebra.tensor_product.assoc_aux_1 Algebra.TensorProduct.assoc_aux_1
+-/
+#print Algebra.TensorProduct.assoc_aux_2 /-
theorem assoc_aux_2 (r : R) :
(TensorProduct.assoc R A B C) (((algebraMap R A) r ⊗ₜ[R] 1) ⊗ₜ[R] 1) =
(algebraMap R (A ⊗ (B ⊗ C))) r :=
rfl
#align algebra.tensor_product.assoc_aux_2 Algebra.TensorProduct.assoc_aux_2
+-/
variable (R A B C)
+#print Algebra.TensorProduct.assoc /-
/-- The associator for tensor product of R-algebras, as an algebra isomorphism. -/
protected def assoc : (A ⊗[R] B) ⊗[R] C ≃ₐ[R] A ⊗[R] B ⊗[R] C :=
algEquivOfLinearEquivTripleTensorProduct
@@ -832,43 +931,55 @@ protected def assoc : (A ⊗[R] B) ⊗[R] C ≃ₐ[R] A ⊗[R] B ⊗[R] C :=
(@Algebra.TensorProduct.assoc_aux_1.{u, v₁, v₂, v₃} R _ A _ _ B _ _ C _ _)
(@Algebra.TensorProduct.assoc_aux_2.{u, v₁, v₂, v₃} R _ A _ _ B _ _ C _ _)
#align algebra.tensor_product.assoc Algebra.TensorProduct.assoc
+-/
variable {R A B C}
+#print Algebra.TensorProduct.assoc_tmul /-
@[simp]
theorem assoc_tmul (a : A) (b : B) (c : C) :
(TensorProduct.assoc R A B C : (A ⊗[R] B) ⊗[R] C → A ⊗[R] B ⊗[R] C) (a ⊗ₜ b ⊗ₜ c) =
a ⊗ₜ (b ⊗ₜ c) :=
rfl
#align algebra.tensor_product.assoc_tmul Algebra.TensorProduct.assoc_tmul
+-/
end
variable {R A B C D}
+#print Algebra.TensorProduct.map /-
/-- The tensor product of a pair of algebra morphisms. -/
def map (f : A →ₐ[R] B) (g : C →ₐ[R] D) : A ⊗[R] C →ₐ[R] B ⊗[R] D :=
algHomOfLinearMapTensorProduct (TensorProduct.map f.toLinearMap g.toLinearMap) (by simp)
(by simp [AlgHom.commutes])
#align algebra.tensor_product.map Algebra.TensorProduct.map
+-/
+#print Algebra.TensorProduct.map_tmul /-
@[simp]
theorem map_tmul (f : A →ₐ[R] B) (g : C →ₐ[R] D) (a : A) (c : C) : map f g (a ⊗ₜ c) = f a ⊗ₜ g c :=
rfl
#align algebra.tensor_product.map_tmul Algebra.TensorProduct.map_tmul
+-/
+#print Algebra.TensorProduct.map_comp_includeLeft /-
@[simp]
theorem map_comp_includeLeft (f : A →ₐ[R] B) (g : C →ₐ[R] D) :
(map f g).comp includeLeft = includeLeft.comp f :=
AlgHom.ext <| by simp
#align algebra.tensor_product.map_comp_include_left Algebra.TensorProduct.map_comp_includeLeft
+-/
+#print Algebra.TensorProduct.map_comp_includeRight /-
@[simp]
theorem map_comp_includeRight (f : A →ₐ[R] B) (g : C →ₐ[R] D) :
(map f g).comp includeRight = includeRight.comp g :=
AlgHom.ext <| by simp
#align algebra.tensor_product.map_comp_include_right Algebra.TensorProduct.map_comp_includeRight
+-/
+#print Algebra.TensorProduct.map_range /-
theorem map_range (f : A →ₐ[R] B) (g : C →ₐ[R] D) :
(map f g).range = (includeLeft.comp f).range ⊔ (includeRight.comp g).range :=
by
@@ -880,25 +991,32 @@ theorem map_range (f : A →ₐ[R] B) (g : C →ₐ[R] D) :
· rw [← map_comp_include_left f g, ← map_comp_include_right f g]
exact sup_le (AlgHom.range_comp_le_range _ _) (AlgHom.range_comp_le_range _ _)
#align algebra.tensor_product.map_range Algebra.TensorProduct.map_range
+-/
+#print Algebra.TensorProduct.congr /-
/-- Construct an isomorphism between tensor products of R-algebras
from isomorphisms between the tensor factors.
-/
def congr (f : A ≃ₐ[R] B) (g : C ≃ₐ[R] D) : A ⊗[R] C ≃ₐ[R] B ⊗[R] D :=
AlgEquiv.ofAlgHom (map f g) (map f.symm g.symm) (ext fun b d => by simp) (ext fun a c => by simp)
#align algebra.tensor_product.congr Algebra.TensorProduct.congr
+-/
+#print Algebra.TensorProduct.congr_apply /-
@[simp]
theorem congr_apply (f : A ≃ₐ[R] B) (g : C ≃ₐ[R] D) (x) :
congr f g x = (map (f : A →ₐ[R] B) (g : C →ₐ[R] D)) x :=
rfl
#align algebra.tensor_product.congr_apply Algebra.TensorProduct.congr_apply
+-/
+#print Algebra.TensorProduct.congr_symm_apply /-
@[simp]
theorem congr_symm_apply (f : A ≃ₐ[R] B) (g : C ≃ₐ[R] D) (x) :
(congr f g).symm x = (map (f.symm : B →ₐ[R] A) (g.symm : D →ₐ[R] C)) x :=
rfl
#align algebra.tensor_product.congr_symm_apply Algebra.TensorProduct.congr_symm_apply
+-/
end
@@ -914,23 +1032,29 @@ variable (f : A →ₐ[R] S) (g : B →ₐ[R] S)
variable (R)
+#print Algebra.TensorProduct.lmul' /-
/-- `linear_map.mul'` is an alg_hom on commutative rings. -/
def lmul' : S ⊗[R] S →ₐ[R] S :=
algHomOfLinearMapTensorProduct (LinearMap.mul' R S)
(fun a₁ a₂ b₁ b₂ => by simp only [LinearMap.mul'_apply, mul_mul_mul_comm]) fun r => by
simp only [LinearMap.mul'_apply, _root_.mul_one]
#align algebra.tensor_product.lmul' Algebra.TensorProduct.lmul'
+-/
variable {R}
+#print Algebra.TensorProduct.lmul'_toLinearMap /-
theorem lmul'_toLinearMap : (lmul' R : _ →ₐ[R] S).toLinearMap = LinearMap.mul' R S :=
rfl
#align algebra.tensor_product.lmul'_to_linear_map Algebra.TensorProduct.lmul'_toLinearMap
+-/
+#print Algebra.TensorProduct.lmul'_apply_tmul /-
@[simp]
theorem lmul'_apply_tmul (a b : S) : lmul' R (a ⊗ₜ[R] b) = a * b :=
rfl
#align algebra.tensor_product.lmul'_apply_tmul Algebra.TensorProduct.lmul'_apply_tmul
+-/
#print Algebra.TensorProduct.lmul'_comp_includeLeft /-
@[simp]
@@ -946,40 +1070,54 @@ theorem lmul'_comp_includeRight : (lmul' R : _ →ₐ[R] S).comp includeRight =
#align algebra.tensor_product.lmul'_comp_include_right Algebra.TensorProduct.lmul'_comp_includeRight
-/
+#print Algebra.TensorProduct.productMap /-
/-- If `S` is commutative, for a pair of morphisms `f : A →ₐ[R] S`, `g : B →ₐ[R] S`,
We obtain a map `A ⊗[R] B →ₐ[R] S` that commutes with `f`, `g` via `a ⊗ b ↦ f(a) * g(b)`.
-/
def productMap : A ⊗[R] B →ₐ[R] S :=
(lmul' R).comp (TensorProduct.map f g)
#align algebra.tensor_product.product_map Algebra.TensorProduct.productMap
+-/
+#print Algebra.TensorProduct.productMap_apply_tmul /-
@[simp]
theorem productMap_apply_tmul (a : A) (b : B) : productMap f g (a ⊗ₜ b) = f a * g b := by
unfold product_map lmul'; simp
#align algebra.tensor_product.product_map_apply_tmul Algebra.TensorProduct.productMap_apply_tmul
+-/
+#print Algebra.TensorProduct.productMap_left_apply /-
theorem productMap_left_apply (a : A) : productMap f g ((includeLeft : A →ₐ[R] A ⊗ B) a) = f a := by
simp
#align algebra.tensor_product.product_map_left_apply Algebra.TensorProduct.productMap_left_apply
+-/
+#print Algebra.TensorProduct.productMap_left /-
@[simp]
theorem productMap_left : (productMap f g).comp includeLeft = f :=
AlgHom.ext <| by simp
#align algebra.tensor_product.product_map_left Algebra.TensorProduct.productMap_left
+-/
+#print Algebra.TensorProduct.productMap_right_apply /-
theorem productMap_right_apply (b : B) : productMap f g (includeRight b) = g b := by simp
#align algebra.tensor_product.product_map_right_apply Algebra.TensorProduct.productMap_right_apply
+-/
+#print Algebra.TensorProduct.productMap_right /-
@[simp]
theorem productMap_right : (productMap f g).comp includeRight = g :=
AlgHom.ext <| by simp
#align algebra.tensor_product.product_map_right Algebra.TensorProduct.productMap_right
+-/
+#print Algebra.TensorProduct.productMap_range /-
theorem productMap_range : (productMap f g).range = f.range ⊔ g.range := by
rw [product_map, AlgHom.range_comp, map_range, map_sup, ← AlgHom.range_comp, ← AlgHom.range_comp,
← AlgHom.comp_assoc, ← AlgHom.comp_assoc, lmul'_comp_include_left, lmul'_comp_include_right,
AlgHom.id_comp, AlgHom.id_comp]
#align algebra.tensor_product.product_map_range Algebra.TensorProduct.productMap_range
+-/
end
@@ -993,12 +1131,14 @@ variable [Algebra R A] [Algebra R A'] [Algebra A A'] [IsScalarTower R A A'] [Alg
variable [Algebra R S] [Algebra A S] [IsScalarTower R A S]
+#print Algebra.TensorProduct.productLeftAlgHom /-
/-- If `A`, `B` are `R`-algebras, `A'` is an `A`-algebra, then the product map of `f : A' →ₐ[A] S`
and `g : B →ₐ[R] S` is an `A`-algebra homomorphism. -/
@[simps]
def productLeftAlgHom (f : A' →ₐ[A] S) (g : B →ₐ[R] S) : A' ⊗[R] B →ₐ[A] S :=
{ (productMap (f.restrictScalars R) g).toRingHom with commutes' := fun r => by dsimp; simp }
#align algebra.tensor_product.product_left_alg_hom Algebra.TensorProduct.productLeftAlgHom
+-/
end
@@ -1007,6 +1147,7 @@ section Basis
variable {k : Type _} [CommRing k] (R : Type _) [Ring R] [Algebra k R] {M : Type _}
[AddCommMonoid M] [Module k M] {ι : Type _} (b : Basis ι k M)
+#print Algebra.TensorProduct.basisAux /-
/-- Given a `k`-algebra `R` and a `k`-basis of `M,` this is a `k`-linear isomorphism
`R ⊗[k] M ≃ (ι →₀ R)` (which is in fact `R`-linear). -/
noncomputable def basisAux : R ⊗[k] M ≃ₗ[k] ι →₀ R :=
@@ -1014,42 +1155,53 @@ noncomputable def basisAux : R ⊗[k] M ≃ₗ[k] ι →₀ R :=
(finsuppTensorFinsupp k R k PUnit ι).trans
(Finsupp.lcongr (Equiv.uniqueProd ι PUnit) (TensorProduct.rid k R))
#align algebra.tensor_product.basis_aux Algebra.TensorProduct.basisAux
+-/
variable {R}
+#print Algebra.TensorProduct.basisAux_tmul /-
theorem basisAux_tmul (r : R) (m : M) :
basisAux R b (r ⊗ₜ m) = r • Finsupp.mapRange (algebraMap k R) (map_zero _) (b.repr m) :=
by
ext
simp [basis_aux, ← Algebra.commutes, Algebra.smul_def]
#align algebra.tensor_product.basis_aux_tmul Algebra.TensorProduct.basisAux_tmul
+-/
+#print Algebra.TensorProduct.basisAux_map_smul /-
theorem basisAux_map_smul (r : R) (x : R ⊗[k] M) : basisAux R b (r • x) = r • basisAux R b x :=
TensorProduct.induction_on x (by simp)
(fun x y => by simp only [TensorProduct.smul_tmul', basis_aux_tmul, smul_assoc])
fun x y hx hy => by simp [hx, hy]
#align algebra.tensor_product.basis_aux_map_smul Algebra.TensorProduct.basisAux_map_smul
+-/
variable (R)
+#print Algebra.TensorProduct.basis /-
/-- Given a `k`-algebra `R`, this is the `R`-basis of `R ⊗[k] M` induced by a `k`-basis of `M`. -/
noncomputable def basis : Basis ι R (R ⊗[k] M)
where repr := { basisAux R b with map_smul' := basisAux_map_smul b }
#align algebra.tensor_product.basis Algebra.TensorProduct.basis
+-/
variable {R}
+#print Algebra.TensorProduct.basis_repr_tmul /-
@[simp]
theorem basis_repr_tmul (r : R) (m : M) :
(basis R b).repr (r ⊗ₜ m) = r • Finsupp.mapRange (algebraMap k R) (map_zero _) (b.repr m) :=
basisAux_tmul _ _ _
#align algebra.tensor_product.basis_repr_tmul Algebra.TensorProduct.basis_repr_tmul
+-/
+#print Algebra.TensorProduct.basis_repr_symm_apply /-
@[simp]
theorem basis_repr_symm_apply (r : R) (i : ι) :
(basis R b).repr.symm (Finsupp.single i r) = r ⊗ₜ b.repr.symm (Finsupp.single i 1) := by
simp [Basis, Equiv.uniqueProd_symm_apply, basis_aux]
#align algebra.tensor_product.basis_repr_symm_apply Algebra.TensorProduct.basis_repr_symm_apply
+-/
end Basis
@@ -1079,14 +1231,17 @@ def endTensorEndAlgHom : End R M ⊗[R] End R N →ₐ[R] End R (M ⊗[R] N) :=
#align module.End_tensor_End_alg_hom Module.endTensorEndAlgHom
-/
+#print Module.endTensorEndAlgHom_apply /-
theorem endTensorEndAlgHom_apply (f : End R M) (g : End R N) :
endTensorEndAlgHom (f ⊗ₜ[R] g) = TensorProduct.map f g := by
simp only [End_tensor_End_alg_hom, Algebra.TensorProduct.algHomOfLinearMapTensorProduct_apply,
hom_tensor_hom_map_apply]
#align module.End_tensor_End_alg_hom_apply Module.endTensorEndAlgHom_apply
+-/
end Module
+#print Subalgebra.finiteDimensional_sup /-
theorem Subalgebra.finiteDimensional_sup {K L : Type _} [Field K] [CommRing L] [Algebra K L]
(E1 E2 : Subalgebra K L) [FiniteDimensional K E1] [FiniteDimensional K E2] :
FiniteDimensional K ↥(E1 ⊔ E2) :=
@@ -1094,6 +1249,7 @@ theorem Subalgebra.finiteDimensional_sup {K L : Type _} [Field K] [CommRing L] [
rw [← E1.range_val, ← E2.range_val, ← Algebra.TensorProduct.productMap_range]
exact (Algebra.TensorProduct.productMap E1.val E2.val).toLinearMap.finiteDimensional_range
#align subalgebra.finite_dimensional_sup Subalgebra.finiteDimensional_sup
+-/
namespace TensorProduct.Algebra
@@ -1107,6 +1263,7 @@ variable [Algebra R A] [Algebra R B]
variable [IsScalarTower R A M] [IsScalarTower R B M]
+#print TensorProduct.Algebra.moduleAux /-
/-- An auxiliary definition, used for constructing the `module (A ⊗[R] B) M` in
`tensor_product.algebra.module` below. -/
def moduleAux : A ⊗[R] B →ₗ[R] M →ₗ[R] M :=
@@ -1116,13 +1273,17 @@ def moduleAux : A ⊗[R] B →ₗ[R] M →ₗ[R] M :=
map_smul' := fun n r => by ext;
simp only [RingHom.id_apply, LinearMap.smul_apply, smul_assoc] }
#align tensor_product.algebra.module_aux TensorProduct.Algebra.moduleAux
+-/
+#print TensorProduct.Algebra.moduleAux_apply /-
theorem moduleAux_apply (a : A) (b : B) (m : M) : moduleAux (a ⊗ₜ[R] b) m = a • b • m :=
rfl
#align tensor_product.algebra.module_aux_apply TensorProduct.Algebra.moduleAux_apply
+-/
variable [SMulCommClass A B M]
+#print TensorProduct.Algebra.module /-
/-- If `M` is a representation of two different `R`-algebras `A` and `B` whose actions commute,
then it is a representation the `R`-algebra `A ⊗[R] B`.
@@ -1166,6 +1327,7 @@ protected def module : Module (A ⊗[R] B) M
simp only at hz hw
simp only [add_mul, hz, hw, map_add, LinearMap.add_apply]
#align tensor_product.algebra.module TensorProduct.Algebra.module
+-/
attribute [local instance] TensorProduct.Algebra.module
mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Johan Commelin
! This file was ported from Lean 3 source module ring_theory.tensor_product
-! leanprover-community/mathlib commit 50251fd6309cca5ca2e747882ffecd2729f38c5d
+! leanprover-community/mathlib commit 69b2e97a276619372b19cf80fc1e91b05ae2baa4
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -485,9 +485,9 @@ def includeLeftRingHom : A →+* A ⊗[R] B
map_mul' := by simp
#align algebra.tensor_product.include_left_ring_hom Algebra.TensorProduct.includeLeftRingHom
-variable {S : Type _} [CommSemiring S] [Algebra R S] [Algebra S A] [IsScalarTower R S A]
+variable {S : Type _} [CommSemiring S] [Algebra S A]
-instance leftAlgebra : Algebra S (A ⊗[R] B) :=
+instance leftAlgebra [SMulCommClass R S A] : Algebra S (A ⊗[R] B) :=
{ TensorProduct.includeLeftRingHom.comp (algebraMap S A),
(by infer_instance :
Module S
@@ -511,13 +511,11 @@ instance : Algebra R (A ⊗[R] B) :=
inferInstance
@[simp]
-theorem algebraMap_apply (r : S) : (algebraMap S (A ⊗[R] B)) r = (algebraMap S A) r ⊗ₜ 1 :=
+theorem algebraMap_apply [SMulCommClass R S A] (r : S) :
+ (algebraMap S (A ⊗[R] B)) r = (algebraMap S A) r ⊗ₜ 1 :=
rfl
#align algebra.tensor_product.algebra_map_apply Algebra.TensorProduct.algebraMap_apply
-instance : IsScalarTower R S (A ⊗[R] B) :=
- ⟨fun a b c => by simp⟩
-
variable {C : Type v₃} [Semiring C] [Algebra R C]
@[ext]
@@ -528,6 +526,7 @@ theorem ext {g h : A ⊗[R] B →ₐ[R] C} (H : ∀ a b, g (a ⊗ₜ b) = h (a
simp [H]
#align algebra.tensor_product.ext Algebra.TensorProduct.ext
+-- TODO: with `smul_comm_class R S A` we can have this as an `S`-algebra morphism
/-- The `R`-algebra morphism `A →ₐ[R] A ⊗[R] B` sending `a` to `a ⊗ₜ 1`. -/
def includeLeft : A →ₐ[R] A ⊗[R] B :=
{ includeLeftRingHom with commutes' := by simp }
@@ -801,7 +800,7 @@ theorem comm_tmul (a : A) (b : B) :
simp [TensorProduct.comm]
#align algebra.tensor_product.comm_tmul Algebra.TensorProduct.comm_tmul
-theorem adjoin_tmul_eq_top : adjoin R { t : A ⊗[R] B | ∃ a b, a ⊗ₜ[R] b = t } = ⊤ :=
+theorem adjoin_tmul_eq_top : adjoin R {t : A ⊗[R] B | ∃ a b, a ⊗ₜ[R] b = t} = ⊤ :=
top_le_iff.mp <| (top_le_iff.mpr <| span_tmul_eq_top R A B).trans (span_le_adjoin R _)
#align algebra.tensor_product.adjoin_tmul_eq_top Algebra.TensorProduct.adjoin_tmul_eq_top
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -415,14 +415,14 @@ theorem mul_assoc' (mul : A ⊗[R] B →ₗ[R] A ⊗[R] B →ₗ[R] A ⊗[R] B)
· simp only [LinearMap.map_zero, forall_const, LinearMap.zero_apply]
apply TensorProduct.induction_on z
· simp only [LinearMap.map_zero, forall_const]
- · intros ; simp only [h]
- · intros ; simp only [LinearMap.map_add, *]
- · intros ; simp only [LinearMap.map_add, *, LinearMap.add_apply]
- · intros ; simp only [LinearMap.map_add, *, LinearMap.add_apply]
+ · intros; simp only [h]
+ · intros; simp only [LinearMap.map_add, *]
+ · intros; simp only [LinearMap.map_add, *, LinearMap.add_apply]
+ · intros; simp only [LinearMap.map_add, *, LinearMap.add_apply]
#align algebra.tensor_product.mul_assoc' Algebra.TensorProduct.mul_assoc'
theorem mul_assoc (x y z : A ⊗[R] B) : mul (mul x y) z = mul x (mul y z) :=
- mul_assoc' mul (by intros ; simp only [mul_apply, mul_assoc]) x y z
+ mul_assoc' mul (by intros; simp only [mul_apply, mul_assoc]) x y z
#align algebra.tensor_product.mul_assoc Algebra.TensorProduct.mul_assoc
theorem one_mul (x : A ⊗[R] B) : mul (1 ⊗ₜ 1) x = x := by
@@ -497,12 +497,12 @@ instance leftAlgebra : Algebra S (A ⊗[R] B) :=
apply TensorProduct.induction_on x
· simp
· intro a b; dsimp; rw [Algebra.commutes, _root_.mul_one, _root_.one_mul]
- · intro y y' h h'; dsimp at h h'⊢; simp only [mul_add, add_mul, h, h']
+ · intro y y' h h'; dsimp at h h' ⊢; simp only [mul_add, add_mul, h, h']
smul_def' := fun r x => by
apply TensorProduct.induction_on x
· simp [smul_zero]
· intro a b; dsimp; rw [TensorProduct.smul_tmul', Algebra.smul_def r a, _root_.one_mul]
- · intros ; dsimp; simp [smul_add, mul_add, *] }
+ · intros; dsimp; simp [smul_add, mul_add, *] }
#align algebra.tensor_product.left_algebra Algebra.TensorProduct.leftAlgebra
-- This is for the `undergrad.yaml` list.
@@ -721,12 +721,12 @@ def algEquivOfLinearEquivTripleTensorProduct (f : (A ⊗[R] B) ⊗[R] C ≃ₗ[R
· intro a₁ b₁
apply TensorProduct.induction_on ab₂
· simp only [zero_tmul, map_zero, MulZeroClass.mul_zero]
- · intros ; simp only [tmul_mul_tmul, w₁]
+ · intros; simp only [tmul_mul_tmul, w₁]
· intro x₁ x₂ h₁ h₂
- simp only [tmul_mul_tmul] at h₁ h₂
+ simp only [tmul_mul_tmul] at h₁ h₂
simp only [tmul_mul_tmul, mul_add, add_tmul, map_add, h₁, h₂]
· intro x₁ x₂ h₁ h₂
- simp only [tmul_mul_tmul] at h₁ h₂
+ simp only [tmul_mul_tmul] at h₁ h₂
simp only [tmul_mul_tmul, add_mul, add_tmul, map_add, h₁, h₂]
· intro x₁ x₂ h₁ h₂
simp only [tmul_mul_tmul, map_add, mul_add, add_mul, h₁, h₂]
@@ -1157,14 +1157,14 @@ protected def module : Module (A ⊗[R] B) M
simp only [module_aux_apply, mul_smul, smul_comm a₁ b₂, Algebra.TensorProduct.tmul_mul_tmul,
LinearMap.mul_apply]
· intro z w hz hw a b
- simp only at hz hw
+ simp only at hz hw
simp only [mul_add, hz, hw, map_add, LinearMap.add_apply]
· intro z w hz hw; simp only [MulZeroClass.mul_zero, map_zero, LinearMap.zero_apply]
· intro a b z w hz hw
- simp only at hz hw
+ simp only at hz hw
simp only [map_add, add_mul, LinearMap.add_apply, hz, hw]
· intro u v hu hv z w hz hw
- simp only at hz hw
+ simp only at hz hw
simp only [add_mul, hz, hw, map_add, LinearMap.add_apply]
#align tensor_product.algebra.module TensorProduct.Algebra.module
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -533,12 +533,10 @@ def includeLeft : A →ₐ[R] A ⊗[R] B :=
{ includeLeftRingHom with commutes' := by simp }
#align algebra.tensor_product.include_left Algebra.TensorProduct.includeLeft
-#print Algebra.TensorProduct.includeLeft_apply /-
@[simp]
theorem includeLeft_apply (a : A) : (includeLeft : A →ₐ[R] A ⊗[R] B) a = a ⊗ₜ 1 :=
rfl
#align algebra.tensor_product.include_left_apply Algebra.TensorProduct.includeLeft_apply
--/
/-- The algebra morphism `B →ₐ[R] A ⊗[R] B` sending `b` to `1 ⊗ₜ b`. -/
def includeRight : B →ₐ[R] A ⊗[R] B where
@@ -554,12 +552,10 @@ def includeRight : B →ₐ[R] A ⊗[R] B where
· simp [Algebra.smul_def]
#align algebra.tensor_product.include_right Algebra.TensorProduct.includeRight
-#print Algebra.TensorProduct.includeRight_apply /-
@[simp]
theorem includeRight_apply (b : B) : (includeRight : B →ₐ[R] A ⊗[R] B) b = 1 ⊗ₜ b :=
rfl
#align algebra.tensor_product.include_right_apply Algebra.TensorProduct.includeRight_apply
--/
theorem includeLeft_comp_algebraMap {R S T : Type _} [CommRing R] [CommRing S] [CommRing T]
[Algebra R S] [Algebra R T] :
@@ -857,12 +853,10 @@ def map (f : A →ₐ[R] B) (g : C →ₐ[R] D) : A ⊗[R] C →ₐ[R] B ⊗[R]
(by simp [AlgHom.commutes])
#align algebra.tensor_product.map Algebra.TensorProduct.map
-#print Algebra.TensorProduct.map_tmul /-
@[simp]
theorem map_tmul (f : A →ₐ[R] B) (g : C →ₐ[R] D) (a : A) (c : C) : map f g (a ⊗ₜ c) = f a ⊗ₜ g c :=
rfl
#align algebra.tensor_product.map_tmul Algebra.TensorProduct.map_tmul
--/
@[simp]
theorem map_comp_includeLeft (f : A →ₐ[R] B) (g : C →ₐ[R] D) :
@@ -934,12 +928,10 @@ theorem lmul'_toLinearMap : (lmul' R : _ →ₐ[R] S).toLinearMap = LinearMap.mu
rfl
#align algebra.tensor_product.lmul'_to_linear_map Algebra.TensorProduct.lmul'_toLinearMap
-#print Algebra.TensorProduct.lmul'_apply_tmul /-
@[simp]
theorem lmul'_apply_tmul (a b : S) : lmul' R (a ⊗ₜ[R] b) = a * b :=
rfl
#align algebra.tensor_product.lmul'_apply_tmul Algebra.TensorProduct.lmul'_apply_tmul
--/
#print Algebra.TensorProduct.lmul'_comp_includeLeft /-
@[simp]
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -53,7 +53,7 @@ fewer type arguments.
universe u v₁ v₂ v₃ v₄
-open TensorProduct
+open scoped TensorProduct
open TensorProduct
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -82,9 +82,6 @@ variable [AddCommMonoid N] [Module R N]
variable [AddCommMonoid P] [Module R P] [Module A P] [IsScalarTower R A P]
-/- warning: tensor_product.algebra_tensor_module.smul_eq_lsmul_rtensor -> TensorProduct.AlgebraTensorModule.smul_eq_lsmul_rTensor is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.algebra_tensor_module.smul_eq_lsmul_rtensor TensorProduct.AlgebraTensorModule.smul_eq_lsmul_rTensorₓ'. -/
theorem smul_eq_lsmul_rTensor (a : A) (x : M ⊗[R] N) : a • x = (lsmul R M a).rTensor N x :=
rfl
#align tensor_product.algebra_tensor_module.smul_eq_lsmul_rtensor TensorProduct.AlgebraTensorModule.smul_eq_lsmul_rTensor
@@ -104,17 +101,11 @@ def curry (f : M ⊗[R] N →ₗ[A] P) : M →ₗ[A] N →ₗ[R] P :=
#align tensor_product.algebra_tensor_module.curry TensorProduct.AlgebraTensorModule.curry
-/
-/- warning: tensor_product.algebra_tensor_module.restrict_scalars_curry -> TensorProduct.AlgebraTensorModule.restrictScalars_curry is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.algebra_tensor_module.restrict_scalars_curry TensorProduct.AlgebraTensorModule.restrictScalars_curryₓ'. -/
theorem restrictScalars_curry (f : M ⊗[R] N →ₗ[A] P) :
RestrictScalars R (curry f) = curry (f.restrictScalars R) :=
rfl
#align tensor_product.algebra_tensor_module.restrict_scalars_curry TensorProduct.AlgebraTensorModule.restrictScalars_curry
-/- warning: tensor_product.algebra_tensor_module.curry_injective -> TensorProduct.AlgebraTensorModule.curry_injective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.algebra_tensor_module.curry_injective TensorProduct.AlgebraTensorModule.curry_injectiveₓ'. -/
/-- Just as `tensor_product.ext` is marked `ext` instead of `tensor_product.ext'`, this is
a better `ext` lemma than `tensor_product.algebra_tensor_module.ext` below.
@@ -126,9 +117,6 @@ theorem curry_injective : Function.Injective (curry : (M ⊗ N →ₗ[A] P) →
curry_injective <| (congr_arg (LinearMap.restrictScalars R) h : _)
#align tensor_product.algebra_tensor_module.curry_injective TensorProduct.AlgebraTensorModule.curry_injective
-/- warning: tensor_product.algebra_tensor_module.ext -> TensorProduct.AlgebraTensorModule.ext is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.algebra_tensor_module.ext TensorProduct.AlgebraTensorModule.extₓ'. -/
theorem ext {g h : M ⊗[R] N →ₗ[A] P} (H : ∀ x y, g (x ⊗ₜ y) = h (x ⊗ₜ y)) : g = h :=
curry_injective <| LinearMap.ext₂ H
#align tensor_product.algebra_tensor_module.ext TensorProduct.AlgebraTensorModule.ext
@@ -167,9 +155,6 @@ def lift (f : M →ₗ[A] N →ₗ[R] P) : M ⊗[R] N →ₗ[A] P :=
#align tensor_product.algebra_tensor_module.lift TensorProduct.AlgebraTensorModule.lift
-/
-/- warning: tensor_product.algebra_tensor_module.lift_tmul -> TensorProduct.AlgebraTensorModule.lift_tmul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.algebra_tensor_module.lift_tmul TensorProduct.AlgebraTensorModule.lift_tmulₓ'. -/
@[simp]
theorem lift_tmul (f : M →ₗ[A] N →ₗ[R] P) (x : M) (y : N) : lift f (x ⊗ₜ y) = f x y :=
rfl
@@ -221,9 +206,6 @@ def lift.equiv : (M →ₗ[A] N →ₗ[R] P) ≃ₗ[A] M ⊗[R] N →ₗ[A] P :=
variable (R A M N P)
-/- warning: tensor_product.algebra_tensor_module.mk -> TensorProduct.AlgebraTensorModule.mk is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.algebra_tensor_module.mk TensorProduct.AlgebraTensorModule.mkₓ'. -/
/-- Heterobasic version of `tensor_product.mk`:
The canonical bilinear map `M →[A] N →[R] M ⊗[R] N`. -/
@@ -298,39 +280,24 @@ def baseChange (f : M →ₗ[R] N) : A ⊗[R] M →ₗ[A] A ⊗[R] N
variable {A}
-/- warning: linear_map.base_change_tmul -> LinearMap.baseChange_tmul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.base_change_tmul LinearMap.baseChange_tmulₓ'. -/
@[simp]
theorem baseChange_tmul (a : A) (x : M) : f.base_change A (a ⊗ₜ x) = a ⊗ₜ f x :=
rfl
#align linear_map.base_change_tmul LinearMap.baseChange_tmul
-/- warning: linear_map.base_change_eq_ltensor -> LinearMap.baseChange_eq_ltensor is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.base_change_eq_ltensor LinearMap.baseChange_eq_ltensorₓ'. -/
theorem baseChange_eq_ltensor : (f.base_change A : A ⊗ M → A ⊗ N) = f.lTensor A :=
rfl
#align linear_map.base_change_eq_ltensor LinearMap.baseChange_eq_ltensor
-/- warning: linear_map.base_change_add -> LinearMap.baseChange_add is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.base_change_add LinearMap.baseChange_addₓ'. -/
@[simp]
theorem baseChange_add : (f + g).base_change A = f.base_change A + g.base_change A := by ext;
simp [base_change_eq_ltensor]
#align linear_map.base_change_add LinearMap.baseChange_add
-/- warning: linear_map.base_change_zero -> LinearMap.baseChange_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.base_change_zero LinearMap.baseChange_zeroₓ'. -/
@[simp]
theorem baseChange_zero : baseChange A (0 : M →ₗ[R] N) = 0 := by ext; simp [base_change_eq_ltensor]
#align linear_map.base_change_zero LinearMap.baseChange_zero
-/- warning: linear_map.base_change_smul -> LinearMap.baseChange_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.base_change_smul LinearMap.baseChange_smulₓ'. -/
@[simp]
theorem baseChange_smul : (r • f).base_change A = r • f.base_change A := by ext;
simp [base_change_tmul]
@@ -361,17 +328,11 @@ variable [AddCommGroup M] [Module R M] [AddCommGroup N] [Module R N]
variable (f g : M →ₗ[R] N)
-/- warning: linear_map.base_change_sub -> LinearMap.baseChange_sub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.base_change_sub LinearMap.baseChange_subₓ'. -/
@[simp]
theorem baseChange_sub : (f - g).base_change A = f.base_change A - g.base_change A := by ext;
simp [base_change_eq_ltensor]
#align linear_map.base_change_sub LinearMap.baseChange_sub
-/- warning: linear_map.base_change_neg -> LinearMap.baseChange_neg is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.base_change_neg LinearMap.baseChange_negₓ'. -/
@[simp]
theorem baseChange_neg : (-f).base_change A = -f.base_change A := by ext;
simp [base_change_eq_ltensor]
@@ -398,12 +359,6 @@ variable {B : Type v₂} [Semiring B] [Algebra R B]
-/
-/- warning: algebra.tensor_product.mul_aux -> Algebra.TensorProduct.mulAux is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4], A -> B -> (LinearMap.{u1, u1, max u2 u3, max u2 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))
-but is expected to have type
- forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4], A -> B -> (LinearMap.{u1, u1, max u3 u2, max u3 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.mul_aux Algebra.TensorProduct.mulAuxₓ'. -/
/-- (Implementation detail)
The multiplication map on `A ⊗[R] B`,
for a fixed pure tensor in the first argument,
@@ -413,18 +368,12 @@ def mulAux (a₁ : A) (b₁ : B) : A ⊗[R] B →ₗ[R] A ⊗[R] B :=
TensorProduct.map (LinearMap.mulLeft R a₁) (LinearMap.mulLeft R b₁)
#align algebra.tensor_product.mul_aux Algebra.TensorProduct.mulAux
-/- warning: algebra.tensor_product.mul_aux_apply -> Algebra.TensorProduct.mulAux_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.mul_aux_apply Algebra.TensorProduct.mulAux_applyₓ'. -/
@[simp]
theorem mulAux_apply (a₁ a₂ : A) (b₁ b₂ : B) :
(mulAux a₁ b₁) (a₂ ⊗ₜ[R] b₂) = (a₁ * a₂) ⊗ₜ[R] (b₁ * b₂) :=
rfl
#align algebra.tensor_product.mul_aux_apply Algebra.TensorProduct.mulAux_apply
-/- warning: algebra.tensor_product.mul -> Algebra.TensorProduct.mul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.mul Algebra.TensorProduct.mulₓ'. -/
/-- (Implementation detail)
The multiplication map on `A ⊗[R] B`,
as an `R`-bilinear map.
@@ -446,18 +395,12 @@ def mul : A ⊗[R] B →ₗ[R] A ⊗[R] B →ₗ[R] A ⊗[R] B :=
simp only [mul_aux_apply, LinearMap.smul_apply, smul_tmul, smul_tmul', smul_mul_assoc]
#align algebra.tensor_product.mul Algebra.TensorProduct.mul
-/- warning: algebra.tensor_product.mul_apply -> Algebra.TensorProduct.mul_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.mul_apply Algebra.TensorProduct.mul_applyₓ'. -/
@[simp]
theorem mul_apply (a₁ a₂ : A) (b₁ b₂ : B) :
mul (a₁ ⊗ₜ[R] b₁) (a₂ ⊗ₜ[R] b₂) = (a₁ * a₂) ⊗ₜ[R] (b₁ * b₂) :=
rfl
#align algebra.tensor_product.mul_apply Algebra.TensorProduct.mul_apply
-/- warning: algebra.tensor_product.mul_assoc' -> Algebra.TensorProduct.mul_assoc' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.mul_assoc' Algebra.TensorProduct.mul_assoc'ₓ'. -/
theorem mul_assoc' (mul : A ⊗[R] B →ₗ[R] A ⊗[R] B →ₗ[R] A ⊗[R] B)
(h :
∀ (a₁ a₂ a₃ : A) (b₁ b₂ b₃ : B),
@@ -478,23 +421,14 @@ theorem mul_assoc' (mul : A ⊗[R] B →ₗ[R] A ⊗[R] B →ₗ[R] A ⊗[R] B)
· intros ; simp only [LinearMap.map_add, *, LinearMap.add_apply]
#align algebra.tensor_product.mul_assoc' Algebra.TensorProduct.mul_assoc'
-/- warning: algebra.tensor_product.mul_assoc -> Algebra.TensorProduct.mul_assoc is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.mul_assoc Algebra.TensorProduct.mul_assocₓ'. -/
theorem mul_assoc (x y z : A ⊗[R] B) : mul (mul x y) z = mul x (mul y z) :=
mul_assoc' mul (by intros ; simp only [mul_apply, mul_assoc]) x y z
#align algebra.tensor_product.mul_assoc Algebra.TensorProduct.mul_assoc
-/- warning: algebra.tensor_product.one_mul -> Algebra.TensorProduct.one_mul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.one_mul Algebra.TensorProduct.one_mulₓ'. -/
theorem one_mul (x : A ⊗[R] B) : mul (1 ⊗ₜ 1) x = x := by
apply TensorProduct.induction_on x <;> simp (config := { contextual := true })
#align algebra.tensor_product.one_mul Algebra.TensorProduct.one_mul
-/- warning: algebra.tensor_product.mul_one -> Algebra.TensorProduct.mul_one is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.mul_one Algebra.TensorProduct.mul_oneₓ'. -/
theorem mul_one (x : A ⊗[R] B) : mul x (1 ⊗ₜ 1) = x := by
apply TensorProduct.induction_on x <;> simp (config := { contextual := true })
#align algebra.tensor_product.mul_one Algebra.TensorProduct.mul_one
@@ -526,18 +460,12 @@ theorem one_def : (1 : A ⊗[R] B) = (1 : A) ⊗ₜ (1 : B) :=
#align algebra.tensor_product.one_def Algebra.TensorProduct.one_def
-/
-/- warning: algebra.tensor_product.tmul_mul_tmul -> Algebra.TensorProduct.tmul_mul_tmul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.tmul_mul_tmul Algebra.TensorProduct.tmul_mul_tmulₓ'. -/
@[simp]
theorem tmul_mul_tmul (a₁ a₂ : A) (b₁ b₂ : B) :
a₁ ⊗ₜ[R] b₁ * a₂ ⊗ₜ[R] b₂ = (a₁ * a₂) ⊗ₜ[R] (b₁ * b₂) :=
rfl
#align algebra.tensor_product.tmul_mul_tmul Algebra.TensorProduct.tmul_mul_tmul
-/- warning: algebra.tensor_product.tmul_pow -> Algebra.TensorProduct.tmul_pow is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.tmul_pow Algebra.TensorProduct.tmul_powₓ'. -/
@[simp]
theorem tmul_pow (a : A) (b : B) (k : ℕ) : a ⊗ₜ[R] b ^ k = (a ^ k) ⊗ₜ[R] (b ^ k) :=
by
@@ -546,12 +474,6 @@ theorem tmul_pow (a : A) (b : B) (k : ℕ) : a ⊗ₜ[R] b ^ k = (a ^ k) ⊗ₜ[
· simp [pow_succ, ih]
#align algebra.tensor_product.tmul_pow Algebra.TensorProduct.tmul_pow
-/- warning: algebra.tensor_product.include_left_ring_hom -> Algebra.TensorProduct.includeLeftRingHom is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.include_left_ring_hom Algebra.TensorProduct.includeLeftRingHomₓ'. -/
/-- The ring morphism `A →+* A ⊗[R] B` sending `a` to `a ⊗ₜ 1`. -/
@[simps]
def includeLeftRingHom : A →+* A ⊗[R] B
@@ -565,12 +487,6 @@ def includeLeftRingHom : A →+* A ⊗[R] B
variable {S : Type _} [CommSemiring S] [Algebra R S] [Algebra S A] [IsScalarTower R S A]
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(CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u4} S (AddMonoid.toAddZeroClass.{u4} S (AddCommMonoid.toAddMonoid.{u4} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_6))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} S (AddMonoid.toAddZeroClass.{u4} S (AddCommMonoid.toAddMonoid.{u4} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_6))))))) (Module.toMulActionWithZero.{u1, u4} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_6)))) (Algebra.toModule.{u1, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_6) _inst_7))))) (SMulZeroClass.toHasSmul.{u4, u2} S A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u4, u2} S A (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_6))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} S A (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_6)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u4, u2} S A (CommSemiring.toSemiring.{u4} S _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u4, u2} S A _inst_6 _inst_2 _inst_8))))) (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))], Algebra.{u4, max u2 u3} S (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) _inst_6 (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5)
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-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.left_algebra Algebra.TensorProduct.leftAlgebraₓ'. -/
instance leftAlgebra : Algebra S (A ⊗[R] B) :=
{ TensorProduct.includeLeftRingHom.comp (algebraMap S A),
(by infer_instance :
@@ -594,9 +510,6 @@ instance leftAlgebra : Algebra S (A ⊗[R] B) :=
instance : Algebra R (A ⊗[R] B) :=
inferInstance
-/- warning: algebra.tensor_product.algebra_map_apply -> Algebra.TensorProduct.algebraMap_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.algebra_map_apply Algebra.TensorProduct.algebraMap_applyₓ'. -/
@[simp]
theorem algebraMap_apply (r : S) : (algebraMap S (A ⊗[R] B)) r = (algebraMap S A) r ⊗ₜ 1 :=
rfl
@@ -607,9 +520,6 @@ instance : IsScalarTower R S (A ⊗[R] B) :=
variable {C : Type v₃} [Semiring C] [Algebra R C]
-/- warning: algebra.tensor_product.ext -> Algebra.TensorProduct.ext is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.ext Algebra.TensorProduct.extₓ'. -/
@[ext]
theorem ext {g h : A ⊗[R] B →ₐ[R] C} (H : ∀ a b, g (a ⊗ₜ b) = h (a ⊗ₜ b)) : g = h :=
by
@@ -618,12 +528,6 @@ theorem ext {g h : A ⊗[R] B →ₐ[R] C} (H : ∀ a b, g (a ⊗ₜ b) = h (a
simp [H]
#align algebra.tensor_product.ext Algebra.TensorProduct.ext
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-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.include_left Algebra.TensorProduct.includeLeftₓ'. -/
/-- The `R`-algebra morphism `A →ₐ[R] A ⊗[R] B` sending `a` to `a ⊗ₜ 1`. -/
def includeLeft : A →ₐ[R] A ⊗[R] B :=
{ includeLeftRingHom with commutes' := by simp }
@@ -636,12 +540,6 @@ theorem includeLeft_apply (a : A) : (includeLeft : A →ₐ[R] A ⊗[R] B) a = a
#align algebra.tensor_product.include_left_apply Algebra.TensorProduct.includeLeft_apply
-/
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-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.include_right Algebra.TensorProduct.includeRightₓ'. -/
/-- The algebra morphism `B →ₐ[R] A ⊗[R] B` sending `b` to `1 ⊗ₜ b`. -/
def includeRight : B →ₐ[R] A ⊗[R] B where
toFun b := 1 ⊗ₜ b
@@ -663,9 +561,6 @@ theorem includeRight_apply (b : B) : (includeRight : B →ₐ[R] A ⊗[R] B) b =
#align algebra.tensor_product.include_right_apply Algebra.TensorProduct.includeRight_apply
-/
-/- warning: algebra.tensor_product.include_left_comp_algebra_map -> Algebra.TensorProduct.includeLeft_comp_algebraMap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.include_left_comp_algebra_map Algebra.TensorProduct.includeLeft_comp_algebraMapₓ'. -/
theorem includeLeft_comp_algebraMap {R S T : Type _} [CommRing R] [CommRing S] [CommRing T]
[Algebra R S] [Algebra R T] :
(includeLeft.toRingHom.comp (algebraMap R S) : R →+* S ⊗[R] T) =
@@ -713,12 +608,6 @@ instance : CommRing (A ⊗[R] B) :=
section RightAlgebra
-/- warning: algebra.tensor_product.right_algebra -> Algebra.TensorProduct.rightAlgebra is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {A : Type.{u2}} [_inst_2 : CommRing.{u2} A] [_inst_3 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] {B : Type.{u3}} [_inst_4 : CommRing.{u3} B] [_inst_5 : Algebra.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4))], Algebra.{u3, max u2 u3} B (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A B (AddCommGroup.toAddCommMonoid.{u2} A (NonUnitalNonAssocRing.toAddCommGroup.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} B (NonUnitalNonAssocRing.toAddCommGroup.{u3} B (NonAssocRing.toNonUnitalNonAssocRing.{u3} B (Ring.toNonAssocRing.{u3} B (CommRing.toRing.{u3} B _inst_4))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) (Algebra.toModule.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_5)) (CommRing.toCommSemiring.{u3} B _inst_4) (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3 B (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_5)
-but is expected to have type
- forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {A : Type.{u2}} [_inst_2 : CommRing.{u2} A] [_inst_3 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] {B : Type.{u3}} [_inst_4 : CommRing.{u3} B] [_inst_5 : Algebra.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u3} B (CommRing.toCommSemiring.{u3} B _inst_4))], Algebra.{u3, max u3 u2} B (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} B (NonAssocRing.toNonUnitalNonAssocRing.{u3} B (Ring.toNonAssocRing.{u3} B (CommRing.toRing.{u3} B _inst_4))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_3) (Algebra.toModule.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u3} B (CommRing.toCommSemiring.{u3} B _inst_4)) _inst_5)) (CommRing.toCommSemiring.{u3} B _inst_4) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_3 B (CommSemiring.toSemiring.{u3} B (CommRing.toCommSemiring.{u3} B _inst_4)) _inst_5)
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.right_algebra Algebra.TensorProduct.rightAlgebraₓ'. -/
/-- `S ⊗[R] T` has a `T`-algebra structure. This is not a global instance or else the action of
`S` on `S ⊗[R] S` would be ambiguous. -/
@[reducible]
@@ -728,9 +617,6 @@ def rightAlgebra : Algebra B (A ⊗[R] B) :=
attribute [local instance] tensor_product.right_algebra
-/- warning: algebra.tensor_product.right_is_scalar_tower -> Algebra.TensorProduct.right_isScalarTower is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.right_is_scalar_tower Algebra.TensorProduct.right_isScalarTowerₓ'. -/
instance right_isScalarTower : IsScalarTower R B (A ⊗[R] B) :=
IsScalarTower.of_algebraMap_eq fun r => (Algebra.TensorProduct.includeRight.commutes r).symm
#align algebra.tensor_product.right_is_scalar_tower Algebra.TensorProduct.right_isScalarTower
@@ -769,9 +655,6 @@ variable {C : Type v₃} [Semiring C] [Algebra R C]
variable {D : Type v₄} [Semiring D] [Algebra R D]
-/- warning: algebra.tensor_product.alg_hom_of_linear_map_tensor_product -> Algebra.TensorProduct.algHomOfLinearMapTensorProduct is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.alg_hom_of_linear_map_tensor_product Algebra.TensorProduct.algHomOfLinearMapTensorProductₓ'. -/
/-- Build an algebra morphism from a linear map out of a tensor product,
and evidence of multiplicativity on pure tensors.
-/
@@ -798,18 +681,12 @@ def algHomOfLinearMapTensorProduct (f : A ⊗[R] B →ₗ[R] C)
commutes' := fun r => by rw [LinearMap.toFun_eq_coe, algebraMap_apply, w₂] }
#align algebra.tensor_product.alg_hom_of_linear_map_tensor_product Algebra.TensorProduct.algHomOfLinearMapTensorProduct
-/- warning: algebra.tensor_product.alg_hom_of_linear_map_tensor_product_apply -> Algebra.TensorProduct.algHomOfLinearMapTensorProduct_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.alg_hom_of_linear_map_tensor_product_apply Algebra.TensorProduct.algHomOfLinearMapTensorProduct_applyₓ'. -/
@[simp]
theorem algHomOfLinearMapTensorProduct_apply (f w₁ w₂ x) :
(algHomOfLinearMapTensorProduct f w₁ w₂ : A ⊗[R] B →ₐ[R] C) x = f x :=
rfl
#align algebra.tensor_product.alg_hom_of_linear_map_tensor_product_apply Algebra.TensorProduct.algHomOfLinearMapTensorProduct_apply
-/- warning: algebra.tensor_product.alg_equiv_of_linear_equiv_tensor_product -> Algebra.TensorProduct.algEquivOfLinearEquivTensorProduct is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.alg_equiv_of_linear_equiv_tensor_product Algebra.TensorProduct.algEquivOfLinearEquivTensorProductₓ'. -/
/-- Build an algebra equivalence from a linear equivalence out of a tensor product,
and evidence of multiplicativity on pure tensors.
-/
@@ -819,18 +696,12 @@ def algEquivOfLinearEquivTensorProduct (f : A ⊗[R] B ≃ₗ[R] C)
{ algHomOfLinearMapTensorProduct (f : A ⊗[R] B →ₗ[R] C) w₁ w₂, f with }
#align algebra.tensor_product.alg_equiv_of_linear_equiv_tensor_product Algebra.TensorProduct.algEquivOfLinearEquivTensorProduct
-/- warning: algebra.tensor_product.alg_equiv_of_linear_equiv_tensor_product_apply -> Algebra.TensorProduct.algEquivOfLinearEquivTensorProduct_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.alg_equiv_of_linear_equiv_tensor_product_apply Algebra.TensorProduct.algEquivOfLinearEquivTensorProduct_applyₓ'. -/
@[simp]
theorem algEquivOfLinearEquivTensorProduct_apply (f w₁ w₂ x) :
(algEquivOfLinearEquivTensorProduct f w₁ w₂ : A ⊗[R] B ≃ₐ[R] C) x = f x :=
rfl
#align algebra.tensor_product.alg_equiv_of_linear_equiv_tensor_product_apply Algebra.TensorProduct.algEquivOfLinearEquivTensorProduct_apply
-/- warning: algebra.tensor_product.alg_equiv_of_linear_equiv_triple_tensor_product -> Algebra.TensorProduct.algEquivOfLinearEquivTripleTensorProduct is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.alg_equiv_of_linear_equiv_triple_tensor_product Algebra.TensorProduct.algEquivOfLinearEquivTripleTensorProductₓ'. -/
/-- Build an algebra equivalence from a linear equivalence out of a triple tensor product,
and evidence of multiplicativity on pure tensors.
-/
@@ -868,9 +739,6 @@ def algEquivOfLinearEquivTripleTensorProduct (f : (A ⊗[R] B) ⊗[R] C ≃ₗ[R
commutes' := fun r => by simp [w₂] }
#align algebra.tensor_product.alg_equiv_of_linear_equiv_triple_tensor_product Algebra.TensorProduct.algEquivOfLinearEquivTripleTensorProduct
-/- warning: algebra.tensor_product.alg_equiv_of_linear_equiv_triple_tensor_product_apply -> Algebra.TensorProduct.algEquivOfLinearEquivTripleTensorProduct_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.alg_equiv_of_linear_equiv_triple_tensor_product_apply Algebra.TensorProduct.algEquivOfLinearEquivTripleTensorProduct_applyₓ'. -/
@[simp]
theorem algEquivOfLinearEquivTripleTensorProduct_apply (f w₁ w₂ x) :
(algEquivOfLinearEquivTripleTensorProduct f w₁ w₂ : (A ⊗[R] B) ⊗[R] C ≃ₐ[R] D) x = f x :=
@@ -893,12 +761,6 @@ section
variable (R A)
-/- warning: algebra.tensor_product.lid -> Algebra.TensorProduct.lid is a dubious translation:
-lean 3 declaration is
- forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (A : Type.{u2}) [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], AlgEquiv.{u1, max u1 u2, u2} R (TensorProduct.{u1, u1, u2} R _inst_1 R A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A _inst_1 (Algebra.TensorProduct.TensorProduct.semiring.{u1, u1, u2} R _inst_1 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) A _inst_2 _inst_3) _inst_2 (Algebra.TensorProduct.TensorProduct.algebra.{u1, u1, u2} R _inst_1 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) A _inst_2 _inst_3) _inst_3
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-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.lid Algebra.TensorProduct.lidₓ'. -/
/-- The base ring is a left identity for the tensor product of algebra, up to algebra isomorphism.
-/
protected def lid : R ⊗[R] A ≃ₐ[R] A :=
@@ -906,20 +768,11 @@ protected def lid : R ⊗[R] A ≃ₐ[R] A :=
(by simp [Algebra.smul_def])
#align algebra.tensor_product.lid Algebra.TensorProduct.lid
-/- warning: algebra.tensor_product.lid_tmul -> Algebra.TensorProduct.lid_tmul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.lid_tmul Algebra.TensorProduct.lid_tmulₓ'. -/
@[simp]
theorem lid_tmul (r : R) (a : A) : (TensorProduct.lid R A : R ⊗ A → A) (r ⊗ₜ a) = r • a := by
simp [TensorProduct.lid]
#align algebra.tensor_product.lid_tmul Algebra.TensorProduct.lid_tmul
-/- warning: algebra.tensor_product.rid -> Algebra.TensorProduct.rid is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.rid Algebra.TensorProduct.ridₓ'. -/
/-- The base ring is a right identity for the tensor product of algebra, up to algebra isomorphism.
-/
protected def rid : A ⊗[R] R ≃ₐ[R] A :=
@@ -927,9 +780,6 @@ protected def rid : A ⊗[R] R ≃ₐ[R] A :=
(by simp [Algebra.smul_def])
#align algebra.tensor_product.rid Algebra.TensorProduct.rid
-/- warning: algebra.tensor_product.rid_tmul -> Algebra.TensorProduct.rid_tmul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.rid_tmul Algebra.TensorProduct.rid_tmulₓ'. -/
@[simp]
theorem rid_tmul (r : R) (a : A) : (TensorProduct.rid R A : A ⊗ R → A) (a ⊗ₜ r) = r • a := by
simp [TensorProduct.rid]
@@ -939,12 +789,6 @@ section
variable (R A B)
-/- warning: algebra.tensor_product.comm -> Algebra.TensorProduct.comm is a dubious translation:
-lean 3 declaration is
- forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (A : Type.{u2}) [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (B : Type.{u3}) [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4], AlgEquiv.{u1, max u2 u3, max u3 u2} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.{u1, u3, u2} R _inst_1 B A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _inst_1 (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (Algebra.TensorProduct.TensorProduct.semiring.{u1, u3, u2} R _inst_1 B _inst_4 _inst_5 A _inst_2 _inst_3) (Algebra.TensorProduct.TensorProduct.algebra.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (Algebra.TensorProduct.TensorProduct.algebra.{u1, u3, u2} R _inst_1 B _inst_4 _inst_5 A _inst_2 _inst_3)
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- forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (A : Type.{u2}) [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (B : Type.{u3}) [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4], AlgEquiv.{u1, max u3 u2, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.{u1, u3, u2} R _inst_1 B A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u3, u2} R _inst_1 B _inst_4 _inst_5 A _inst_2 _inst_3) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u3, u2} R _inst_1 B _inst_4 _inst_5 A _inst_2 _inst_3)
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.comm Algebra.TensorProduct.commₓ'. -/
/-- The tensor product of R-algebras is commutative, up to algebra isomorphism.
-/
protected def comm : A ⊗[R] B ≃ₐ[R] B ⊗[R] A :=
@@ -955,18 +799,12 @@ protected def comm : A ⊗[R] B ≃ₐ[R] B ⊗[R] A :=
· simp [Algebra.smul_def]
#align algebra.tensor_product.comm Algebra.TensorProduct.comm
-/- warning: algebra.tensor_product.comm_tmul -> Algebra.TensorProduct.comm_tmul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.comm_tmul Algebra.TensorProduct.comm_tmulₓ'. -/
@[simp]
theorem comm_tmul (a : A) (b : B) :
(TensorProduct.comm R A B : A ⊗[R] B → B ⊗[R] A) (a ⊗ₜ b) = b ⊗ₜ a := by
simp [TensorProduct.comm]
#align algebra.tensor_product.comm_tmul Algebra.TensorProduct.comm_tmul
-/- warning: algebra.tensor_product.adjoin_tmul_eq_top -> Algebra.TensorProduct.adjoin_tmul_eq_top is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.adjoin_tmul_eq_top Algebra.TensorProduct.adjoin_tmul_eq_topₓ'. -/
theorem adjoin_tmul_eq_top : adjoin R { t : A ⊗[R] B | ∃ a b, a ⊗ₜ[R] b = t } = ⊤ :=
top_le_iff.mp <| (top_le_iff.mpr <| span_tmul_eq_top R A B).trans (span_le_adjoin R _)
#align algebra.tensor_product.adjoin_tmul_eq_top Algebra.TensorProduct.adjoin_tmul_eq_top
@@ -977,9 +815,6 @@ section
variable {R A B C}
-/- warning: algebra.tensor_product.assoc_aux_1 -> Algebra.TensorProduct.assoc_aux_1 is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.assoc_aux_1 Algebra.TensorProduct.assoc_aux_1ₓ'. -/
theorem assoc_aux_1 (a₁ a₂ : A) (b₁ b₂ : B) (c₁ c₂ : C) :
(TensorProduct.assoc R A B C) (((a₁ * a₂) ⊗ₜ[R] (b₁ * b₂)) ⊗ₜ[R] (c₁ * c₂)) =
(TensorProduct.assoc R A B C) ((a₁ ⊗ₜ[R] b₁) ⊗ₜ[R] c₁) *
@@ -987,9 +822,6 @@ theorem assoc_aux_1 (a₁ a₂ : A) (b₁ b₂ : B) (c₁ c₂ : C) :
rfl
#align algebra.tensor_product.assoc_aux_1 Algebra.TensorProduct.assoc_aux_1
-/- warning: algebra.tensor_product.assoc_aux_2 -> Algebra.TensorProduct.assoc_aux_2 is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.assoc_aux_2 Algebra.TensorProduct.assoc_aux_2ₓ'. -/
theorem assoc_aux_2 (r : R) :
(TensorProduct.assoc R A B C) (((algebraMap R A) r ⊗ₜ[R] 1) ⊗ₜ[R] 1) =
(algebraMap R (A ⊗ (B ⊗ C))) r :=
@@ -998,9 +830,6 @@ theorem assoc_aux_2 (r : R) :
variable (R A B C)
-/- warning: algebra.tensor_product.assoc -> Algebra.TensorProduct.assoc is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.assoc Algebra.TensorProduct.assocₓ'. -/
/-- The associator for tensor product of R-algebras, as an algebra isomorphism. -/
protected def assoc : (A ⊗[R] B) ⊗[R] C ≃ₐ[R] A ⊗[R] B ⊗[R] C :=
algEquivOfLinearEquivTripleTensorProduct
@@ -1011,9 +840,6 @@ protected def assoc : (A ⊗[R] B) ⊗[R] C ≃ₐ[R] A ⊗[R] B ⊗[R] C :=
variable {R A B C}
-/- warning: algebra.tensor_product.assoc_tmul -> Algebra.TensorProduct.assoc_tmul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.assoc_tmul Algebra.TensorProduct.assoc_tmulₓ'. -/
@[simp]
theorem assoc_tmul (a : A) (b : B) (c : C) :
(TensorProduct.assoc R A B C : (A ⊗[R] B) ⊗[R] C → A ⊗[R] B ⊗[R] C) (a ⊗ₜ b ⊗ₜ c) =
@@ -1025,9 +851,6 @@ end
variable {R A B C D}
-/- warning: algebra.tensor_product.map -> Algebra.TensorProduct.map is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.map Algebra.TensorProduct.mapₓ'. -/
/-- The tensor product of a pair of algebra morphisms. -/
def map (f : A →ₐ[R] B) (g : C →ₐ[R] D) : A ⊗[R] C →ₐ[R] B ⊗[R] D :=
algHomOfLinearMapTensorProduct (TensorProduct.map f.toLinearMap g.toLinearMap) (by simp)
@@ -1041,27 +864,18 @@ theorem map_tmul (f : A →ₐ[R] B) (g : C →ₐ[R] D) (a : A) (c : C) : map f
#align algebra.tensor_product.map_tmul Algebra.TensorProduct.map_tmul
-/
-/- warning: algebra.tensor_product.map_comp_include_left -> Algebra.TensorProduct.map_comp_includeLeft is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.map_comp_include_left Algebra.TensorProduct.map_comp_includeLeftₓ'. -/
@[simp]
theorem map_comp_includeLeft (f : A →ₐ[R] B) (g : C →ₐ[R] D) :
(map f g).comp includeLeft = includeLeft.comp f :=
AlgHom.ext <| by simp
#align algebra.tensor_product.map_comp_include_left Algebra.TensorProduct.map_comp_includeLeft
-/- warning: algebra.tensor_product.map_comp_include_right -> Algebra.TensorProduct.map_comp_includeRight is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.map_comp_include_right Algebra.TensorProduct.map_comp_includeRightₓ'. -/
@[simp]
theorem map_comp_includeRight (f : A →ₐ[R] B) (g : C →ₐ[R] D) :
(map f g).comp includeRight = includeRight.comp g :=
AlgHom.ext <| by simp
#align algebra.tensor_product.map_comp_include_right Algebra.TensorProduct.map_comp_includeRight
-/- warning: algebra.tensor_product.map_range -> Algebra.TensorProduct.map_range is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.map_range Algebra.TensorProduct.map_rangeₓ'. -/
theorem map_range (f : A →ₐ[R] B) (g : C →ₐ[R] D) :
(map f g).range = (includeLeft.comp f).range ⊔ (includeRight.comp g).range :=
by
@@ -1074,9 +888,6 @@ theorem map_range (f : A →ₐ[R] B) (g : C →ₐ[R] D) :
exact sup_le (AlgHom.range_comp_le_range _ _) (AlgHom.range_comp_le_range _ _)
#align algebra.tensor_product.map_range Algebra.TensorProduct.map_range
-/- warning: algebra.tensor_product.congr -> Algebra.TensorProduct.congr is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.congr Algebra.TensorProduct.congrₓ'. -/
/-- Construct an isomorphism between tensor products of R-algebras
from isomorphisms between the tensor factors.
-/
@@ -1084,18 +895,12 @@ def congr (f : A ≃ₐ[R] B) (g : C ≃ₐ[R] D) : A ⊗[R] C ≃ₐ[R] B ⊗[R
AlgEquiv.ofAlgHom (map f g) (map f.symm g.symm) (ext fun b d => by simp) (ext fun a c => by simp)
#align algebra.tensor_product.congr Algebra.TensorProduct.congr
-/- warning: algebra.tensor_product.congr_apply -> Algebra.TensorProduct.congr_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.congr_apply Algebra.TensorProduct.congr_applyₓ'. -/
@[simp]
theorem congr_apply (f : A ≃ₐ[R] B) (g : C ≃ₐ[R] D) (x) :
congr f g x = (map (f : A →ₐ[R] B) (g : C →ₐ[R] D)) x :=
rfl
#align algebra.tensor_product.congr_apply Algebra.TensorProduct.congr_apply
-/- warning: algebra.tensor_product.congr_symm_apply -> Algebra.TensorProduct.congr_symm_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.congr_symm_apply Algebra.TensorProduct.congr_symm_applyₓ'. -/
@[simp]
theorem congr_symm_apply (f : A ≃ₐ[R] B) (g : C ≃ₐ[R] D) (x) :
(congr f g).symm x = (map (f.symm : B →ₐ[R] A) (g.symm : D →ₐ[R] C)) x :=
@@ -1116,12 +921,6 @@ variable (f : A →ₐ[R] S) (g : B →ₐ[R] S)
variable (R)
-/- warning: algebra.tensor_product.lmul' -> Algebra.TensorProduct.lmul' is a dubious translation:
-lean 3 declaration is
- forall (R : Type.{u1}) {S : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_4 : CommSemiring.{u2} S] [_inst_7 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_4)], AlgHom.{u1, u2, u2} R (TensorProduct.{u1, u2, u2} R _inst_1 S S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_4)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_4) _inst_7) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_4) _inst_7)) S _inst_1 (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u2} R _inst_1 S (CommSemiring.toSemiring.{u2} S _inst_4) _inst_7 S (CommSemiring.toSemiring.{u2} S _inst_4) _inst_7) (CommSemiring.toSemiring.{u2} S _inst_4) (Algebra.TensorProduct.TensorProduct.algebra.{u1, u2, u2} R _inst_1 S (CommSemiring.toSemiring.{u2} S _inst_4) _inst_7 S (CommSemiring.toSemiring.{u2} S _inst_4) _inst_7) _inst_7
-but is expected to have type
- forall (R : Type.{u1}) {S : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_4 : CommSemiring.{u2} S] [_inst_7 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_4)], AlgHom.{u1, u2, u2} R (TensorProduct.{u1, u2, u2} R _inst_1 S S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_4)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_4) _inst_7) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_4) _inst_7)) S _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u2} R _inst_1 S (CommSemiring.toSemiring.{u2} S _inst_4) _inst_7 S (CommSemiring.toSemiring.{u2} S _inst_4) _inst_7) (CommSemiring.toSemiring.{u2} S _inst_4) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u2} R _inst_1 S (CommSemiring.toSemiring.{u2} S _inst_4) _inst_7 S (CommSemiring.toSemiring.{u2} S _inst_4) _inst_7) _inst_7
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.lmul' Algebra.TensorProduct.lmul'ₓ'. -/
/-- `linear_map.mul'` is an alg_hom on commutative rings. -/
def lmul' : S ⊗[R] S →ₐ[R] S :=
algHomOfLinearMapTensorProduct (LinearMap.mul' R S)
@@ -1131,9 +930,6 @@ def lmul' : S ⊗[R] S →ₐ[R] S :=
variable {R}
-/- warning: algebra.tensor_product.lmul'_to_linear_map -> Algebra.TensorProduct.lmul'_toLinearMap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.lmul'_to_linear_map Algebra.TensorProduct.lmul'_toLinearMapₓ'. -/
theorem lmul'_toLinearMap : (lmul' R : _ →ₐ[R] S).toLinearMap = LinearMap.mul' R S :=
rfl
#align algebra.tensor_product.lmul'_to_linear_map Algebra.TensorProduct.lmul'_toLinearMap
@@ -1159,12 +955,6 @@ theorem lmul'_comp_includeRight : (lmul' R : _ →ₐ[R] S).comp includeRight =
#align algebra.tensor_product.lmul'_comp_include_right Algebra.TensorProduct.lmul'_comp_includeRight
-/
-/- warning: algebra.tensor_product.product_map -> Algebra.TensorProduct.productMap is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} {S : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Semiring.{u3} B] [_inst_4 : CommSemiring.{u4} S] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_6 : Algebra.{u1, u3} R B _inst_1 _inst_3] [_inst_7 : Algebra.{u1, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_4)], (AlgHom.{u1, u2, u4} R A S _inst_1 _inst_2 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_5 _inst_7) -> (AlgHom.{u1, u3, u4} R B S _inst_1 _inst_3 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_6 _inst_7) -> (AlgHom.{u1, max u2 u3, u4} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_3 _inst_6)) S _inst_1 (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u3} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) (CommSemiring.toSemiring.{u4} S _inst_4) (Algebra.TensorProduct.TensorProduct.algebra.{u1, u2, u3} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) _inst_7)
-but is expected to have type
- forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} {S : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Semiring.{u3} B] [_inst_4 : CommSemiring.{u4} S] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_6 : Algebra.{u1, u3} R B _inst_1 _inst_3] [_inst_7 : Algebra.{u1, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_4)], (AlgHom.{u1, u2, u4} R A S _inst_1 _inst_2 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_5 _inst_7) -> (AlgHom.{u1, u3, u4} R B S _inst_1 _inst_3 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_6 _inst_7) -> (AlgHom.{u1, max u3 u2, u4} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_3 _inst_6)) S _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) (CommSemiring.toSemiring.{u4} S _inst_4) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) _inst_7)
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.product_map Algebra.TensorProduct.productMapₓ'. -/
/-- If `S` is commutative, for a pair of morphisms `f : A →ₐ[R] S`, `g : B →ₐ[R] S`,
We obtain a map `A ⊗[R] B →ₐ[R] S` that commutes with `f`, `g` via `a ⊗ b ↦ f(a) * g(b)`.
-/
@@ -1172,46 +962,28 @@ def productMap : A ⊗[R] B →ₐ[R] S :=
(lmul' R).comp (TensorProduct.map f g)
#align algebra.tensor_product.product_map Algebra.TensorProduct.productMap
-/- warning: algebra.tensor_product.product_map_apply_tmul -> Algebra.TensorProduct.productMap_apply_tmul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.product_map_apply_tmul Algebra.TensorProduct.productMap_apply_tmulₓ'. -/
@[simp]
theorem productMap_apply_tmul (a : A) (b : B) : productMap f g (a ⊗ₜ b) = f a * g b := by
unfold product_map lmul'; simp
#align algebra.tensor_product.product_map_apply_tmul Algebra.TensorProduct.productMap_apply_tmul
-/- warning: algebra.tensor_product.product_map_left_apply -> Algebra.TensorProduct.productMap_left_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.product_map_left_apply Algebra.TensorProduct.productMap_left_applyₓ'. -/
theorem productMap_left_apply (a : A) : productMap f g ((includeLeft : A →ₐ[R] A ⊗ B) a) = f a := by
simp
#align algebra.tensor_product.product_map_left_apply Algebra.TensorProduct.productMap_left_apply
-/- warning: algebra.tensor_product.product_map_left -> Algebra.TensorProduct.productMap_left is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.product_map_left Algebra.TensorProduct.productMap_leftₓ'. -/
@[simp]
theorem productMap_left : (productMap f g).comp includeLeft = f :=
AlgHom.ext <| by simp
#align algebra.tensor_product.product_map_left Algebra.TensorProduct.productMap_left
-/- warning: algebra.tensor_product.product_map_right_apply -> Algebra.TensorProduct.productMap_right_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.product_map_right_apply Algebra.TensorProduct.productMap_right_applyₓ'. -/
theorem productMap_right_apply (b : B) : productMap f g (includeRight b) = g b := by simp
#align algebra.tensor_product.product_map_right_apply Algebra.TensorProduct.productMap_right_apply
-/- warning: algebra.tensor_product.product_map_right -> Algebra.TensorProduct.productMap_right is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.product_map_right Algebra.TensorProduct.productMap_rightₓ'. -/
@[simp]
theorem productMap_right : (productMap f g).comp includeRight = g :=
AlgHom.ext <| by simp
#align algebra.tensor_product.product_map_right Algebra.TensorProduct.productMap_right
-/- warning: algebra.tensor_product.product_map_range -> Algebra.TensorProduct.productMap_range is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.product_map_range Algebra.TensorProduct.productMap_rangeₓ'. -/
theorem productMap_range : (productMap f g).range = f.range ⊔ g.range := by
rw [product_map, AlgHom.range_comp, map_range, map_sup, ← AlgHom.range_comp, ← AlgHom.range_comp,
← AlgHom.comp_assoc, ← AlgHom.comp_assoc, lmul'_comp_include_left, lmul'_comp_include_right,
@@ -1230,9 +1002,6 @@ variable [Algebra R A] [Algebra R A'] [Algebra A A'] [IsScalarTower R A A'] [Alg
variable [Algebra R S] [Algebra A S] [IsScalarTower R A S]
-/- warning: algebra.tensor_product.product_left_alg_hom -> Algebra.TensorProduct.productLeftAlgHom is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.product_left_alg_hom Algebra.TensorProduct.productLeftAlgHomₓ'. -/
/-- If `A`, `B` are `R`-algebras, `A'` is an `A`-algebra, then the product map of `f : A' →ₐ[A] S`
and `g : B →ₐ[R] S` is an `A`-algebra homomorphism. -/
@[simps]
@@ -1247,12 +1016,6 @@ section Basis
variable {k : Type _} [CommRing k] (R : Type _) [Ring R] [Algebra k R] {M : Type _}
[AddCommMonoid M] [Module k M] {ι : Type _} (b : Basis ι k M)
-/- warning: algebra.tensor_product.basis_aux -> Algebra.TensorProduct.basisAux is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u_1}} [_inst_1 : CommRing.{u_1} k] (R : Type.{u_2}) [_inst_2 : Ring.{u_2} R] [_inst_3 : Algebra.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2)] {M : Type.{u_3}} [_inst_4 : AddCommMonoid.{u_3} M] [_inst_5 : Module.{u_1, u_3} k M (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) _inst_4] {ι : Type.{u_4}}, (Basis.{u_4, u_1, u_3} ι k M (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) _inst_4 _inst_5) -> (LinearEquiv.{u_1, u_1, max u_2 u_3, max u_4 u_2} k k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (Algebra.TensorProduct.basisAux._proof_1.{u_1} k _inst_1) (Algebra.TensorProduct.basisAux._proof_2.{u_1} k _inst_1) (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))))) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.module.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3)))
-but is expected to have type
- forall {k : Type.{u_1}} [_inst_1 : CommRing.{u_1} k] (R : Type.{u_2}) [_inst_2 : Ring.{u_2} R] [_inst_3 : Algebra.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2)] {M : Type.{u_3}} [_inst_4 : AddCommMonoid.{u_3} M] [_inst_5 : Module.{u_1, u_3} k M (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) _inst_4] {ι : Type.{u_4}}, (Basis.{u_4, u_1, u_3} ι k M (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) _inst_4 _inst_5) -> (LinearEquiv.{u_1, u_1, max u_3 u_2, max u_2 u_4} k k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3)))
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.basis_aux Algebra.TensorProduct.basisAuxₓ'. -/
/-- Given a `k`-algebra `R` and a `k`-basis of `M,` this is a `k`-linear isomorphism
`R ⊗[k] M ≃ (ι →₀ R)` (which is in fact `R`-linear). -/
noncomputable def basisAux : R ⊗[k] M ≃ₗ[k] ι →₀ R :=
@@ -1263,9 +1026,6 @@ noncomputable def basisAux : R ⊗[k] M ≃ₗ[k] ι →₀ R :=
variable {R}
-/- warning: algebra.tensor_product.basis_aux_tmul -> Algebra.TensorProduct.basisAux_tmul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.basis_aux_tmul Algebra.TensorProduct.basisAux_tmulₓ'. -/
theorem basisAux_tmul (r : R) (m : M) :
basisAux R b (r ⊗ₜ m) = r • Finsupp.mapRange (algebraMap k R) (map_zero _) (b.repr m) :=
by
@@ -1273,9 +1033,6 @@ theorem basisAux_tmul (r : R) (m : M) :
simp [basis_aux, ← Algebra.commutes, Algebra.smul_def]
#align algebra.tensor_product.basis_aux_tmul Algebra.TensorProduct.basisAux_tmul
-/- warning: algebra.tensor_product.basis_aux_map_smul -> Algebra.TensorProduct.basisAux_map_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.basis_aux_map_smul Algebra.TensorProduct.basisAux_map_smulₓ'. -/
theorem basisAux_map_smul (r : R) (x : R ⊗[k] M) : basisAux R b (r • x) = r • basisAux R b x :=
TensorProduct.induction_on x (by simp)
(fun x y => by simp only [TensorProduct.smul_tmul', basis_aux_tmul, smul_assoc])
@@ -1284,12 +1041,6 @@ theorem basisAux_map_smul (r : R) (x : R ⊗[k] M) : basisAux R b (r • x) = r
variable (R)
-/- warning: algebra.tensor_product.basis -> Algebra.TensorProduct.basis is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u_1}} [_inst_1 : CommRing.{u_1} k] (R : Type.{u_2}) [_inst_2 : Ring.{u_2} R] [_inst_3 : Algebra.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2)] {M : Type.{u_3}} [_inst_4 : AddCommMonoid.{u_3} M] [_inst_5 : Module.{u_1, u_3} k M (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) _inst_4] {ι : Type.{u_4}}, (Basis.{u_4, u_1, u_3} ι k M (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) _inst_4 _inst_5) -> (Basis.{u_4, u_2, max u_2 u_3} ι R (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Ring.toSemiring.{u_2} R _inst_2) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (TensorProduct.leftModule.{u_1, u_2, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R (Ring.toSemiring.{u_2} R _inst_2) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5 (Semiring.toModule.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)) (Algebra.TensorProduct.basis._proof_1.{u_1, u_2} k _inst_1 R _inst_2 _inst_3)))
-but is expected to have type
- forall {k : Type.{u_1}} [_inst_1 : CommRing.{u_1} k] (R : Type.{u_2}) [_inst_2 : Ring.{u_2} R] [_inst_3 : Algebra.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2)] {M : Type.{u_3}} [_inst_4 : AddCommMonoid.{u_3} M] [_inst_5 : Module.{u_1, u_3} k M (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) _inst_4] {ι : Type.{u_4}}, (Basis.{u_4, u_1, u_3} ι k M (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) _inst_4 _inst_5) -> (Basis.{u_4, u_2, max u_3 u_2} ι R (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Ring.toSemiring.{u_2} R _inst_2) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (TensorProduct.leftModule.{u_1, u_2, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R (Ring.toSemiring.{u_2} R _inst_2) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5 (Semiring.toModule.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)) (Algebra.to_smulCommClass.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3)))
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.basis Algebra.TensorProduct.basisₓ'. -/
/-- Given a `k`-algebra `R`, this is the `R`-basis of `R ⊗[k] M` induced by a `k`-basis of `M`. -/
noncomputable def basis : Basis ι R (R ⊗[k] M)
where repr := { basisAux R b with map_smul' := basisAux_map_smul b }
@@ -1297,18 +1048,12 @@ noncomputable def basis : Basis ι R (R ⊗[k] M)
variable {R}
-/- warning: algebra.tensor_product.basis_repr_tmul -> Algebra.TensorProduct.basis_repr_tmul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.basis_repr_tmul Algebra.TensorProduct.basis_repr_tmulₓ'. -/
@[simp]
theorem basis_repr_tmul (r : R) (m : M) :
(basis R b).repr (r ⊗ₜ m) = r • Finsupp.mapRange (algebraMap k R) (map_zero _) (b.repr m) :=
basisAux_tmul _ _ _
#align algebra.tensor_product.basis_repr_tmul Algebra.TensorProduct.basis_repr_tmul
-/- warning: algebra.tensor_product.basis_repr_symm_apply -> Algebra.TensorProduct.basis_repr_symm_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.basis_repr_symm_apply Algebra.TensorProduct.basis_repr_symm_applyₓ'. -/
@[simp]
theorem basis_repr_symm_apply (r : R) (i : ι) :
(basis R b).repr.symm (Finsupp.single i r) = r ⊗ₜ b.repr.symm (Finsupp.single i 1) := by
@@ -1343,9 +1088,6 @@ def endTensorEndAlgHom : End R M ⊗[R] End R N →ₐ[R] End R (M ⊗[R] N) :=
#align module.End_tensor_End_alg_hom Module.endTensorEndAlgHom
-/
-/- warning: module.End_tensor_End_alg_hom_apply -> Module.endTensorEndAlgHom_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align module.End_tensor_End_alg_hom_apply Module.endTensorEndAlgHom_applyₓ'. -/
theorem endTensorEndAlgHom_apply (f : End R M) (g : End R N) :
endTensorEndAlgHom (f ⊗ₜ[R] g) = TensorProduct.map f g := by
simp only [End_tensor_End_alg_hom, Algebra.TensorProduct.algHomOfLinearMapTensorProduct_apply,
@@ -1354,9 +1096,6 @@ theorem endTensorEndAlgHom_apply (f : End R M) (g : End R N) :
end Module
-/- warning: subalgebra.finite_dimensional_sup -> Subalgebra.finiteDimensional_sup is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align subalgebra.finite_dimensional_sup Subalgebra.finiteDimensional_supₓ'. -/
theorem Subalgebra.finiteDimensional_sup {K L : Type _} [Field K] [CommRing L] [Algebra K L]
(E1 E2 : Subalgebra K L) [FiniteDimensional K E1] [FiniteDimensional K E2] :
FiniteDimensional K ↥(E1 ⊔ E2) :=
@@ -1377,9 +1116,6 @@ variable [Algebra R A] [Algebra R B]
variable [IsScalarTower R A M] [IsScalarTower R B M]
-/- warning: tensor_product.algebra.module_aux -> TensorProduct.Algebra.moduleAux is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.algebra.module_aux TensorProduct.Algebra.moduleAuxₓ'. -/
/-- An auxiliary definition, used for constructing the `module (A ⊗[R] B) M` in
`tensor_product.algebra.module` below. -/
def moduleAux : A ⊗[R] B →ₗ[R] M →ₗ[R] M :=
@@ -1390,18 +1126,12 @@ def moduleAux : A ⊗[R] B →ₗ[R] M →ₗ[R] M :=
simp only [RingHom.id_apply, LinearMap.smul_apply, smul_assoc] }
#align tensor_product.algebra.module_aux TensorProduct.Algebra.moduleAux
-/- warning: tensor_product.algebra.module_aux_apply -> TensorProduct.Algebra.moduleAux_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.algebra.module_aux_apply TensorProduct.Algebra.moduleAux_applyₓ'. -/
theorem moduleAux_apply (a : A) (b : B) (m : M) : moduleAux (a ⊗ₜ[R] b) m = a • b • m :=
rfl
#align tensor_product.algebra.module_aux_apply TensorProduct.Algebra.moduleAux_apply
variable [SMulCommClass A B M]
-/- warning: tensor_product.algebra.module -> TensorProduct.Algebra.module is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.algebra.module TensorProduct.Algebra.moduleₓ'. -/
/-- If `M` is a representation of two different `R`-algebras `A` and `B` whose actions commute,
then it is a representation the `R`-algebra `A ⊗[R] B`.
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -243,14 +243,9 @@ def assoc : (M ⊗[A] P) ⊗[R] N ≃ₗ[A] M ⊗[A] P ⊗[R] N :=
(lift <|
TensorProduct.uncurry A _ _ _ <| comp (lcurry R A _ _ _) <| TensorProduct.mk A M (P ⊗[R] N))
(TensorProduct.uncurry A _ _ _ <|
- comp (uncurry R A _ _ _) <| by
- apply TensorProduct.curry
- exact mk R A _ _)
- (by
- ext
- rfl)
- (by
- ext
+ comp (uncurry R A _ _ _) <| by apply TensorProduct.curry; exact mk R A _ _)
+ (by ext; rfl)
+ (by ext;
simp only [curry_apply, TensorProduct.curry_apply, mk_apply, TensorProduct.mk_apply,
uncurry_apply, TensorProduct.uncurry_apply, id_apply, lift_tmul, compr₂_apply,
restrict_scalars_apply, Function.comp_apply, to_fun_eq_coe, lcurry_apply,
@@ -322,9 +317,7 @@ theorem baseChange_eq_ltensor : (f.base_change A : A ⊗ M → A ⊗ N) = f.lTen
<too large>
Case conversion may be inaccurate. Consider using '#align linear_map.base_change_add LinearMap.baseChange_addₓ'. -/
@[simp]
-theorem baseChange_add : (f + g).base_change A = f.base_change A + g.base_change A :=
- by
- ext
+theorem baseChange_add : (f + g).base_change A = f.base_change A + g.base_change A := by ext;
simp [base_change_eq_ltensor]
#align linear_map.base_change_add LinearMap.baseChange_add
@@ -332,19 +325,14 @@ theorem baseChange_add : (f + g).base_change A = f.base_change A + g.base_change
<too large>
Case conversion may be inaccurate. Consider using '#align linear_map.base_change_zero LinearMap.baseChange_zeroₓ'. -/
@[simp]
-theorem baseChange_zero : baseChange A (0 : M →ₗ[R] N) = 0 :=
- by
- ext
- simp [base_change_eq_ltensor]
+theorem baseChange_zero : baseChange A (0 : M →ₗ[R] N) = 0 := by ext; simp [base_change_eq_ltensor]
#align linear_map.base_change_zero LinearMap.baseChange_zero
/- warning: linear_map.base_change_smul -> LinearMap.baseChange_smul is a dubious translation:
<too large>
Case conversion may be inaccurate. Consider using '#align linear_map.base_change_smul LinearMap.baseChange_smulₓ'. -/
@[simp]
-theorem baseChange_smul : (r • f).base_change A = r • f.base_change A :=
- by
- ext
+theorem baseChange_smul : (r • f).base_change A = r • f.base_change A := by ext;
simp [base_change_tmul]
#align linear_map.base_change_smul LinearMap.baseChange_smul
@@ -377,9 +365,7 @@ variable (f g : M →ₗ[R] N)
<too large>
Case conversion may be inaccurate. Consider using '#align linear_map.base_change_sub LinearMap.baseChange_subₓ'. -/
@[simp]
-theorem baseChange_sub : (f - g).base_change A = f.base_change A - g.base_change A :=
- by
- ext
+theorem baseChange_sub : (f - g).base_change A = f.base_change A - g.base_change A := by ext;
simp [base_change_eq_ltensor]
#align linear_map.base_change_sub LinearMap.baseChange_sub
@@ -387,9 +373,7 @@ theorem baseChange_sub : (f - g).base_change A = f.base_change A - g.base_change
<too large>
Case conversion may be inaccurate. Consider using '#align linear_map.base_change_neg LinearMap.baseChange_negₓ'. -/
@[simp]
-theorem baseChange_neg : (-f).base_change A = -f.base_change A :=
- by
- ext
+theorem baseChange_neg : (-f).base_change A = -f.base_change A := by ext;
simp [base_change_eq_ltensor]
#align linear_map.base_change_neg LinearMap.baseChange_neg
@@ -488,25 +472,17 @@ theorem mul_assoc' (mul : A ⊗[R] B →ₗ[R] A ⊗[R] B →ₗ[R] A ⊗[R] B)
· simp only [LinearMap.map_zero, forall_const, LinearMap.zero_apply]
apply TensorProduct.induction_on z
· simp only [LinearMap.map_zero, forall_const]
- · intros
- simp only [h]
- · intros
- simp only [LinearMap.map_add, *]
- · intros
- simp only [LinearMap.map_add, *, LinearMap.add_apply]
- · intros
- simp only [LinearMap.map_add, *, LinearMap.add_apply]
+ · intros ; simp only [h]
+ · intros ; simp only [LinearMap.map_add, *]
+ · intros ; simp only [LinearMap.map_add, *, LinearMap.add_apply]
+ · intros ; simp only [LinearMap.map_add, *, LinearMap.add_apply]
#align algebra.tensor_product.mul_assoc' Algebra.TensorProduct.mul_assoc'
/- warning: algebra.tensor_product.mul_assoc -> Algebra.TensorProduct.mul_assoc is a dubious translation:
<too large>
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.mul_assoc Algebra.TensorProduct.mul_assocₓ'. -/
theorem mul_assoc (x y z : A ⊗[R] B) : mul (mul x y) z = mul x (mul y z) :=
- mul_assoc' mul
- (by
- intros
- simp only [mul_apply, mul_assoc])
- x y z
+ mul_assoc' mul (by intros ; simp only [mul_apply, mul_assoc]) x y z
#align algebra.tensor_product.mul_assoc Algebra.TensorProduct.mul_assoc
/- warning: algebra.tensor_product.one_mul -> Algebra.TensorProduct.one_mul is a dubious translation:
@@ -604,21 +580,13 @@ instance leftAlgebra : Algebra S (A ⊗[R] B) :=
commutes' := fun r x => by
apply TensorProduct.induction_on x
· simp
- · intro a b
- dsimp
- rw [Algebra.commutes, _root_.mul_one, _root_.one_mul]
- · intro y y' h h'
- dsimp at h h'⊢
- simp only [mul_add, add_mul, h, h']
+ · intro a b; dsimp; rw [Algebra.commutes, _root_.mul_one, _root_.one_mul]
+ · intro y y' h h'; dsimp at h h'⊢; simp only [mul_add, add_mul, h, h']
smul_def' := fun r x => by
apply TensorProduct.induction_on x
· simp [smul_zero]
- · intro a b
- dsimp
- rw [TensorProduct.smul_tmul', Algebra.smul_def r a, _root_.one_mul]
- · intros
- dsimp
- simp [smul_add, mul_add, *] }
+ · intro a b; dsimp; rw [TensorProduct.smul_tmul', Algebra.smul_def r a, _root_.one_mul]
+ · intros ; dsimp; simp [smul_add, mul_add, *] }
#align algebra.tensor_product.left_algebra Algebra.TensorProduct.leftAlgebra
-- This is for the `undergrad.yaml` list.
@@ -684,8 +652,7 @@ def includeRight : B →ₐ[R] A ⊗[R] B where
commutes' r := by
simp only [algebraMap_apply]
trans r • (1 : A) ⊗ₜ[R] (1 : B)
- · rw [← tmul_smul, Algebra.smul_def]
- simp
+ · rw [← tmul_smul, Algebra.smul_def]; simp
· simp [Algebra.smul_def]
#align algebra.tensor_product.include_right Algebra.TensorProduct.includeRight
@@ -703,9 +670,7 @@ theorem includeLeft_comp_algebraMap {R S T : Type _} [CommRing R] [CommRing S] [
[Algebra R S] [Algebra R T] :
(includeLeft.toRingHom.comp (algebraMap R S) : R →+* S ⊗[R] T) =
includeRight.toRingHom.comp (algebraMap R T) :=
- by
- ext
- simp
+ by ext; simp
#align algebra.tensor_product.include_left_comp_algebra_map Algebra.TensorProduct.includeLeft_comp_algebraMap
end Semiring
@@ -889,8 +854,7 @@ def algEquivOfLinearEquivTripleTensorProduct (f : (A ⊗[R] B) ⊗[R] C ≃ₗ[R
· intro a₁ b₁
apply TensorProduct.induction_on ab₂
· simp only [zero_tmul, map_zero, MulZeroClass.mul_zero]
- · intros
- simp only [tmul_mul_tmul, w₁]
+ · intros ; simp only [tmul_mul_tmul, w₁]
· intro x₁ x₂ h₁ h₂
simp only [tmul_mul_tmul] at h₁ h₂
simp only [tmul_mul_tmul, mul_add, add_tmul, map_add, h₁, h₂]
@@ -987,8 +951,7 @@ protected def comm : A ⊗[R] B ≃ₐ[R] B ⊗[R] A :=
algEquivOfLinearEquivTensorProduct (TensorProduct.comm R A B) (by simp) fun r =>
by
trans r • (1 : B) ⊗ₜ[R] (1 : A)
- · rw [← tmul_smul, Algebra.smul_def]
- simp
+ · rw [← tmul_smul, Algebra.smul_def]; simp
· simp [Algebra.smul_def]
#align algebra.tensor_product.comm Algebra.TensorProduct.comm
@@ -1213,10 +1176,8 @@ def productMap : A ⊗[R] B →ₐ[R] S :=
<too large>
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.product_map_apply_tmul Algebra.TensorProduct.productMap_apply_tmulₓ'. -/
@[simp]
-theorem productMap_apply_tmul (a : A) (b : B) : productMap f g (a ⊗ₜ b) = f a * g b :=
- by
- unfold product_map lmul'
- simp
+theorem productMap_apply_tmul (a : A) (b : B) : productMap f g (a ⊗ₜ b) = f a * g b := by
+ unfold product_map lmul'; simp
#align algebra.tensor_product.product_map_apply_tmul Algebra.TensorProduct.productMap_apply_tmul
/- warning: algebra.tensor_product.product_map_left_apply -> Algebra.TensorProduct.productMap_left_apply is a dubious translation:
@@ -1276,10 +1237,7 @@ Case conversion may be inaccurate. Consider using '#align algebra.tensor_product
and `g : B →ₐ[R] S` is an `A`-algebra homomorphism. -/
@[simps]
def productLeftAlgHom (f : A' →ₐ[A] S) (g : B →ₐ[R] S) : A' ⊗[R] B →ₐ[A] S :=
- { (productMap (f.restrictScalars R) g).toRingHom with
- commutes' := fun r => by
- dsimp
- simp }
+ { (productMap (f.restrictScalars R) g).toRingHom with commutes' := fun r => by dsimp; simp }
#align algebra.tensor_product.product_left_alg_hom Algebra.TensorProduct.productLeftAlgHom
end
@@ -1381,8 +1339,7 @@ def endTensorEndAlgHom : End R M ⊗[R] End R N →ₐ[R] End R (M ⊗[R] N) :=
simp only [hom_tensor_hom_map_apply, TensorProduct.map_mul]
· intro r
simp only [hom_tensor_hom_map_apply]
- ext (m n)
- simp [smul_tmul]
+ ext (m n); simp [smul_tmul]
#align module.End_tensor_End_alg_hom Module.endTensorEndAlgHom
-/
@@ -1428,11 +1385,8 @@ Case conversion may be inaccurate. Consider using '#align tensor_product.algebra
def moduleAux : A ⊗[R] B →ₗ[R] M →ₗ[R] M :=
TensorProduct.lift
{ toFun := fun a => a • (Algebra.lsmul R M : B →ₐ[R] Module.End R M).toLinearMap
- map_add' := fun r t => by
- ext
- simp only [add_smul, LinearMap.add_apply]
- map_smul' := fun n r => by
- ext
+ map_add' := fun r t => by ext; simp only [add_smul, LinearMap.add_apply]
+ map_smul' := fun n r => by ext;
simp only [RingHom.id_apply, LinearMap.smul_apply, smul_assoc] }
#align tensor_product.algebra.module_aux TensorProduct.Algebra.moduleAux
@@ -1474,20 +1428,16 @@ protected def module : Module (A ⊗[R] B) M
by
apply TensorProduct.induction_on x <;> apply TensorProduct.induction_on y
· simp only [MulZeroClass.mul_zero, map_zero, LinearMap.zero_apply]
- · intro a b
- simp only [MulZeroClass.zero_mul, map_zero, LinearMap.zero_apply]
- · intro z w hz hw
- simp only [MulZeroClass.zero_mul, map_zero, LinearMap.zero_apply]
- · intro a b
- simp only [MulZeroClass.mul_zero, map_zero, LinearMap.zero_apply]
+ · intro a b; simp only [MulZeroClass.zero_mul, map_zero, LinearMap.zero_apply]
+ · intro z w hz hw; simp only [MulZeroClass.zero_mul, map_zero, LinearMap.zero_apply]
+ · intro a b; simp only [MulZeroClass.mul_zero, map_zero, LinearMap.zero_apply]
· intro a₁ b₁ a₂ b₂
simp only [module_aux_apply, mul_smul, smul_comm a₁ b₂, Algebra.TensorProduct.tmul_mul_tmul,
LinearMap.mul_apply]
· intro z w hz hw a b
simp only at hz hw
simp only [mul_add, hz, hw, map_add, LinearMap.add_apply]
- · intro z w hz hw
- simp only [MulZeroClass.mul_zero, map_zero, LinearMap.zero_apply]
+ · intro z w hz hw; simp only [MulZeroClass.mul_zero, map_zero, LinearMap.zero_apply]
· intro a b z w hz hw
simp only at hz hw
simp only [map_add, add_mul, LinearMap.add_apply, hz, hw]
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -83,10 +83,7 @@ variable [AddCommMonoid N] [Module R N]
variable [AddCommMonoid P] [Module R P] [Module A P] [IsScalarTower R A P]
/- warning: tensor_product.algebra_tensor_module.smul_eq_lsmul_rtensor -> TensorProduct.AlgebraTensorModule.smul_eq_lsmul_rTensor is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {A : Type.{u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} A M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u2, u3} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toHasSmul.{u1, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))] [_inst_8 : AddCommMonoid.{u4} N] [_inst_9 : Module.{u1, u4} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8] (a : A) (x : TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9), Eq.{succ (max u3 u4)} (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (SMul.smul.{u2, max u3 u4} A (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (TensorProduct.leftHasSMul.{u1, u2, u3, u4} R _inst_1 A (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) M N _inst_4 _inst_8 _inst_5 _inst_9 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- forall {R : Type.{u4}} {A : Type.{u1}} {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u4, u1} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] [_inst_6 : Module.{u1, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u4, u1, u3} R A M (Algebra.toSMul.{u4, u1} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u1, u3} A M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u1, u3} A M (MonoidWithZero.toZero.{u1} A (Semiring.toMonoidWithZero.{u1} A _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u1, u3} A M (Semiring.toMonoidWithZero.{u1} A _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u1, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toSMul.{u4, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u4, u3} R M (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u4, u3} R M (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5))))] [_inst_8 : AddCommMonoid.{u2} N] [_inst_9 : Module.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8] (a : A) (x : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9), Eq.{max (succ u3) (succ u2)} (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (HSMul.hSMul.{u1, max u3 u2, max u3 u2} A (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) 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_inst_5 _inst_9) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (TensorProduct.addCommMonoid.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (TensorProduct.addCommMonoid.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.rTensor.{u4, u2, u3, u3} R _inst_1 N M M _inst_8 _inst_4 _inst_4 _inst_9 _inst_5 _inst_5 (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (AlgHom.{u4, u1, u3} R A (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u4, u3} R M _inst_1 _inst_4 _inst_5)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _x) (SMulHomClass.toFunLike.{max u3 u1, u4, u1, u3} (AlgHom.{u4, u1, u3} R A (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u4, u3} R M _inst_1 _inst_4 _inst_5)) R A (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (SMulZeroClass.toSMul.{u4, u1} R A (AddMonoid.toZero.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u4, u1} R A 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(Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5)))))) (DistribSMul.toSMulZeroClass.{u4, u3} R (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (AddMonoid.toAddZeroClass.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} 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(CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5)))) (Algebra.toModule.{u4, u3} R (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_1 (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Module.instAlgebraEndToSemiringSemiring.{u4, u3} R M _inst_1 _inst_4 _inst_5))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u1, u4, u1, u3} (AlgHom.{u4, u1, u3} R A (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u4, u3} R M _inst_1 _inst_4 _inst_5)) R A (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5))) (Module.toDistribMulAction.{u4, u1} R A (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u4, u1} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u4, u3} R (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5)))) (Algebra.toModule.{u4, u3} R (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_1 (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Module.instAlgebraEndToSemiringSemiring.{u4, u3} R M _inst_1 _inst_4 _inst_5))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u4, u1, u3, max u3 u1} R A (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u4, u3} R M _inst_1 _inst_4 _inst_5) (AlgHom.{u4, u1, u3} R A (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u4, u3} R M _inst_1 _inst_4 _inst_5)) (AlgHom.algHomClass.{u4, u1, u3} R A (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u4, u3} R M _inst_1 _inst_4 _inst_5)))))) (Algebra.lsmul.{u4, u1, u3} R A M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) a)) x)
+<too large>
Case conversion may be inaccurate. Consider using '#align tensor_product.algebra_tensor_module.smul_eq_lsmul_rtensor TensorProduct.AlgebraTensorModule.smul_eq_lsmul_rTensorₓ'. -/
theorem smul_eq_lsmul_rTensor (a : A) (x : M ⊗[R] N) : a • x = (lsmul R M a).rTensor N x :=
rfl
@@ -108,10 +105,7 @@ def curry (f : M ⊗[R] N →ₗ[A] P) : M →ₗ[A] N →ₗ[R] P :=
-/
/- warning: tensor_product.algebra_tensor_module.restrict_scalars_curry -> TensorProduct.AlgebraTensorModule.restrictScalars_curry is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {A : Type.{u2}} {M : Type.{u3}} {N : Type.{u4}} {P : Type.{u5}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} A M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u2, u3} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toHasSmul.{u1, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))] [_inst_8 : AddCommMonoid.{u4} N] [_inst_9 : Module.{u1, u4} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8] [_inst_10 : AddCommMonoid.{u5} P] [_inst_11 : Module.{u1, u5} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_10] [_inst_12 : Module.{u2, u5} A P _inst_2 _inst_10] [_inst_13 : IsScalarTower.{u1, u2, u5} R A P (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u5} A P (AddZeroClass.toHasZero.{u5} P (AddMonoid.toAddZeroClass.{u5} P (AddCommMonoid.toAddMonoid.{u5} P _inst_10))) (SMulWithZero.toSmulZeroClass.{u2, u5} A P (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u5} P (AddMonoid.toAddZeroClass.{u5} P (AddCommMonoid.toAddMonoid.{u5} P _inst_10))) (MulActionWithZero.toSMulWithZero.{u2, u5} A P (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u5} P (AddMonoid.toAddZeroClass.{u5} P (AddCommMonoid.toAddMonoid.{u5} P _inst_10))) (Module.toMulActionWithZero.{u2, u5} A P _inst_2 _inst_10 _inst_12)))) (SMulZeroClass.toHasSmul.{u1, u5} R P (AddZeroClass.toHasZero.{u5} P (AddMonoid.toAddZeroClass.{u5} P (AddCommMonoid.toAddMonoid.{u5} P _inst_10))) (SMulWithZero.toSmulZeroClass.{u1, u5} R P (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u5} P (AddMonoid.toAddZeroClass.{u5} P (AddCommMonoid.toAddMonoid.{u5} P _inst_10))) (MulActionWithZero.toSMulWithZero.{u1, u5} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u5} P (AddMonoid.toAddZeroClass.{u5} P (AddCommMonoid.toAddMonoid.{u5} P _inst_10))) (Module.toMulActionWithZero.{u1, u5} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_10 _inst_11))))] (f : LinearMap.{u2, u2, max u3 u4, u5} A A _inst_2 _inst_2 (RingHom.id.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) P (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) _inst_10 (TensorProduct.leftModule.{u1, u2, u3, u4} R _inst_1 A _inst_2 M N _inst_4 _inst_8 _inst_5 _inst_9 _inst_6 (IsScalarTower.to_smulCommClass.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 M _inst_4 _inst_6 _inst_5 _inst_7)) _inst_12), Eq.{max (succ u3) (succ (max u4 u5))} (LinearMap.{u1, u1, u3, max u4 u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u4, u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_8 _inst_10 _inst_9 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u1, u1, u4, u5} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8 _inst_10 _inst_9 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u4, u5} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8 _inst_10 _inst_9 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_11 (smulCommClass_self.{u1, u5} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u5} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u5} P (AddMonoid.toAddZeroClass.{u5} P (AddCommMonoid.toAddMonoid.{u5} P _inst_10))) (Module.toMulActionWithZero.{u1, u5} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_10 _inst_11))))) (LinearMap.restrictScalars.{u1, u2, u3, max u4 u5} R A M (LinearMap.{u1, u1, u4, u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_8 _inst_10 _inst_9 _inst_11) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 (LinearMap.addCommMonoid.{u1, u1, u4, u5} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8 _inst_10 _inst_9 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u4, u5} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8 _inst_10 _inst_9 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_11 (smulCommClass_self.{u1, u5} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u5} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u5} P (AddMonoid.toAddZeroClass.{u5} P (AddCommMonoid.toAddMonoid.{u5} P _inst_10))) (Module.toMulActionWithZero.{u1, u5} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_10 _inst_11)))) _inst_6 (LinearMap.module.{u1, u1, u2, u4, u5} R R A N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8 _inst_10 _inst_9 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_2 _inst_12 (IsScalarTower.to_smulCommClass.{u1, u2, u5} R _inst_1 A _inst_2 _inst_3 P _inst_10 _inst_12 _inst_11 _inst_13)) (LinearMap.IsScalarTower.compatibleSMul.{u3, max u4 u5, u1, u2} M (LinearMap.{u1, u1, u4, u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_8 _inst_10 _inst_9 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u1, u1, u4, u5} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8 _inst_10 _inst_9 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R A _inst_2 (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toHasSmul.{u1, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))) _inst_6 _inst_7 (SMulZeroClass.toHasSmul.{u1, max u4 u5} R (LinearMap.{u1, u1, u4, u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_8 _inst_10 _inst_9 _inst_11) (AddZeroClass.toHasZero.{max u4 u5} (LinearMap.{u1, u1, u4, u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_8 _inst_10 _inst_9 _inst_11) (AddMonoid.toAddZeroClass.{max u4 u5} (LinearMap.{u1, u1, u4, u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_8 _inst_10 _inst_9 _inst_11) (AddCommMonoid.toAddMonoid.{max u4 u5} (LinearMap.{u1, u1, u4, u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_8 _inst_10 _inst_9 _inst_11) (LinearMap.addCommMonoid.{u1, u1, u4, u5} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8 _inst_10 _inst_9 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (SMulWithZero.toSmulZeroClass.{u1, max u4 u5} R (LinearMap.{u1, u1, u4, u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_8 _inst_10 _inst_9 _inst_11) (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{max u4 u5} (LinearMap.{u1, u1, u4, u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_8 _inst_10 _inst_9 _inst_11) (AddMonoid.toAddZeroClass.{max u4 u5} (LinearMap.{u1, u1, u4, u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_8 _inst_10 _inst_9 _inst_11) (AddCommMonoid.toAddMonoid.{max u4 u5} (LinearMap.{u1, u1, u4, u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_8 _inst_10 _inst_9 _inst_11) (LinearMap.addCommMonoid.{u1, u1, u4, u5} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8 _inst_10 _inst_9 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, max u4 u5} R (LinearMap.{u1, u1, u4, u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_8 _inst_10 _inst_9 _inst_11) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{max u4 u5} (LinearMap.{u1, u1, u4, u5} 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(IsScalarTower.to_smulCommClass.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 M _inst_4 _inst_6 _inst_5 _inst_7)) _inst_12 (LinearMap.IsScalarTower.compatibleSMul.{max u3 u4, u5, u1, u2} (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) P (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) _inst_10 R A _inst_2 (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A 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(TensorProduct.isScalarTower_left.{u1, u2, u3, u4, u1} R _inst_1 A (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) M N _inst_4 _inst_8 _inst_5 _inst_9 (Module.toDistribMulAction.{u2, u3} A M _inst_2 _inst_4 _inst_6) (IsScalarTower.to_smulCommClass.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 M _inst_4 _inst_6 _inst_5 _inst_7) R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.toDistribMulAction.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (smulCommClass_self.{u1, u3} R M (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))) (SMulZeroClass.toHasSmul.{u1, u2} 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) _inst_7) (SMulZeroClass.toHasSmul.{u1, u5} R P (AddZeroClass.toHasZero.{u5} P (AddMonoid.toAddZeroClass.{u5} P (AddCommMonoid.toAddMonoid.{u5} P _inst_10))) (SMulWithZero.toSmulZeroClass.{u1, u5} R P (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u5} P (AddMonoid.toAddZeroClass.{u5} P (AddCommMonoid.toAddMonoid.{u5} P _inst_10))) (MulActionWithZero.toSMulWithZero.{u1, u5} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u5} P (AddMonoid.toAddZeroClass.{u5} P (AddCommMonoid.toAddMonoid.{u5} P _inst_10))) (Module.toMulActionWithZero.{u1, u5} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_10 _inst_11)))) _inst_12 _inst_13) f))
-but is expected to have type
- forall {R : Type.{u1}} {A : Type.{u5}} {M : Type.{u3}} {N : Type.{u4}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u5} A] [_inst_3 : Algebra.{u1, u5} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u5, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u5, u3} R A M (Algebra.toSMul.{u1, u5} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u5, u3} A M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u5, u3} A M (MonoidWithZero.toZero.{u5} A (Semiring.toMonoidWithZero.{u5} A _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u5, u3} A M (Semiring.toMonoidWithZero.{u5} A _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u5, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))] [_inst_8 : AddCommMonoid.{u4} N] [_inst_9 : Module.{u1, u4} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8] [_inst_10 : AddCommMonoid.{u2} P] [_inst_11 : Module.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_10] [_inst_12 : Module.{u5, u2} A P _inst_2 _inst_10] [_inst_13 : IsScalarTower.{u1, u5, u2} R A P (Algebra.toSMul.{u1, u5} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u5, u2} A P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_10)) (SMulWithZero.toSMulZeroClass.{u5, u2} A P (MonoidWithZero.toZero.{u5} A (Semiring.toMonoidWithZero.{u5} A _inst_2)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_10)) (MulActionWithZero.toSMulWithZero.{u5, u2} A P (Semiring.toMonoidWithZero.{u5} A _inst_2) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_10)) (Module.toMulActionWithZero.{u5, u2} A P _inst_2 _inst_10 _inst_12)))) (SMulZeroClass.toSMul.{u1, u2} R P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_10)) (SMulWithZero.toSMulZeroClass.{u1, u2} R P (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_10)) (MulActionWithZero.toSMulWithZero.{u1, u2} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_10)) (Module.toMulActionWithZero.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_10 _inst_11))))] (f : LinearMap.{u5, u5, max u4 u3, u2} A A _inst_2 _inst_2 (RingHom.id.{u5} A (Semiring.toNonAssocSemiring.{u5} A _inst_2)) (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) P (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) _inst_10 (TensorProduct.leftModule.{u1, u5, u3, u4} R _inst_1 A _inst_2 M N _inst_4 _inst_8 _inst_5 _inst_9 _inst_6 (IsScalarTower.to_smulCommClass.{u1, u5, u3} R _inst_1 A _inst_2 _inst_3 M _inst_4 _inst_6 _inst_5 _inst_7)) _inst_12), Eq.{max (max (succ u3) (succ u4)) (succ u2)} (LinearMap.{u1, u1, u3, max u2 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u4, u2} R R 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(CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_8 _inst_10 _inst_9 _inst_11) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u4, u2} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8 _inst_10 _inst_9 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u4, u2} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8 _inst_10 _inst_9 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_11 (smulCommClass_self.{u1, u2} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u2} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_10)) (Module.toMulActionWithZero.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_10 _inst_11)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u5, u4, u2} R R A N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8 _inst_10 _inst_9 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_2 _inst_12 (IsScalarTower.to_smulCommClass.{u1, u5, u2} R _inst_1 A _inst_2 _inst_3 P _inst_10 _inst_12 _inst_11 _inst_13)) (LinearMap.instIsScalarTowerLinearMapInstSMulLinearMapInstSMulLinearMap.{u1, u1, u1, u5, u4, u2} R R R A N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8 _inst_10 _inst_9 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.toDistribMulAction.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_10 _inst_11) (smulCommClass_self.{u1, u2} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u2} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_10)) (Module.toMulActionWithZero.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_10 _inst_11))) (MonoidWithZero.toMonoid.{u5} A (Semiring.toMonoidWithZero.{u5} A _inst_2)) (Module.toDistribMulAction.{u5, u2} A P _inst_2 _inst_10 _inst_12) (IsScalarTower.to_smulCommClass.{u1, u5, u2} R _inst_1 A _inst_2 _inst_3 P _inst_10 _inst_12 _inst_11 _inst_13) (Algebra.toSMul.{u1, u5} R A _inst_1 _inst_2 _inst_3) _inst_13)) (TensorProduct.AlgebraTensorModule.curry.{u1, u5, u3, u4, u2} R A M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 _inst_12 _inst_13 f)) (TensorProduct.curry.{u1, u3, u4, u2} R _inst_1 M N P _inst_4 _inst_8 _inst_10 _inst_5 _inst_9 _inst_11 (LinearMap.restrictScalars.{u1, u5, max u3 u4, u2} R A (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) _inst_10 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) _inst_11 (TensorProduct.leftModule.{u1, u5, u3, u4} R _inst_1 A _inst_2 M N _inst_4 _inst_8 _inst_5 _inst_9 _inst_6 (IsScalarTower.to_smulCommClass.{u1, u5, u3} R _inst_1 A _inst_2 _inst_3 M _inst_4 _inst_6 _inst_5 _inst_7)) _inst_12 (LinearMap.IsScalarTower.compatibleSMul.{max u3 u4, u2, u1, u5} (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) P (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) _inst_10 R A _inst_2 (Algebra.toSMul.{u1, u5} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u1, max u3 u4} R (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (AddMonoid.toZero.{max u3 u4} (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (AddCommMonoid.toAddMonoid.{max u3 u4} (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9))) (SMulWithZero.toSMulZeroClass.{u1, max u3 u4} R (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{max u3 u4} (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (AddCommMonoid.toAddMonoid.{max u3 u4} (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9))) (MulActionWithZero.toSMulWithZero.{u1, max u3 u4} R (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{max u3 u4} (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (AddCommMonoid.toAddMonoid.{max u3 u4} (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9))) (Module.toMulActionWithZero.{u1, max u3 u4} R (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9))))) (TensorProduct.leftModule.{u1, u5, u3, u4} R _inst_1 A _inst_2 M N _inst_4 _inst_8 _inst_5 _inst_9 _inst_6 (IsScalarTower.to_smulCommClass.{u1, u5, u3} R _inst_1 A _inst_2 _inst_3 M _inst_4 _inst_6 _inst_5 _inst_7)) (TensorProduct.isScalarTower_left.{u1, u5, u3, u4, u1} R _inst_1 A (MonoidWithZero.toMonoid.{u5} A (Semiring.toMonoidWithZero.{u5} A _inst_2)) M N _inst_4 _inst_8 _inst_5 _inst_9 (Module.toDistribMulAction.{u5, u3} A M _inst_2 _inst_4 _inst_6) (IsScalarTower.to_smulCommClass.{u1, u5, u3} R _inst_1 A _inst_2 _inst_3 M _inst_4 _inst_6 _inst_5 _inst_7) R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.toDistribMulAction.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (IsScalarTower.to_smulCommClass.{u1, u1, u3} R _inst_1 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) M _inst_4 _inst_5 _inst_5 (IsScalarTower.left.{u1, u3} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulActionWithZero.toMulAction.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))) (Algebra.toSMul.{u1, u5} R A _inst_1 _inst_2 _inst_3) _inst_7) (SMulZeroClass.toSMul.{u1, u2} R P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_10)) (SMulWithZero.toSMulZeroClass.{u1, u2} R P (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_10)) (MulActionWithZero.toSMulWithZero.{u1, u2} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_10)) (Module.toMulActionWithZero.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_10 _inst_11)))) _inst_12 _inst_13) f))
+<too large>
Case conversion may be inaccurate. Consider using '#align tensor_product.algebra_tensor_module.restrict_scalars_curry TensorProduct.AlgebraTensorModule.restrictScalars_curryₓ'. -/
theorem restrictScalars_curry (f : M ⊗[R] N →ₗ[A] P) :
RestrictScalars R (curry f) = curry (f.restrictScalars R) :=
@@ -119,10 +113,7 @@ theorem restrictScalars_curry (f : M ⊗[R] N →ₗ[A] P) :
#align tensor_product.algebra_tensor_module.restrict_scalars_curry TensorProduct.AlgebraTensorModule.restrictScalars_curry
/- warning: tensor_product.algebra_tensor_module.curry_injective -> TensorProduct.AlgebraTensorModule.curry_injective is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {A : Type.{u2}} {M : Type.{u3}} {N : Type.{u4}} {P : Type.{u5}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} A M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u2, u3} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toHasSmul.{u1, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))] [_inst_8 : AddCommMonoid.{u4} N] [_inst_9 : Module.{u1, u4} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8] [_inst_10 : AddCommMonoid.{u5} P] [_inst_11 : Module.{u1, u5} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_10] [_inst_12 : Module.{u2, u5} A P _inst_2 _inst_10] [_inst_13 : IsScalarTower.{u1, u2, u5} R A P (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u5} A P (AddZeroClass.toHasZero.{u5} P (AddMonoid.toAddZeroClass.{u5} P (AddCommMonoid.toAddMonoid.{u5} P _inst_10))) (SMulWithZero.toSmulZeroClass.{u2, u5} A P (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u5} P (AddMonoid.toAddZeroClass.{u5} P (AddCommMonoid.toAddMonoid.{u5} P _inst_10))) (MulActionWithZero.toSMulWithZero.{u2, u5} A P (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u5} P (AddMonoid.toAddZeroClass.{u5} P (AddCommMonoid.toAddMonoid.{u5} P _inst_10))) (Module.toMulActionWithZero.{u2, u5} A P _inst_2 _inst_10 _inst_12)))) (SMulZeroClass.toHasSmul.{u1, u5} R P (AddZeroClass.toHasZero.{u5} P (AddMonoid.toAddZeroClass.{u5} P (AddCommMonoid.toAddMonoid.{u5} P _inst_10))) (SMulWithZero.toSmulZeroClass.{u1, u5} R P (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u5} P (AddMonoid.toAddZeroClass.{u5} P (AddCommMonoid.toAddMonoid.{u5} P _inst_10))) (MulActionWithZero.toSMulWithZero.{u1, u5} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u5} P (AddMonoid.toAddZeroClass.{u5} P (AddCommMonoid.toAddMonoid.{u5} P _inst_10))) (Module.toMulActionWithZero.{u1, u5} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_10 _inst_11))))], Function.Injective.{max (succ (max u3 u4)) (succ u5), max (succ u3) (succ (max u4 u5))} (LinearMap.{u2, u2, max u3 u4, u5} A A _inst_2 _inst_2 (RingHom.id.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) P (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) _inst_10 (TensorProduct.leftModule.{u1, u2, u3, u4} R _inst_1 A _inst_2 M N _inst_4 _inst_8 _inst_5 _inst_9 _inst_6 (IsScalarTower.to_smulCommClass.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 M _inst_4 _inst_6 _inst_5 _inst_7)) _inst_12) (LinearMap.{u2, u2, u3, max u4 u5} A A _inst_2 _inst_2 (RingHom.id.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) M (LinearMap.{u1, u1, u4, u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_8 _inst_10 _inst_9 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u1, u1, u4, u5} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8 _inst_10 _inst_9 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_6 (LinearMap.module.{u1, u1, u2, u4, u5} R R A N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8 _inst_10 _inst_9 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_2 _inst_12 (IsScalarTower.to_smulCommClass.{u1, u2, u5} R _inst_1 A _inst_2 _inst_3 P _inst_10 _inst_12 _inst_11 _inst_13))) (TensorProduct.AlgebraTensorModule.curry.{u1, u2, u3, u4, u5} R A M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 _inst_12 _inst_13)
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- forall {R : Type.{u1}} {A : Type.{u2}} {M : Type.{u5}} {N : Type.{u4}} {P : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u5} M] [_inst_5 : Module.{u1, u5} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u5} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u5} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u2, u5} A M (AddMonoid.toZero.{u5} M (AddCommMonoid.toAddMonoid.{u5} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u5} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddMonoid.toZero.{u5} M (AddCommMonoid.toAddMonoid.{u5} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u5} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddMonoid.toZero.{u5} M (AddCommMonoid.toAddMonoid.{u5} M _inst_4)) (Module.toMulActionWithZero.{u2, u5} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toSMul.{u1, u5} R M (AddMonoid.toZero.{u5} M (AddCommMonoid.toAddMonoid.{u5} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u1, u5} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u5} M (AddCommMonoid.toAddMonoid.{u5} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u1, u5} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u5} M (AddCommMonoid.toAddMonoid.{u5} M _inst_4)) (Module.toMulActionWithZero.{u1, u5} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))] [_inst_8 : AddCommMonoid.{u4} N] [_inst_9 : Module.{u1, u4} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8] [_inst_10 : AddCommMonoid.{u3} P] [_inst_11 : Module.{u1, u3} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_10] [_inst_12 : Module.{u2, u3} A P _inst_2 _inst_10] [_inst_13 : IsScalarTower.{u1, u2, u3} R A P (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u2, u3} A P (AddMonoid.toZero.{u3} P (AddCommMonoid.toAddMonoid.{u3} P _inst_10)) (SMulWithZero.toSMulZeroClass.{u2, u3} A P (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddMonoid.toZero.{u3} P (AddCommMonoid.toAddMonoid.{u3} P _inst_10)) (MulActionWithZero.toSMulWithZero.{u2, u3} A P (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddMonoid.toZero.{u3} P (AddCommMonoid.toAddMonoid.{u3} P _inst_10)) (Module.toMulActionWithZero.{u2, u3} A P _inst_2 _inst_10 _inst_12)))) (SMulZeroClass.toSMul.{u1, u3} R P (AddMonoid.toZero.{u3} P (AddCommMonoid.toAddMonoid.{u3} P _inst_10)) (SMulWithZero.toSMulZeroClass.{u1, u3} R P (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} P (AddCommMonoid.toAddMonoid.{u3} P _inst_10)) (MulActionWithZero.toSMulWithZero.{u1, u3} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} P (AddCommMonoid.toAddMonoid.{u3} P _inst_10)) (Module.toMulActionWithZero.{u1, u3} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_10 _inst_11))))], Function.Injective.{max (max (succ u5) (succ u4)) (succ u3), max (max (succ u5) (succ u4)) (succ u3)} (LinearMap.{u2, u2, max u4 u5, u3} A A _inst_2 _inst_2 (RingHom.id.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (TensorProduct.{u1, u5, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) P (TensorProduct.addCommMonoid.{u1, u5, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) _inst_10 (TensorProduct.leftModule.{u1, u2, u5, u4} R _inst_1 A _inst_2 M N _inst_4 _inst_8 _inst_5 _inst_9 _inst_6 (IsScalarTower.to_smulCommClass.{u1, u2, u5} R _inst_1 A _inst_2 _inst_3 M _inst_4 _inst_6 _inst_5 _inst_7)) _inst_12) (LinearMap.{u2, u2, u5, max u3 u4} A A _inst_2 _inst_2 (RingHom.id.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) M (LinearMap.{u1, u1, u4, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_8 _inst_10 _inst_9 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u1, u1, u4, u3} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8 _inst_10 _inst_9 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_6 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u2, u4, u3} R R A N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8 _inst_10 _inst_9 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_2 _inst_12 (IsScalarTower.to_smulCommClass.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 P _inst_10 _inst_12 _inst_11 _inst_13))) (TensorProduct.AlgebraTensorModule.curry.{u1, u2, u5, u4, u3} R A M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 _inst_12 _inst_13)
+<too large>
Case conversion may be inaccurate. Consider using '#align tensor_product.algebra_tensor_module.curry_injective TensorProduct.AlgebraTensorModule.curry_injectiveₓ'. -/
/-- Just as `tensor_product.ext` is marked `ext` instead of `tensor_product.ext'`, this is
a better `ext` lemma than `tensor_product.algebra_tensor_module.ext` below.
@@ -136,10 +127,7 @@ theorem curry_injective : Function.Injective (curry : (M ⊗ N →ₗ[A] P) →
#align tensor_product.algebra_tensor_module.curry_injective TensorProduct.AlgebraTensorModule.curry_injective
/- warning: tensor_product.algebra_tensor_module.ext -> TensorProduct.AlgebraTensorModule.ext is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {A : Type.{u2}} {M : Type.{u3}} {N : Type.{u4}} {P : Type.{u5}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} A M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u2, u3} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toHasSmul.{u1, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))] [_inst_8 : AddCommMonoid.{u4} N] [_inst_9 : Module.{u1, u4} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8] [_inst_10 : AddCommMonoid.{u5} P] [_inst_11 : Module.{u1, u5} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_10] [_inst_12 : Module.{u2, u5} A P _inst_2 _inst_10] [_inst_13 : IsScalarTower.{u1, u2, u5} R A P (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u5} A P (AddZeroClass.toHasZero.{u5} P (AddMonoid.toAddZeroClass.{u5} P (AddCommMonoid.toAddMonoid.{u5} P _inst_10))) (SMulWithZero.toSmulZeroClass.{u2, u5} A P (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u5} P (AddMonoid.toAddZeroClass.{u5} P (AddCommMonoid.toAddMonoid.{u5} P _inst_10))) (MulActionWithZero.toSMulWithZero.{u2, u5} A P (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u5} P (AddMonoid.toAddZeroClass.{u5} P (AddCommMonoid.toAddMonoid.{u5} P _inst_10))) (Module.toMulActionWithZero.{u2, u5} A P _inst_2 _inst_10 _inst_12)))) (SMulZeroClass.toHasSmul.{u1, u5} R P 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Case conversion may be inaccurate. Consider using '#align tensor_product.algebra_tensor_module.ext TensorProduct.AlgebraTensorModule.extₓ'. -/
theorem ext {g h : M ⊗[R] N →ₗ[A] P} (H : ∀ x y, g (x ⊗ₜ y) = h (x ⊗ₜ y)) : g = h :=
curry_injective <| LinearMap.ext₂ H
@@ -180,10 +168,7 @@ def lift (f : M →ₗ[A] N →ₗ[R] P) : M ⊗[R] N →ₗ[A] P :=
-/
/- warning: tensor_product.algebra_tensor_module.lift_tmul -> TensorProduct.AlgebraTensorModule.lift_tmul is a dubious translation:
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(AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))] [_inst_8 : AddCommMonoid.{u4} N] [_inst_9 : Module.{u1, u4} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8] [_inst_10 : AddCommMonoid.{u5} P] [_inst_11 : Module.{u1, u5} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_10] [_inst_12 : Module.{u2, u5} A P (CommSemiring.toSemiring.{u2} A _inst_2) _inst_10] [_inst_13 : IsScalarTower.{u1, u2, u5} R A P (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u5} A P (AddZeroClass.toHasZero.{u5} P (AddMonoid.toAddZeroClass.{u5} P (AddCommMonoid.toAddMonoid.{u5} P _inst_10))) (SMulWithZero.toSmulZeroClass.{u2, u5} A P (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) (AddZeroClass.toHasZero.{u5} P (AddMonoid.toAddZeroClass.{u5} P (AddCommMonoid.toAddMonoid.{u5} P _inst_10))) (MulActionWithZero.toSMulWithZero.{u2, u5} A P (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (AddZeroClass.toHasZero.{u5} P (AddMonoid.toAddZeroClass.{u5} P (AddCommMonoid.toAddMonoid.{u5} P _inst_10))) (Module.toMulActionWithZero.{u2, u5} A P (CommSemiring.toSemiring.{u2} A _inst_2) _inst_10 _inst_12)))) (SMulZeroClass.toHasSmul.{u1, u5} R P (AddZeroClass.toHasZero.{u5} P (AddMonoid.toAddZeroClass.{u5} P (AddCommMonoid.toAddMonoid.{u5} P _inst_10))) (SMulWithZero.toSmulZeroClass.{u1, u5} R P (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u5} P (AddMonoid.toAddZeroClass.{u5} P (AddCommMonoid.toAddMonoid.{u5} P _inst_10))) (MulActionWithZero.toSMulWithZero.{u1, u5} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u5} P (AddMonoid.toAddZeroClass.{u5} P (AddCommMonoid.toAddMonoid.{u5} P _inst_10))) (Module.toMulActionWithZero.{u1, u5} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_10 _inst_11))))] (f : LinearMap.{u2, u2, u3, max u4 u5} A A (CommSemiring.toSemiring.{u2} A _inst_2) (CommSemiring.toSemiring.{u2} A _inst_2) (RingHom.id.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))) M (LinearMap.{u1, u1, u4, u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_8 _inst_10 _inst_9 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u1, u1, u4, u5} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) 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(Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) f x) y)
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- forall {R : Type.{u1}} {A : Type.{u5}} {M : Type.{u4}} {N : Type.{u2}} {P : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u5} A] [_inst_3 : Algebra.{u1, u5} R A _inst_1 (CommSemiring.toSemiring.{u5} A _inst_2)] [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : Module.{u1, u4} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u5, u4} A M (CommSemiring.toSemiring.{u5} A _inst_2) _inst_4] [_inst_7 : IsScalarTower.{u1, u5, u4} R A M (Algebra.toSMul.{u1, u5} R A _inst_1 (CommSemiring.toSemiring.{u5} A _inst_2) _inst_3) (SMulZeroClass.toSMul.{u5, u4} A M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u5, u4} A M (CommMonoidWithZero.toZero.{u5} A (CommSemiring.toCommMonoidWithZero.{u5} A _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u5, u4} A M (Semiring.toMonoidWithZero.{u5} A (CommSemiring.toSemiring.{u5} A _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_4)) (Module.toMulActionWithZero.{u5, u4} A M (CommSemiring.toSemiring.{u5} A _inst_2) _inst_4 _inst_6)))) (SMulZeroClass.toSMul.{u1, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u1, u4} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u1, u4} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_4)) (Module.toMulActionWithZero.{u1, u4} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))] [_inst_8 : AddCommMonoid.{u2} N] [_inst_9 : Module.{u1, u2} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8] [_inst_10 : AddCommMonoid.{u3} P] [_inst_11 : Module.{u1, u3} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_10] [_inst_12 : Module.{u5, u3} A P (CommSemiring.toSemiring.{u5} A _inst_2) _inst_10] [_inst_13 : IsScalarTower.{u1, u5, u3} R A P (Algebra.toSMul.{u1, u5} R A _inst_1 (CommSemiring.toSemiring.{u5} A _inst_2) _inst_3) (SMulZeroClass.toSMul.{u5, u3} A P (AddMonoid.toZero.{u3} P (AddCommMonoid.toAddMonoid.{u3} P _inst_10)) (SMulWithZero.toSMulZeroClass.{u5, u3} A P (CommMonoidWithZero.toZero.{u5} A (CommSemiring.toCommMonoidWithZero.{u5} A _inst_2)) (AddMonoid.toZero.{u3} P (AddCommMonoid.toAddMonoid.{u3} P _inst_10)) (MulActionWithZero.toSMulWithZero.{u5, u3} A P (Semiring.toMonoidWithZero.{u5} A (CommSemiring.toSemiring.{u5} A _inst_2)) (AddMonoid.toZero.{u3} P (AddCommMonoid.toAddMonoid.{u3} P _inst_10)) (Module.toMulActionWithZero.{u5, u3} A P (CommSemiring.toSemiring.{u5} A _inst_2) _inst_10 _inst_12)))) (SMulZeroClass.toSMul.{u1, u3} R P (AddMonoid.toZero.{u3} P (AddCommMonoid.toAddMonoid.{u3} P _inst_10)) (SMulWithZero.toSMulZeroClass.{u1, u3} R P (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} P (AddCommMonoid.toAddMonoid.{u3} P _inst_10)) (MulActionWithZero.toSMulWithZero.{u1, u3} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} P (AddCommMonoid.toAddMonoid.{u3} P _inst_10)) (Module.toMulActionWithZero.{u1, u3} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_10 _inst_11))))] (f : LinearMap.{u5, u5, u4, max u3 u2} A A (CommSemiring.toSemiring.{u5} A _inst_2) (CommSemiring.toSemiring.{u5} A _inst_2) (RingHom.id.{u5} A (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_2))) M (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_8 _inst_10 _inst_9 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) 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+<too large>
Case conversion may be inaccurate. Consider using '#align tensor_product.algebra_tensor_module.lift_tmul TensorProduct.AlgebraTensorModule.lift_tmulₓ'. -/
@[simp]
theorem lift_tmul (f : M →ₗ[A] N →ₗ[R] P) (x : M) (y : N) : lift f (x ⊗ₜ y) = f x y :=
@@ -237,10 +222,7 @@ def lift.equiv : (M →ₗ[A] N →ₗ[R] P) ≃ₗ[A] M ⊗[R] N →ₗ[A] P :=
variable (R A M N P)
/- warning: tensor_product.algebra_tensor_module.mk -> TensorProduct.AlgebraTensorModule.mk is a dubious translation:
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(AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))] [_inst_8 : AddCommMonoid.{u4} N] [_inst_9 : Module.{u1, u4} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8], LinearMap.{u2, u2, u3, max u3 u4} A A (CommSemiring.toSemiring.{u2} A _inst_2) (CommSemiring.toSemiring.{u2} A _inst_2) (RingHom.id.{u2} A 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(AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u2, u3} A M (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))] [_inst_8 : AddCommMonoid.{u4} N] [_inst_9 : Module.{u1, u4} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8], LinearMap.{u2, u2, u3, max u4 u3} A A (CommSemiring.toSemiring.{u2} A _inst_2) (CommSemiring.toSemiring.{u2} A _inst_2) (RingHom.id.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))) M (LinearMap.{u1, u1, u4, max u4 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) _inst_8 (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) _inst_9 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9)) _inst_4 (LinearMap.addCommMonoid.{u1, u1, u4, max u3 u4} R R N (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8 (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) _inst_9 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_6 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u2, u4, max u3 u4} R R A N (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8 (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) _inst_9 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} A _inst_2) (TensorProduct.leftModule.{u1, u2, u3, u4} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) M N _inst_4 _inst_8 _inst_5 _inst_9 _inst_6 (IsScalarTower.to_smulCommClass.{u1, u2, u3} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3 M _inst_4 _inst_6 _inst_5 _inst_7)) (IsScalarTower.to_smulCommClass.{u1, u2, max u3 u4} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3 (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (TensorProduct.leftModule.{u1, u2, u3, u4} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) M N _inst_4 _inst_8 _inst_5 _inst_9 _inst_6 (IsScalarTower.to_smulCommClass.{u1, u2, u3} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3 M _inst_4 _inst_6 _inst_5 _inst_7)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (TensorProduct.isScalarTower_left.{u1, u2, u3, u4, u1} R _inst_1 A (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))) M N _inst_4 _inst_8 _inst_5 _inst_9 (Module.toDistribMulAction.{u2, u3} A M (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4 _inst_6) (IsScalarTower.to_smulCommClass.{u1, u2, u3} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3 M _inst_4 _inst_6 _inst_5 _inst_7) R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.toDistribMulAction.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (smulCommClass_self.{u1, u3} R M (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))) (Algebra.toSMul.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) _inst_7)))
+<too large>
Case conversion may be inaccurate. Consider using '#align tensor_product.algebra_tensor_module.mk TensorProduct.AlgebraTensorModule.mkₓ'. -/
/-- Heterobasic version of `tensor_product.mk`:
@@ -322,10 +304,7 @@ def baseChange (f : M →ₗ[R] N) : A ⊗[R] M →ₗ[A] A ⊗[R] N
variable {A}
/- warning: linear_map.base_change_tmul -> LinearMap.baseChange_tmul is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align linear_map.base_change_tmul LinearMap.baseChange_tmulₓ'. -/
@[simp]
theorem baseChange_tmul (a : A) (x : M) : f.base_change A (a ⊗ₜ x) = a ⊗ₜ f x :=
@@ -333,20 +312,14 @@ theorem baseChange_tmul (a : A) (x : M) : f.base_change A (a ⊗ₜ x) = a ⊗
#align linear_map.base_change_tmul LinearMap.baseChange_tmul
/- warning: linear_map.base_change_eq_ltensor -> LinearMap.baseChange_eq_ltensor is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align linear_map.base_change_eq_ltensor LinearMap.baseChange_eq_ltensorₓ'. -/
theorem baseChange_eq_ltensor : (f.base_change A : A ⊗ M → A ⊗ N) = f.lTensor A :=
rfl
#align linear_map.base_change_eq_ltensor LinearMap.baseChange_eq_ltensor
/- warning: linear_map.base_change_add -> LinearMap.baseChange_add is a dubious translation:
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A _inst_2))) _inst_6 (Algebra.toModule.{u1, u4} R A _inst_1 _inst_2 _inst_3) _inst_7 (Semiring.toModule.{u4} A _inst_2) (Algebra.to_smulCommClass.{u1, u4} R A _inst_1 _inst_2 _inst_3)) (TensorProduct.leftModule.{u1, u4, u4, u2} R _inst_1 A _inst_2 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u4} R A _inst_1 _inst_2 _inst_3) _inst_9 (Semiring.toModule.{u4} A _inst_2) (Algebra.to_smulCommClass.{u1, u4} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2)))) (LinearMap.baseChange.{u1, u4, u3, u2} R A M N _inst_1 _inst_2 _inst_3 _inst_6 _inst_7 _inst_8 _inst_9 f) (LinearMap.baseChange.{u1, u4, u3, u2} R A M N _inst_1 _inst_2 _inst_3 _inst_6 _inst_7 _inst_8 _inst_9 g))
+<too large>
Case conversion may be inaccurate. Consider using '#align linear_map.base_change_add LinearMap.baseChange_addₓ'. -/
@[simp]
theorem baseChange_add : (f + g).base_change A = f.base_change A + g.base_change A :=
@@ -356,10 +329,7 @@ theorem baseChange_add : (f + g).base_change A = f.base_change A + g.base_change
#align linear_map.base_change_add LinearMap.baseChange_add
/- warning: linear_map.base_change_zero -> LinearMap.baseChange_zero is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {A : Type.{u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_6 : AddCommMonoid.{u3} M] [_inst_7 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] [_inst_8 : AddCommMonoid.{u4} N] [_inst_9 : Module.{u1, u4} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8], Eq.{max (succ (max u2 u3)) (succ (max u2 u4))} (LinearMap.{u2, u2, max u2 u3, max u2 u4} A A _inst_2 _inst_2 (RingHom.id.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (TensorProduct.{u1, u2, u3} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_6 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_7) (TensorProduct.{u1, u2, u4} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A 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+<too large>
Case conversion may be inaccurate. Consider using '#align linear_map.base_change_zero LinearMap.baseChange_zeroₓ'. -/
@[simp]
theorem baseChange_zero : baseChange A (0 : M →ₗ[R] N) = 0 :=
@@ -369,10 +339,7 @@ theorem baseChange_zero : baseChange A (0 : M →ₗ[R] N) = 0 :=
#align linear_map.base_change_zero LinearMap.baseChange_zero
/- warning: linear_map.base_change_smul -> LinearMap.baseChange_smul is a dubious translation:
-lean 3 declaration is
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(Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_6 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_7) (TensorProduct.{u1, u2, u4} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_9) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_6 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_7) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_9) (TensorProduct.leftModule.{u1, u2, u2, u3} R _inst_1 A _inst_2 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_6 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_7 (Semiring.toModule.{u2} A _inst_2) (Algebra.to_smulCommClass.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (TensorProduct.leftModule.{u1, u2, u2, u4} R _inst_1 A _inst_2 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_9 (Semiring.toModule.{u2} A _inst_2) (Algebra.to_smulCommClass.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.baseChange.{u1, u2, u3, u4} R A M N _inst_1 _inst_2 _inst_3 _inst_6 _inst_7 _inst_8 _inst_9 (SMul.smul.{u1, max u3 u4} R (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M N _inst_6 _inst_8 _inst_7 _inst_9) (LinearMap.hasSmul.{u1, u1, u1, u3, u4} R R R M N (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_8 _inst_7 _inst_9 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.toDistribMulAction.{u1, u4} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8 _inst_9) (smulCommClass_self.{u1, u4} R N (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R N (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} N (AddMonoid.toAddZeroClass.{u4} N (AddCommMonoid.toAddMonoid.{u4} N _inst_8))) (Module.toMulActionWithZero.{u1, u4} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8 _inst_9)))) r f)) (SMul.smul.{u1, max (max u2 u3) u2 u4} R (LinearMap.{u2, u2, max u2 u3, max u2 u4} A A _inst_2 _inst_2 (RingHom.id.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (TensorProduct.{u1, u2, u3} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_6 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_7) (TensorProduct.{u1, u2, u4} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_9) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_6 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_7) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_9) (TensorProduct.leftModule.{u1, u2, u2, u3} R _inst_1 A _inst_2 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_6 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_7 (Semiring.toModule.{u2} A _inst_2) (Algebra.to_smulCommClass.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (TensorProduct.leftModule.{u1, u2, u2, u4} R _inst_1 A _inst_2 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_9 (Semiring.toModule.{u2} A _inst_2) (Algebra.to_smulCommClass.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.hasSmul.{u2, u2, u1, max u2 u3, max u2 u4} A A R (TensorProduct.{u1, u2, u3} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_6 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_7) (TensorProduct.{u1, u2, u4} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_9) _inst_2 _inst_2 (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_6 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_7) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_9) (TensorProduct.leftModule.{u1, u2, u2, u3} R _inst_1 A _inst_2 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_6 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_7 (Semiring.toModule.{u2} A _inst_2) (Algebra.to_smulCommClass.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (TensorProduct.leftModule.{u1, u2, u2, u4} R _inst_1 A _inst_2 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_9 (Semiring.toModule.{u2} A _inst_2) (Algebra.to_smulCommClass.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.distribMulAction.{u1, u2, u4} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_9) (IsScalarTower.to_smulCommClass'.{u1, u2, max u2 u4} R _inst_1 A _inst_2 _inst_3 (TensorProduct.{u1, u2, u4} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_9) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_9) (TensorProduct.leftModule.{u1, u2, u2, u4} R _inst_1 A _inst_2 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_9 (Semiring.toModule.{u2} A _inst_2) (Algebra.to_smulCommClass.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (TensorProduct.module.{u1, u2, u4} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_9) (TensorProduct.isScalarTower_left.{u1, u2, u2, u4, u1} R _inst_1 A (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_9 (Module.toDistribMulAction.{u2, u2} A A _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Semiring.toModule.{u2} A _inst_2)) (Algebra.to_smulCommClass.{u1, u2} R A _inst_1 _inst_2 _inst_3) R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (smulCommClass_self.{u1, u2} R A (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (IsScalarTower.right.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) r (LinearMap.baseChange.{u1, u2, u3, u4} R A M N _inst_1 _inst_2 _inst_3 _inst_6 _inst_7 _inst_8 _inst_9 f))
-but is expected to have type
- forall {R : Type.{u1}} {A : Type.{u4}} {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u4} A] [_inst_3 : Algebra.{u1, u4} R A _inst_1 _inst_2] [_inst_6 : AddCommMonoid.{u3} M] [_inst_7 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] [_inst_8 : AddCommMonoid.{u2} N] [_inst_9 : Module.{u1, u2} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8] (r : R) (f : LinearMap.{u1, u1, u3, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M N _inst_6 _inst_8 _inst_7 _inst_9), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (LinearMap.{u4, u4, max u3 u4, max u2 u4} A A _inst_2 _inst_2 (RingHom.id.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2)) (TensorProduct.{u1, u4, u3} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_6 (Algebra.toModule.{u1, u4} R A _inst_1 _inst_2 _inst_3) _inst_7) (TensorProduct.{u1, u4, u2} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u4} R A _inst_1 _inst_2 _inst_3) _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u3} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_6 (Algebra.toModule.{u1, u4} R A _inst_1 _inst_2 _inst_3) _inst_7) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u4} R A _inst_1 _inst_2 _inst_3) _inst_9) (TensorProduct.leftModule.{u1, u4, u4, u3} R _inst_1 A _inst_2 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_6 (Algebra.toModule.{u1, u4} R A _inst_1 _inst_2 _inst_3) _inst_7 (Semiring.toModule.{u4} A _inst_2) (Algebra.to_smulCommClass.{u1, u4} R A _inst_1 _inst_2 _inst_3)) (TensorProduct.leftModule.{u1, u4, u4, u2} R _inst_1 A _inst_2 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u4} R A _inst_1 _inst_2 _inst_3) _inst_9 (Semiring.toModule.{u4} A _inst_2) (Algebra.to_smulCommClass.{u1, u4} R A _inst_1 _inst_2 _inst_3))) (LinearMap.baseChange.{u1, u4, u3, u2} R A M N _inst_1 _inst_2 _inst_3 _inst_6 _inst_7 _inst_8 _inst_9 (HSMul.hSMul.{u1, max u3 u2, max u3 u2} R (LinearMap.{u1, u1, u3, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M N _inst_6 _inst_8 _inst_7 _inst_9) (LinearMap.{u1, u1, u3, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M N _inst_6 _inst_8 _inst_7 _inst_9) (instHSMul.{u1, max u3 u2} R (LinearMap.{u1, u1, u3, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M N _inst_6 _inst_8 _inst_7 _inst_9) (LinearMap.instSMulLinearMap.{u1, u1, u1, u3, u2} R R R M N (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_8 _inst_7 _inst_9 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.toDistribMulAction.{u1, u2} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8 _inst_9) (smulCommClass_self.{u1, u2} R N (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u2} R N (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_8)) (Module.toMulActionWithZero.{u1, u2} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8 _inst_9))))) r f)) (HSMul.hSMul.{u1, max (max u4 u3) u2, max (max u4 u3) u2} R (LinearMap.{u4, u4, max u3 u4, max u2 u4} A A _inst_2 _inst_2 (RingHom.id.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2)) (TensorProduct.{u1, u4, u3} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_6 (Algebra.toModule.{u1, u4} R A _inst_1 _inst_2 _inst_3) _inst_7) (TensorProduct.{u1, u4, u2} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u4} R A _inst_1 _inst_2 _inst_3) _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u3} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_6 (Algebra.toModule.{u1, u4} R A _inst_1 _inst_2 _inst_3) _inst_7) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u4} R A _inst_1 _inst_2 _inst_3) _inst_9) (TensorProduct.leftModule.{u1, u4, u4, u3} R _inst_1 A _inst_2 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_6 (Algebra.toModule.{u1, u4} R A _inst_1 _inst_2 _inst_3) _inst_7 (Semiring.toModule.{u4} A _inst_2) (Algebra.to_smulCommClass.{u1, u4} R A _inst_1 _inst_2 _inst_3)) (TensorProduct.leftModule.{u1, u4, u4, u2} R _inst_1 A _inst_2 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u4} R A _inst_1 _inst_2 _inst_3) _inst_9 (Semiring.toModule.{u4} A _inst_2) (Algebra.to_smulCommClass.{u1, u4} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u4, u4, max u3 u4, max u2 u4} A A _inst_2 _inst_2 (RingHom.id.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2)) (TensorProduct.{u1, u4, u3} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_6 (Algebra.toModule.{u1, u4} R A _inst_1 _inst_2 _inst_3) _inst_7) (TensorProduct.{u1, u4, u2} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u4} R A _inst_1 _inst_2 _inst_3) _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u3} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_6 (Algebra.toModule.{u1, u4} R A _inst_1 _inst_2 _inst_3) _inst_7) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u4} R A _inst_1 _inst_2 _inst_3) _inst_9) (TensorProduct.leftModule.{u1, u4, u4, u3} R _inst_1 A _inst_2 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_6 (Algebra.toModule.{u1, u4} R A _inst_1 _inst_2 _inst_3) _inst_7 (Semiring.toModule.{u4} A _inst_2) (Algebra.to_smulCommClass.{u1, u4} R A _inst_1 _inst_2 _inst_3)) (TensorProduct.leftModule.{u1, u4, u4, u2} R _inst_1 A _inst_2 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u4} R A _inst_1 _inst_2 _inst_3) _inst_9 (Semiring.toModule.{u4} A _inst_2) (Algebra.to_smulCommClass.{u1, u4} R A _inst_1 _inst_2 _inst_3))) (instHSMul.{u1, max (max u4 u3) u2} R (LinearMap.{u4, u4, max u3 u4, max u2 u4} A A _inst_2 _inst_2 (RingHom.id.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2)) (TensorProduct.{u1, u4, u3} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_6 (Algebra.toModule.{u1, u4} R A _inst_1 _inst_2 _inst_3) _inst_7) (TensorProduct.{u1, u4, u2} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u4} R A _inst_1 _inst_2 _inst_3) _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u3} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_6 (Algebra.toModule.{u1, u4} R A _inst_1 _inst_2 _inst_3) _inst_7) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u4} R A _inst_1 _inst_2 _inst_3) _inst_9) (TensorProduct.leftModule.{u1, u4, u4, u3} R _inst_1 A _inst_2 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_6 (Algebra.toModule.{u1, u4} R A _inst_1 _inst_2 _inst_3) _inst_7 (Semiring.toModule.{u4} A _inst_2) (Algebra.to_smulCommClass.{u1, u4} R A _inst_1 _inst_2 _inst_3)) (TensorProduct.leftModule.{u1, u4, u4, u2} R _inst_1 A _inst_2 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u4} R A _inst_1 _inst_2 _inst_3) _inst_9 (Semiring.toModule.{u4} A _inst_2) (Algebra.to_smulCommClass.{u1, u4} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSMulLinearMap.{u4, u4, u1, max u4 u3, max u4 u2} A A R (TensorProduct.{u1, u4, u3} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_6 (Algebra.toModule.{u1, u4} R A _inst_1 _inst_2 _inst_3) _inst_7) (TensorProduct.{u1, u4, u2} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u4} R A _inst_1 _inst_2 _inst_3) _inst_9) _inst_2 _inst_2 (TensorProduct.addCommMonoid.{u1, u4, u3} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_6 (Algebra.toModule.{u1, u4} R A _inst_1 _inst_2 _inst_3) _inst_7) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u4} R A _inst_1 _inst_2 _inst_3) _inst_9) (TensorProduct.leftModule.{u1, u4, u4, u3} R _inst_1 A _inst_2 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_6 (Algebra.toModule.{u1, u4} R A _inst_1 _inst_2 _inst_3) _inst_7 (Semiring.toModule.{u4} A _inst_2) (Algebra.to_smulCommClass.{u1, u4} R A _inst_1 _inst_2 _inst_3)) (TensorProduct.leftModule.{u1, u4, u4, u2} R _inst_1 A _inst_2 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u4} R A _inst_1 _inst_2 _inst_3) _inst_9 (Semiring.toModule.{u4} A _inst_2) (Algebra.to_smulCommClass.{u1, u4} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.instDistribMulActionTensorProductToMonoidToMonoidWithZeroToSemiringToAddMonoidAddCommMonoid.{u1, u4, u2} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u4} R A _inst_1 _inst_2 _inst_3) _inst_9) (IsScalarTower.to_smulCommClass'.{u1, u4, max u4 u2} R _inst_1 A _inst_2 _inst_3 (TensorProduct.{u1, u4, u2} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u4} R A _inst_1 _inst_2 _inst_3) _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u2} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u4} R A _inst_1 _inst_2 _inst_3) _inst_9) (TensorProduct.leftModule.{u1, u4, u4, u2} R _inst_1 A _inst_2 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u4} R A _inst_1 _inst_2 _inst_3) _inst_9 (Semiring.toModule.{u4} A _inst_2) (Algebra.to_smulCommClass.{u1, u4} R A _inst_1 _inst_2 _inst_3)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u4, u2} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u4} R A _inst_1 _inst_2 _inst_3) _inst_9) (TensorProduct.isScalarTower_left.{u1, u4, u4, u2, u1} R _inst_1 A (MonoidWithZero.toMonoid.{u4} A (Semiring.toMonoidWithZero.{u4} A _inst_2)) A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u4} R A _inst_1 _inst_2 _inst_3) _inst_9 (Module.toDistribMulAction.{u4, u4} A A _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) (Semiring.toModule.{u4} A _inst_2)) (Algebra.to_smulCommClass.{u1, u4} R A _inst_1 _inst_2 _inst_3) R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.toDistribMulAction.{u1, u4} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) (Algebra.toModule.{u1, u4} R A _inst_1 _inst_2 _inst_3)) (smulCommClass_self.{u1, u4} R A (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toZero.{u4} A (Semiring.toMonoidWithZero.{u4} A _inst_2)) (Module.toMulActionWithZero.{u1, u4} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) (Algebra.toModule.{u1, u4} R A _inst_1 _inst_2 _inst_3)))) (Algebra.toSMul.{u1, u4} R A _inst_1 _inst_2 _inst_3) (IsScalarTower.right.{u1, u4} R A _inst_1 _inst_2 _inst_3))))) r (LinearMap.baseChange.{u1, u4, u3, u2} R A M N _inst_1 _inst_2 _inst_3 _inst_6 _inst_7 _inst_8 _inst_9 f))
+<too large>
Case conversion may be inaccurate. Consider using '#align linear_map.base_change_smul LinearMap.baseChange_smulₓ'. -/
@[simp]
theorem baseChange_smul : (r • f).base_change A = r • f.base_change A :=
@@ -407,10 +374,7 @@ variable [AddCommGroup M] [Module R M] [AddCommGroup N] [Module R N]
variable (f g : M →ₗ[R] N)
/- warning: linear_map.base_change_sub -> LinearMap.baseChange_sub is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {A : Type.{u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Ring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2)] [_inst_6 : AddCommGroup.{u3} M] [_inst_7 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6)] [_inst_8 : AddCommGroup.{u4} N] [_inst_9 : Module.{u1, u4} R N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u4} N _inst_8)] (f : LinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u4} N _inst_8) _inst_7 _inst_9) (g : LinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u4} N _inst_8) _inst_7 _inst_9), Eq.{max (succ (max u2 u3)) (succ (max u2 u4))} (LinearMap.{u2, u2, max u2 u3, max u2 u4} A A (Ring.toSemiring.{u2} A _inst_2) (Ring.toSemiring.{u2} A _inst_2) (RingHom.id.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2))) (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3) _inst_7) (TensorProduct.{u1, u2, u4} R (CommRing.toCommSemiring.{u1} R _inst_1) A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u4} N _inst_8) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3) _inst_9) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3) _inst_7) (TensorProduct.addCommMonoid.{u1, u2, u4} R (CommRing.toCommSemiring.{u1} R _inst_1) A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u4} N _inst_8) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3) _inst_9) (TensorProduct.leftModule.{u1, u2, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A (Ring.toSemiring.{u2} A _inst_2) A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3) _inst_7 (Semiring.toModule.{u2} A (Ring.toSemiring.{u2} A _inst_2)) (Algebra.to_smulCommClass.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3)) (TensorProduct.leftModule.{u1, u2, u2, u4} R (CommRing.toCommSemiring.{u1} R _inst_1) A (Ring.toSemiring.{u2} A _inst_2) A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u4} N _inst_8) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3) _inst_9 (Semiring.toModule.{u2} A (Ring.toSemiring.{u2} A _inst_2)) (Algebra.to_smulCommClass.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3))) (LinearMap.baseChange.{u1, u2, u3, u4} R A M N (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_7 (AddCommGroup.toAddCommMonoid.{u4} N _inst_8) _inst_9 (HSub.hSub.{max u3 u4, max u3 u4, max u3 u4} (LinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u4} N _inst_8) _inst_7 _inst_9) (LinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u4} N _inst_8) _inst_7 _inst_9) (LinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u4} N _inst_8) _inst_7 _inst_9) (instHSub.{max u3 u4} (LinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u4} N _inst_8) _inst_7 _inst_9) (LinearMap.hasSub.{u1, u1, u3, u4} R R M N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8 _inst_7 _inst_9 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) f g)) (HSub.hSub.{max (max u2 u3) u2 u4, max (max u2 u3) u2 u4, max (max u2 u3) u2 u4} (LinearMap.{u2, u2, max u2 u3, max u2 u4} A A (Ring.toSemiring.{u2} A _inst_2) (Ring.toSemiring.{u2} A _inst_2) (RingHom.id.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2))) (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3) _inst_7) (TensorProduct.{u1, u2, u4} R (CommRing.toCommSemiring.{u1} R _inst_1) A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u4} N _inst_8) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3) _inst_9) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3) _inst_7) (TensorProduct.addCommMonoid.{u1, u2, u4} R (CommRing.toCommSemiring.{u1} R _inst_1) A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u4} N _inst_8) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3) _inst_9) (TensorProduct.leftModule.{u1, u2, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A (Ring.toSemiring.{u2} A _inst_2) A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3) _inst_7 (Semiring.toModule.{u2} A (Ring.toSemiring.{u2} A _inst_2)) (Algebra.to_smulCommClass.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3)) (TensorProduct.leftModule.{u1, u2, u2, u4} R (CommRing.toCommSemiring.{u1} R _inst_1) A (Ring.toSemiring.{u2} A _inst_2) A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u4} N _inst_8) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3) _inst_9 (Semiring.toModule.{u2} A (Ring.toSemiring.{u2} A _inst_2)) (Algebra.to_smulCommClass.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3))) (LinearMap.{u2, u2, max u2 u3, max u2 u4} A A (Ring.toSemiring.{u2} A _inst_2) (Ring.toSemiring.{u2} A _inst_2) (RingHom.id.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2))) (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3) _inst_7) (TensorProduct.{u1, u2, u4} R (CommRing.toCommSemiring.{u1} R _inst_1) A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u4} N _inst_8) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3) _inst_9) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3) _inst_7) (TensorProduct.addCommMonoid.{u1, u2, u4} R (CommRing.toCommSemiring.{u1} R _inst_1) A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u4} N _inst_8) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3) _inst_9) (TensorProduct.leftModule.{u1, u2, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A (Ring.toSemiring.{u2} A _inst_2) A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3) _inst_7 (Semiring.toModule.{u2} A (Ring.toSemiring.{u2} A _inst_2)) (Algebra.to_smulCommClass.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3)) (TensorProduct.leftModule.{u1, u2, u2, u4} R (CommRing.toCommSemiring.{u1} R _inst_1) A (Ring.toSemiring.{u2} A _inst_2) A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u4} N _inst_8) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3) _inst_9 (Semiring.toModule.{u2} A (Ring.toSemiring.{u2} A _inst_2)) (Algebra.to_smulCommClass.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3))) (LinearMap.{u2, u2, max u2 u3, max u2 u4} A A (Ring.toSemiring.{u2} A _inst_2) (Ring.toSemiring.{u2} A _inst_2) (RingHom.id.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2))) (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3) _inst_7) (TensorProduct.{u1, u2, u4} R (CommRing.toCommSemiring.{u1} R _inst_1) A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u4} N _inst_8) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3) _inst_9) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3) _inst_7) (TensorProduct.addCommMonoid.{u1, u2, u4} R (CommRing.toCommSemiring.{u1} R _inst_1) A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(CommRing.toCommSemiring.{u1} R _inst_1) A (Ring.toSemiring.{u2} A _inst_2) A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u4} N _inst_8) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3) _inst_9 (Semiring.toModule.{u2} A (Ring.toSemiring.{u2} A _inst_2)) (Algebra.to_smulCommClass.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3))) (instHSub.{max (max u2 u3) u2 u4} (LinearMap.{u2, u2, max u2 u3, max u2 u4} A A (Ring.toSemiring.{u2} A _inst_2) (Ring.toSemiring.{u2} A _inst_2) (RingHom.id.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_2))) (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(Ring.toSemiring.{u4} A _inst_2) _inst_3))) (instHSub.{max (max u4 u3) u2} (LinearMap.{u4, u4, max u3 u4, max u2 u4} A A (Ring.toSemiring.{u4} A _inst_2) (Ring.toSemiring.{u4} A _inst_2) (RingHom.id.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_2))) (TensorProduct.{u1, u4, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (Algebra.toModule.{u1, u4} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} A _inst_2) _inst_3) _inst_7) (TensorProduct.{u1, u4, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_8) 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(Algebra.toModule.{u1, u4} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} A _inst_2) _inst_3) _inst_9 (Semiring.toModule.{u4} A (Ring.toSemiring.{u4} A _inst_2)) (Algebra.to_smulCommClass.{u1, u4} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} A _inst_2) _inst_3))) (LinearMap.instSubLinearMapToAddCommMonoid.{u4, u4, max u4 u3, max u4 u2} A A (TensorProduct.{u1, u4, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (Algebra.toModule.{u1, u4} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} A _inst_2) _inst_3) _inst_7) (TensorProduct.{u1, u4, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_8) (Algebra.toModule.{u1, u4} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} A _inst_2) _inst_3) _inst_9) (Ring.toSemiring.{u4} A _inst_2) (Ring.toSemiring.{u4} A _inst_2) (TensorProduct.addCommMonoid.{u1, u4, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (Algebra.toModule.{u1, u4} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} A _inst_2) _inst_3) _inst_7) (TensorProduct.addCommGroup.{u1, u4, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) A N (Ring.toAddCommGroup.{u4} A _inst_2) _inst_8 (Algebra.toModule.{u1, u4} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} A _inst_2) _inst_3) _inst_9) (TensorProduct.leftModule.{u1, u4, u4, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A (Ring.toSemiring.{u4} A _inst_2) A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (Algebra.toModule.{u1, u4} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} A _inst_2) _inst_3) _inst_7 (Semiring.toModule.{u4} A (Ring.toSemiring.{u4} A _inst_2)) (Algebra.to_smulCommClass.{u1, u4} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} A _inst_2) _inst_3)) (TensorProduct.leftModule.{u1, u4, u4, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) A (Ring.toSemiring.{u4} A _inst_2) A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_8) (Algebra.toModule.{u1, u4} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} A _inst_2) _inst_3) _inst_9 (Semiring.toModule.{u4} A (Ring.toSemiring.{u4} A _inst_2)) (Algebra.to_smulCommClass.{u1, u4} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} A _inst_2) _inst_3)) (RingHom.id.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_2))))) (LinearMap.baseChange.{u1, u4, u3, u2} R A M N (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} A _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_7 (AddCommGroup.toAddCommMonoid.{u2} N _inst_8) _inst_9 f) (LinearMap.baseChange.{u1, u4, u3, u2} R A M N (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} A _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_7 (AddCommGroup.toAddCommMonoid.{u2} N _inst_8) _inst_9 g))
+<too large>
Case conversion may be inaccurate. Consider using '#align linear_map.base_change_sub LinearMap.baseChange_subₓ'. -/
@[simp]
theorem baseChange_sub : (f - g).base_change A = f.base_change A - g.base_change A :=
@@ -420,10 +384,7 @@ theorem baseChange_sub : (f - g).base_change A = f.base_change A - g.base_change
#align linear_map.base_change_sub LinearMap.baseChange_sub
/- warning: linear_map.base_change_neg -> LinearMap.baseChange_neg is a dubious translation:
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-but is expected to have type
- forall {R : Type.{u1}} {A : Type.{u4}} {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Ring.{u4} A] [_inst_3 : Algebra.{u1, u4} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} A _inst_2)] [_inst_6 : AddCommGroup.{u3} M] [_inst_7 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6)] [_inst_8 : AddCommGroup.{u2} N] [_inst_9 : Module.{u1, u2} R N (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} N _inst_8)] (f : LinearMap.{u1, u1, u3, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u2} N _inst_8) _inst_7 _inst_9), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (LinearMap.{u4, u4, max u3 u4, max u2 u4} A A (Ring.toSemiring.{u4} A _inst_2) (Ring.toSemiring.{u4} A _inst_2) (RingHom.id.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_2))) (TensorProduct.{u1, u4, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (Algebra.toModule.{u1, u4} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} A _inst_2) _inst_3) _inst_7) (TensorProduct.{u1, u4, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_8) (Algebra.toModule.{u1, u4} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} A _inst_2) _inst_3) _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (Algebra.toModule.{u1, u4} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} A _inst_2) _inst_3) _inst_7) (TensorProduct.addCommMonoid.{u1, u4, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_8) (Algebra.toModule.{u1, u4} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} A _inst_2) _inst_3) _inst_9) (TensorProduct.leftModule.{u1, u4, u4, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A (Ring.toSemiring.{u4} A _inst_2) A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (Algebra.toModule.{u1, u4} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} A _inst_2) _inst_3) _inst_7 (Semiring.toModule.{u4} A (Ring.toSemiring.{u4} A _inst_2)) (Algebra.to_smulCommClass.{u1, u4} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} A _inst_2) _inst_3)) (TensorProduct.leftModule.{u1, u4, u4, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) A (Ring.toSemiring.{u4} A _inst_2) A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_8) (Algebra.toModule.{u1, u4} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} A _inst_2) _inst_3) _inst_9 (Semiring.toModule.{u4} A (Ring.toSemiring.{u4} A _inst_2)) (Algebra.to_smulCommClass.{u1, u4} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} A _inst_2) _inst_3))) (LinearMap.baseChange.{u1, u4, u3, u2} R A M N (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} A _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_7 (AddCommGroup.toAddCommMonoid.{u2} N _inst_8) _inst_9 (Neg.neg.{max u3 u2} (LinearMap.{u1, u1, u3, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u2} N _inst_8) _inst_7 _inst_9) (LinearMap.instNegLinearMapToAddCommMonoid.{u1, u1, u3, u2} R R M N (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8 _inst_7 _inst_9 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) f)) (Neg.neg.{max (max u4 u3) u2} (LinearMap.{u4, u4, max u3 u4, max u2 u4} A A (Ring.toSemiring.{u4} A _inst_2) (Ring.toSemiring.{u4} A _inst_2) (RingHom.id.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_2))) (TensorProduct.{u1, u4, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (Algebra.toModule.{u1, u4} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} A _inst_2) _inst_3) _inst_7) (TensorProduct.{u1, u4, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_8) (Algebra.toModule.{u1, u4} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} A _inst_2) _inst_3) _inst_9) (TensorProduct.addCommMonoid.{u1, u4, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (Algebra.toModule.{u1, u4} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} A _inst_2) _inst_3) _inst_7) (TensorProduct.addCommMonoid.{u1, u4, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_8) (Algebra.toModule.{u1, u4} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} A _inst_2) _inst_3) _inst_9) (TensorProduct.leftModule.{u1, u4, u4, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A (Ring.toSemiring.{u4} A _inst_2) A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (Algebra.toModule.{u1, u4} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} A _inst_2) _inst_3) _inst_7 (Semiring.toModule.{u4} A (Ring.toSemiring.{u4} A _inst_2)) (Algebra.to_smulCommClass.{u1, u4} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} A _inst_2) _inst_3)) (TensorProduct.leftModule.{u1, u4, u4, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) A (Ring.toSemiring.{u4} A _inst_2) A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_8) (Algebra.toModule.{u1, u4} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} A _inst_2) _inst_3) _inst_9 (Semiring.toModule.{u4} A (Ring.toSemiring.{u4} A _inst_2)) (Algebra.to_smulCommClass.{u1, u4} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} A _inst_2) _inst_3))) (LinearMap.instNegLinearMapToAddCommMonoid.{u4, u4, max u4 u3, max u4 u2} A A (TensorProduct.{u1, u4, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (Algebra.toModule.{u1, u4} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} A _inst_2) _inst_3) _inst_7) (TensorProduct.{u1, u4, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_8) (Algebra.toModule.{u1, u4} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} A _inst_2) _inst_3) _inst_9) (Ring.toSemiring.{u4} A _inst_2) (Ring.toSemiring.{u4} A _inst_2) (TensorProduct.addCommMonoid.{u1, u4, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (Algebra.toModule.{u1, u4} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} A _inst_2) _inst_3) _inst_7) (TensorProduct.addCommGroup.{u1, u4, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) A N (Ring.toAddCommGroup.{u4} A _inst_2) _inst_8 (Algebra.toModule.{u1, u4} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} A _inst_2) _inst_3) _inst_9) (TensorProduct.leftModule.{u1, u4, u4, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A (Ring.toSemiring.{u4} A _inst_2) A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (Algebra.toModule.{u1, u4} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} A _inst_2) _inst_3) _inst_7 (Semiring.toModule.{u4} A (Ring.toSemiring.{u4} A _inst_2)) (Algebra.to_smulCommClass.{u1, u4} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} A _inst_2) _inst_3)) (TensorProduct.leftModule.{u1, u4, u4, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) A (Ring.toSemiring.{u4} A _inst_2) A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} N _inst_8) (Algebra.toModule.{u1, u4} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} A _inst_2) _inst_3) _inst_9 (Semiring.toModule.{u4} A (Ring.toSemiring.{u4} A _inst_2)) (Algebra.to_smulCommClass.{u1, u4} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} A _inst_2) _inst_3)) (RingHom.id.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_2)))) (LinearMap.baseChange.{u1, u4, u3, u2} R A M N (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} A _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_7 (AddCommGroup.toAddCommMonoid.{u2} N _inst_8) _inst_9 f))
+<too large>
Case conversion may be inaccurate. Consider using '#align linear_map.base_change_neg LinearMap.baseChange_negₓ'. -/
@[simp]
theorem baseChange_neg : (-f).base_change A = -f.base_change A :=
@@ -469,10 +430,7 @@ def mulAux (a₁ : A) (b₁ : B) : A ⊗[R] B →ₗ[R] A ⊗[R] B :=
#align algebra.tensor_product.mul_aux Algebra.TensorProduct.mulAux
/- warning: algebra.tensor_product.mul_aux_apply -> Algebra.TensorProduct.mulAux_apply is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (a₁ : A) (a₂ : A) (b₁ : B) (b₂ : B), Eq.{succ (max u2 u3)} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (coeFn.{succ (max u2 u3), succ (max u2 u3)} (LinearMap.{u1, u1, max u2 u3, max u2 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.TensorProduct.mulAux.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5 a₁ b₁) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a₂ b₂)) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) a₁ a₂) (HMul.hMul.{u3, u3, u3} B B B (instHMul.{u3} B (NonUnitalNonAssocSemiring.toMul.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) b₁ b₂))
+<too large>
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.mul_aux_apply Algebra.TensorProduct.mulAux_applyₓ'. -/
@[simp]
theorem mulAux_apply (a₁ a₂ : A) (b₁ b₂ : B) :
@@ -481,10 +439,7 @@ theorem mulAux_apply (a₁ a₂ : A) (b₁ b₂ : B) :
#align algebra.tensor_product.mul_aux_apply Algebra.TensorProduct.mulAux_apply
/- warning: algebra.tensor_product.mul -> Algebra.TensorProduct.mul is a dubious translation:
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_inst_4 _inst_5))))))
+<too large>
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.mul Algebra.TensorProduct.mulₓ'. -/
/-- (Implementation detail)
The multiplication map on `A ⊗[R] B`,
@@ -508,10 +463,7 @@ def mul : A ⊗[R] B →ₗ[R] A ⊗[R] B →ₗ[R] A ⊗[R] B :=
#align algebra.tensor_product.mul Algebra.TensorProduct.mul
/- warning: algebra.tensor_product.mul_apply -> Algebra.TensorProduct.mul_apply is a dubious translation:
-lean 3 declaration is
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.TensorProduct.mul.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a₁ b₁)) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a₂ b₂)) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) a₁ a₂) (HMul.hMul.{u3, u3, u3} B B B (instHMul.{u3} B (NonUnitalNonAssocSemiring.toMul.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) b₁ b₂))
+<too large>
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.mul_apply Algebra.TensorProduct.mul_applyₓ'. -/
@[simp]
theorem mul_apply (a₁ a₂ : A) (b₁ b₂ : B) :
@@ -520,10 +472,7 @@ theorem mul_apply (a₁ a₂ : A) (b₁ b₂ : B) :
#align algebra.tensor_product.mul_apply Algebra.TensorProduct.mul_apply
/- warning: algebra.tensor_product.mul_assoc' -> Algebra.TensorProduct.mul_assoc' is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (mul : LinearMap.{u1, u1, max u2 u3, max u2 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (LinearMap.{u1, u1, max u2 u3, max u2 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, max u2 u3} R R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, max u2 u3} R R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (LinearMap.module.{u1, u1, u1, max u2 u3, max u2 u3} R R R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (smulCommClass_self.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (Module.toMulActionWithZero.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))))) => (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) 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(TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => LinearMap.{u1, u1, max u3 u2, max u3 u2} R R 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(CommSemiring.toSemiring.{u1} R _inst_1)))) mul y) z)))
+<too large>
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.mul_assoc' Algebra.TensorProduct.mul_assoc'ₓ'. -/
theorem mul_assoc' (mul : A ⊗[R] B →ₗ[R] A ⊗[R] B →ₗ[R] A ⊗[R] B)
(h :
@@ -550,10 +499,7 @@ theorem mul_assoc' (mul : A ⊗[R] B →ₗ[R] A ⊗[R] B →ₗ[R] A ⊗[R] B)
#align algebra.tensor_product.mul_assoc' Algebra.TensorProduct.mul_assoc'
/- warning: algebra.tensor_product.mul_assoc -> Algebra.TensorProduct.mul_assoc is a dubious translation:
-lean 3 declaration is
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(Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (coeFn.{succ (max u2 u3), succ (max u2 u3)} (LinearMap.{u1, u1, max u2 u3, max u2 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A 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R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => LinearMap.{u1, u1, max u3 u2, max u3 u2} R R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A 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+<too large>
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.mul_assoc Algebra.TensorProduct.mul_assocₓ'. -/
theorem mul_assoc (x y z : A ⊗[R] B) : mul (mul x y) z = mul x (mul y z) :=
mul_assoc' mul
@@ -564,20 +510,14 @@ theorem mul_assoc (x y z : A ⊗[R] B) : mul (mul x y) z = mul x (mul y z) :=
#align algebra.tensor_product.mul_assoc Algebra.TensorProduct.mul_assoc
/- warning: algebra.tensor_product.one_mul -> Algebra.TensorProduct.one_mul is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.one_mul Algebra.TensorProduct.one_mulₓ'. -/
theorem one_mul (x : A ⊗[R] B) : mul (1 ⊗ₜ 1) x = x := by
apply TensorProduct.induction_on x <;> simp (config := { contextual := true })
#align algebra.tensor_product.one_mul Algebra.TensorProduct.one_mul
/- warning: algebra.tensor_product.mul_one -> Algebra.TensorProduct.mul_one is a dubious translation:
-lean 3 declaration is
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} 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+<too large>
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.mul_one Algebra.TensorProduct.mul_oneₓ'. -/
theorem mul_one (x : A ⊗[R] B) : mul x (1 ⊗ₜ 1) = x := by
apply TensorProduct.induction_on x <;> simp (config := { contextual := true })
@@ -611,10 +551,7 @@ theorem one_def : (1 : A ⊗[R] B) = (1 : A) ⊗ₜ (1 : B) :=
-/
/- warning: algebra.tensor_product.tmul_mul_tmul -> Algebra.TensorProduct.tmul_mul_tmul is a dubious translation:
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5))))) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a₁ b₁) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a₂ b₂)) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) a₁ a₂) (HMul.hMul.{u3, u3, u3} B B B (instHMul.{u3} B (NonUnitalNonAssocSemiring.toMul.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) b₁ b₂))
+<too large>
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.tmul_mul_tmul Algebra.TensorProduct.tmul_mul_tmulₓ'. -/
@[simp]
theorem tmul_mul_tmul (a₁ a₂ : A) (b₁ b₂ : B) :
@@ -623,10 +560,7 @@ theorem tmul_mul_tmul (a₁ a₂ : A) (b₁ b₂ : B) :
#align algebra.tensor_product.tmul_mul_tmul Algebra.TensorProduct.tmul_mul_tmul
/- warning: algebra.tensor_product.tmul_pow -> Algebra.TensorProduct.tmul_pow is a dubious translation:
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(Semiring.toMonoidWithZero.{u2} A _inst_2)))) a k) (HPow.hPow.{u3, 0, u3} B Nat B (instHPow.{u3, 0} B Nat (Monoid.Pow.{u3} B (MonoidWithZero.toMonoid.{u3} B (Semiring.toMonoidWithZero.{u3} B _inst_4)))) b k))
+<too large>
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.tmul_pow Algebra.TensorProduct.tmul_powₓ'. -/
@[simp]
theorem tmul_pow (a : A) (b : B) (k : ℕ) : a ⊗ₜ[R] b ^ k = (a ^ k) ⊗ₜ[R] (b ^ k) :=
@@ -693,10 +627,7 @@ instance : Algebra R (A ⊗[R] B) :=
inferInstance
/- warning: algebra.tensor_product.algebra_map_apply -> Algebra.TensorProduct.algebraMap_apply is a dubious translation:
-lean 3 declaration is
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(CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u4} S (AddMonoid.toAddZeroClass.{u4} S (AddCommMonoid.toAddMonoid.{u4} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_6))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} S (AddMonoid.toAddZeroClass.{u4} S (AddCommMonoid.toAddMonoid.{u4} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_6))))))) (Module.toMulActionWithZero.{u1, u4} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_6)))) (Algebra.toModule.{u1, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_6) _inst_7))))) (SMulZeroClass.toHasSmul.{u4, u2} S A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u4, u2} S A (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_6))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} S A (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_6)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u4, u2} S A (CommSemiring.toSemiring.{u4} S _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u4, u2} S A _inst_6 _inst_2 _inst_8))))) (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))] (r 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))) (RingHom.hasCoeToFun.{u4, max u2 u3} S (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_6)) 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- forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {A : Type.{u3}} [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] {B : Type.{u4}} [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u2, u4} R B _inst_1 _inst_4] {S : Type.{u1}} [_inst_6 : CommSemiring.{u1} S] [_inst_7 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_6)] [_inst_8 : Algebra.{u1, u3} S A _inst_6 _inst_2] [_inst_9 : IsScalarTower.{u2, u1, u3} R S A (Algebra.toSMul.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_6) _inst_7) (Algebra.toSMul.{u1, u3} S A _inst_6 _inst_2 _inst_8) (Algebra.toSMul.{u2, u3} R A _inst_1 _inst_2 _inst_3)] (r : S), Eq.{max (succ u3) (succ u4)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => TensorProduct.{u2, u3, u4} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B 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_inst_4 _inst_5) (Algebra.TensorProduct.leftAlgebra.{u2, u3, u4, u1} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5 S _inst_6 _inst_7 _inst_8 _inst_9)) r) (TensorProduct.tmul.{u2, u3, u4} R _inst_1 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) r) B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) r) (Semiring.toNonAssocSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) r) _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (RingHom.{u1, u3} S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_6)) (Semiring.toNonAssocSemiring.{u3} A _inst_2)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) _x) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (RingHom.{u1, u3} S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_6)) (Semiring.toNonAssocSemiring.{u3} A _inst_2)) S A (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_6)))) (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u1, u3} (RingHom.{u1, u3} S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_6)) (Semiring.toNonAssocSemiring.{u3} A _inst_2)) S A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_6))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u1, u3} (RingHom.{u1, u3} S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_6)) (Semiring.toNonAssocSemiring.{u3} A _inst_2)) S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_6)) (Semiring.toNonAssocSemiring.{u3} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u3} S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_6)) (Semiring.toNonAssocSemiring.{u3} A _inst_2))))) (algebraMap.{u1, u3} S A _inst_6 _inst_2 _inst_8) r) (OfNat.ofNat.{u4} B 1 (One.toOfNat1.{u4} B (Semiring.toOne.{u4} B _inst_4))))
+<too large>
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.algebra_map_apply Algebra.TensorProduct.algebraMap_applyₓ'. -/
@[simp]
theorem algebraMap_apply (r : S) : (algebraMap S (A ⊗[R] B)) r = (algebraMap S A) r ⊗ₜ 1 :=
@@ -709,10 +640,7 @@ instance : IsScalarTower R S (A ⊗[R] B) :=
variable {C : Type v₃} [Semiring C] [Algebra R C]
/- warning: algebra.tensor_product.ext -> Algebra.TensorProduct.ext is a dubious translation:
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(Algebra.TensorProduct.TensorProduct.algebra.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_11} {h : AlgHom.{u1, max u2 u3, u4} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C _inst_1 (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_10 (Algebra.TensorProduct.TensorProduct.algebra.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_11}, (forall (a : A) (b : B), Eq.{succ u4} C (coeFn.{max (succ (max u2 u3)) (succ u4), max (succ (max u2 u3)) (succ u4)} (AlgHom.{u1, max u2 u3, u4} R 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_inst_2 _inst_3 B _inst_4 _inst_5) _inst_10 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_11) R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R 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(Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => C) _x) (SMulHomClass.toFunLike.{max (max u2 u3) u4, u1, max u2 u3, u4} (AlgHom.{u1, max u3 u2, u4} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_10 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_11) R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (SMulZeroClass.toSMul.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (TensorProduct.{u1, 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(Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5)))))) (DistribSMul.toSMulZeroClass.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Semiring.toNonAssocSemiring.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A 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_inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5))))) (Module.toDistribMulAction.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 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_inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Semiring.toNonAssocSemiring.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5)))) (Algebra.toModule.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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_inst_3 B _inst_4 _inst_5)))))) (SMulZeroClass.toSMul.{u1, u4} R C (AddMonoid.toZero.{u4} C (AddCommMonoid.toAddMonoid.{u4} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_10))))) (DistribSMul.toSMulZeroClass.{u1, u4} R C (AddMonoid.toAddZeroClass.{u4} C (AddCommMonoid.toAddMonoid.{u4} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_10))))) (DistribMulAction.toDistribSMul.{u1, u4} R C (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u4} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_10)))) (Module.toDistribMulAction.{u1, u4} R C (CommSemiring.toSemiring.{u1} R _inst_1) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_10 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_11))))) h (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a b))) -> (Eq.{max (max (succ u2) (succ u3)) (succ u4)} (AlgHom.{u1, max u3 u2, u4} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C _inst_1 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+<too large>
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.ext Algebra.TensorProduct.extₓ'. -/
@[ext]
theorem ext {g h : A ⊗[R] B →ₐ[R] C} (H : ∀ a b, g (a ⊗ₜ b) = h (a ⊗ₜ b)) : g = h :=
@@ -769,10 +697,7 @@ theorem includeRight_apply (b : B) : (includeRight : B →ₐ[R] A ⊗[R] B) b =
-/
/- warning: algebra.tensor_product.include_left_comp_algebra_map -> Algebra.TensorProduct.includeLeft_comp_algebraMap is a dubious translation:
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(CommRing.toCommSemiring.{u1} R _inst_12) (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_14)) _inst_16))
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(CommRing.toCommSemiring.{u1} T _inst_14))))) (Algebra.toModule.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_12) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_13)) _inst_15) (Algebra.toModule.{u3, u1} R T (CommRing.toCommSemiring.{u3} R _inst_12) (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_14)) _inst_16)) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_12))) (Semiring.toNonAssocSemiring.{max u1 u2} (TensorProduct.{u3, u2, u1} R (CommRing.toCommSemiring.{u3} R _inst_12) S T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_13))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_14))))) (Algebra.toModule.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_12) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_13)) _inst_15) (Algebra.toModule.{u3, u1} R T (CommRing.toCommSemiring.{u3} R _inst_12) (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_14)) _inst_16)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R (CommRing.toCommSemiring.{u3} R _inst_12) S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_13)) _inst_15 T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_14)) _inst_16))) (RingHom.comp.{u3, u2, max u1 u2} R S (TensorProduct.{u3, u2, u1} R (CommRing.toCommSemiring.{u3} R _inst_12) S T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_13))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_14))))) (Algebra.toModule.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_12) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_13)) _inst_15) (Algebra.toModule.{u3, u1} R T (CommRing.toCommSemiring.{u3} R _inst_12) (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_14)) _inst_16)) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_12))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_13))) (Semiring.toNonAssocSemiring.{max u1 u2} (TensorProduct.{u3, u2, u1} R (CommRing.toCommSemiring.{u3} R _inst_12) S T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_13))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_14))))) (Algebra.toModule.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_12) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_13)) _inst_15) (Algebra.toModule.{u3, u1} R T (CommRing.toCommSemiring.{u3} R _inst_12) (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_14)) _inst_16)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R (CommRing.toCommSemiring.{u3} R _inst_12) S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_13)) _inst_15 T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_14)) _inst_16)) (AlgHom.toRingHom.{u3, u2, max u1 u2} R S (TensorProduct.{u3, u2, u1} R (CommRing.toCommSemiring.{u3} R _inst_12) S T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_13))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_14))))) (Algebra.toModule.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_12) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_13)) _inst_15) (Algebra.toModule.{u3, u1} R T (CommRing.toCommSemiring.{u3} R _inst_12) (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_14)) _inst_16)) (CommRing.toCommSemiring.{u3} R _inst_12) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_13)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R (CommRing.toCommSemiring.{u3} R _inst_12) S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_13)) _inst_15 T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_14)) _inst_16) _inst_15 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R (CommRing.toCommSemiring.{u3} R _inst_12) S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_13)) _inst_15 T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_14)) _inst_16) (Algebra.TensorProduct.includeLeft.{u3, u2, u1} R (CommRing.toCommSemiring.{u3} R _inst_12) S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_13)) _inst_15 T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_14)) _inst_16)) (algebraMap.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_12) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_13)) _inst_15)) (RingHom.comp.{u3, u1, max u2 u1} R T (TensorProduct.{u3, u2, u1} R (CommRing.toCommSemiring.{u3} R _inst_12) S T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_13))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_14))))) (Algebra.toModule.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_12) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_13)) _inst_15) (Algebra.toModule.{u3, u1} R T (CommRing.toCommSemiring.{u3} R _inst_12) (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_14)) _inst_16)) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_12))) (Semiring.toNonAssocSemiring.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_14))) (Semiring.toNonAssocSemiring.{max u2 u1} (TensorProduct.{u3, u2, u1} R (CommRing.toCommSemiring.{u3} R _inst_12) S T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_13))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_14))))) (Algebra.toModule.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_12) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_13)) _inst_15) (Algebra.toModule.{u3, u1} R T (CommRing.toCommSemiring.{u3} R _inst_12) (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_14)) _inst_16)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R (CommRing.toCommSemiring.{u3} R _inst_12) S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_13)) _inst_15 T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_14)) _inst_16)) (AlgHom.toRingHom.{u3, u1, max u2 u1} R T (TensorProduct.{u3, u2, u1} R (CommRing.toCommSemiring.{u3} R _inst_12) S T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_13))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} T (Semiring.toNonAssocSemiring.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_14))))) (Algebra.toModule.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_12) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_13)) _inst_15) (Algebra.toModule.{u3, u1} R T (CommRing.toCommSemiring.{u3} R _inst_12) (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_14)) _inst_16)) (CommRing.toCommSemiring.{u3} R _inst_12) (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_14)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R (CommRing.toCommSemiring.{u3} R _inst_12) S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_13)) _inst_15 T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_14)) _inst_16) _inst_16 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R (CommRing.toCommSemiring.{u3} R _inst_12) S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_13)) _inst_15 T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_14)) _inst_16) (Algebra.TensorProduct.includeRight.{u3, u2, u1} R (CommRing.toCommSemiring.{u3} R _inst_12) S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_13)) _inst_15 T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_14)) _inst_16)) (algebraMap.{u3, u1} R T (CommRing.toCommSemiring.{u3} R _inst_12) (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_14)) _inst_16))
+<too large>
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.include_left_comp_algebra_map Algebra.TensorProduct.includeLeft_comp_algebraMapₓ'. -/
theorem includeLeft_comp_algebraMap {R S T : Type _} [CommRing R] [CommRing S] [CommRing T]
[Algebra R S] [Algebra R T] :
@@ -839,10 +764,7 @@ def rightAlgebra : Algebra B (A ⊗[R] B) :=
attribute [local instance] tensor_product.right_algebra
/- warning: algebra.tensor_product.right_is_scalar_tower -> Algebra.TensorProduct.right_isScalarTower is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {A : Type.{u2}} [_inst_2 : CommRing.{u2} A] [_inst_3 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] {B : Type.{u3}} [_inst_4 : CommRing.{u3} B] [_inst_5 : Algebra.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4))], IsScalarTower.{u1, u3, max u2 u3} R B (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A B (AddCommGroup.toAddCommMonoid.{u2} A (NonUnitalNonAssocRing.toAddCommGroup.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} B (NonUnitalNonAssocRing.toAddCommGroup.{u3} B (NonAssocRing.toNonUnitalNonAssocRing.{u3} B (Ring.toNonAssocRing.{u3} B (CommRing.toRing.{u3} B _inst_4))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) (Algebra.toModule.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_5)) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)))))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4))))) (Algebra.toModule.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_5))))) (SMulZeroClass.toHasSmul.{u3, max u2 u3} B (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A B (AddCommGroup.toAddCommMonoid.{u2} A (NonUnitalNonAssocRing.toAddCommGroup.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} B (NonUnitalNonAssocRing.toAddCommGroup.{u3} B (NonAssocRing.toNonUnitalNonAssocRing.{u3} B (Ring.toNonAssocRing.{u3} B (CommRing.toRing.{u3} B _inst_4))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) (Algebra.toModule.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_5)) (AddZeroClass.toHasZero.{max u2 u3} (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A B (AddCommGroup.toAddCommMonoid.{u2} A (NonUnitalNonAssocRing.toAddCommGroup.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} B (NonUnitalNonAssocRing.toAddCommGroup.{u3} B (NonAssocRing.toNonUnitalNonAssocRing.{u3} B (Ring.toNonAssocRing.{u3} B (CommRing.toRing.{u3} B _inst_4))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) (Algebra.toModule.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A B (AddCommGroup.toAddCommMonoid.{u2} A (NonUnitalNonAssocRing.toAddCommGroup.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} B (NonUnitalNonAssocRing.toAddCommGroup.{u3} B (NonAssocRing.toNonUnitalNonAssocRing.{u3} B (Ring.toNonAssocRing.{u3} B (CommRing.toRing.{u3} B _inst_4))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) (Algebra.toModule.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A B (AddCommGroup.toAddCommMonoid.{u2} A (NonUnitalNonAssocRing.toAddCommGroup.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} B (NonUnitalNonAssocRing.toAddCommGroup.{u3} B (NonAssocRing.toNonUnitalNonAssocRing.{u3} B (Ring.toNonAssocRing.{u3} B (CommRing.toRing.{u3} B _inst_4))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) (Algebra.toModule.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A B (AddCommGroup.toAddCommMonoid.{u2} A (NonUnitalNonAssocRing.toAddCommGroup.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} B (NonUnitalNonAssocRing.toAddCommGroup.{u3} B (NonAssocRing.toNonUnitalNonAssocRing.{u3} B (Ring.toNonAssocRing.{u3} B (CommRing.toRing.{u3} B _inst_4))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) (Algebra.toModule.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_5)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A B (AddCommGroup.toAddCommMonoid.{u2} A (NonUnitalNonAssocRing.toAddCommGroup.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} B (NonUnitalNonAssocRing.toAddCommGroup.{u3} B (NonAssocRing.toNonUnitalNonAssocRing.{u3} B (Ring.toNonAssocRing.{u3} B (CommRing.toRing.{u3} B _inst_4))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) (Algebra.toModule.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_5)) (Semiring.toNonAssocSemiring.{max u2 u3} (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A B (AddCommGroup.toAddCommMonoid.{u2} A (NonUnitalNonAssocRing.toAddCommGroup.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} B (NonUnitalNonAssocRing.toAddCommGroup.{u3} B (NonAssocRing.toNonUnitalNonAssocRing.{u3} B (Ring.toNonAssocRing.{u3} B (CommRing.toRing.{u3} B _inst_4))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) (Algebra.toModule.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_5)) (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3 B (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_5))))))) (SMulWithZero.toSmulZeroClass.{u3, max u2 u3} B (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A B (AddCommGroup.toAddCommMonoid.{u2} A (NonUnitalNonAssocRing.toAddCommGroup.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} B (NonUnitalNonAssocRing.toAddCommGroup.{u3} B (NonAssocRing.toNonUnitalNonAssocRing.{u3} B (Ring.toNonAssocRing.{u3} B (CommRing.toRing.{u3} B _inst_4))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) (Algebra.toModule.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_5)) (MulZeroClass.toHasZero.{u3} B (MulZeroOneClass.toMulZeroClass.{u3} B (MonoidWithZero.toMulZeroOneClass.{u3} B (Semiring.toMonoidWithZero.{u3} B (CommSemiring.toSemiring.{u3} B (CommRing.toCommSemiring.{u3} B _inst_4)))))) (AddZeroClass.toHasZero.{max u2 u3} (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A B (AddCommGroup.toAddCommMonoid.{u2} A (NonUnitalNonAssocRing.toAddCommGroup.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} B (NonUnitalNonAssocRing.toAddCommGroup.{u3} B (NonAssocRing.toNonUnitalNonAssocRing.{u3} B (Ring.toNonAssocRing.{u3} B (CommRing.toRing.{u3} B _inst_4))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) (Algebra.toModule.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A B (AddCommGroup.toAddCommMonoid.{u2} A (NonUnitalNonAssocRing.toAddCommGroup.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} B (NonUnitalNonAssocRing.toAddCommGroup.{u3} B (NonAssocRing.toNonUnitalNonAssocRing.{u3} B (Ring.toNonAssocRing.{u3} B (CommRing.toRing.{u3} B _inst_4))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) (Algebra.toModule.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A B (AddCommGroup.toAddCommMonoid.{u2} A (NonUnitalNonAssocRing.toAddCommGroup.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} B (NonUnitalNonAssocRing.toAddCommGroup.{u3} B (NonAssocRing.toNonUnitalNonAssocRing.{u3} B (Ring.toNonAssocRing.{u3} B (CommRing.toRing.{u3} B _inst_4))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) (Algebra.toModule.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A B (AddCommGroup.toAddCommMonoid.{u2} A (NonUnitalNonAssocRing.toAddCommGroup.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} B (NonUnitalNonAssocRing.toAddCommGroup.{u3} B (NonAssocRing.toNonUnitalNonAssocRing.{u3} B (Ring.toNonAssocRing.{u3} B (CommRing.toRing.{u3} B _inst_4))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) (Algebra.toModule.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_5)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A B (AddCommGroup.toAddCommMonoid.{u2} A (NonUnitalNonAssocRing.toAddCommGroup.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} B (NonUnitalNonAssocRing.toAddCommGroup.{u3} B (NonAssocRing.toNonUnitalNonAssocRing.{u3} B (Ring.toNonAssocRing.{u3} B (CommRing.toRing.{u3} B _inst_4))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) (Algebra.toModule.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_5)) (Semiring.toNonAssocSemiring.{max u2 u3} (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A B (AddCommGroup.toAddCommMonoid.{u2} A (NonUnitalNonAssocRing.toAddCommGroup.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} B (NonUnitalNonAssocRing.toAddCommGroup.{u3} B (NonAssocRing.toNonUnitalNonAssocRing.{u3} B (Ring.toNonAssocRing.{u3} B (CommRing.toRing.{u3} B _inst_4))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) (Algebra.toModule.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_5)) (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3 B (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_5))))))) (MulActionWithZero.toSMulWithZero.{u3, max u2 u3} B (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A B (AddCommGroup.toAddCommMonoid.{u2} A (NonUnitalNonAssocRing.toAddCommGroup.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} B (NonUnitalNonAssocRing.toAddCommGroup.{u3} B (NonAssocRing.toNonUnitalNonAssocRing.{u3} B (Ring.toNonAssocRing.{u3} B (CommRing.toRing.{u3} B _inst_4))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) (Algebra.toModule.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_5)) (Semiring.toMonoidWithZero.{u3} B (CommSemiring.toSemiring.{u3} B (CommRing.toCommSemiring.{u3} B _inst_4))) (AddZeroClass.toHasZero.{max u2 u3} (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A B (AddCommGroup.toAddCommMonoid.{u2} A (NonUnitalNonAssocRing.toAddCommGroup.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} B (NonUnitalNonAssocRing.toAddCommGroup.{u3} B (NonAssocRing.toNonUnitalNonAssocRing.{u3} B (Ring.toNonAssocRing.{u3} B (CommRing.toRing.{u3} B _inst_4))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) (Algebra.toModule.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A B (AddCommGroup.toAddCommMonoid.{u2} A (NonUnitalNonAssocRing.toAddCommGroup.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} B (NonUnitalNonAssocRing.toAddCommGroup.{u3} B (NonAssocRing.toNonUnitalNonAssocRing.{u3} B (Ring.toNonAssocRing.{u3} B (CommRing.toRing.{u3} B _inst_4))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) (Algebra.toModule.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A B (AddCommGroup.toAddCommMonoid.{u2} A (NonUnitalNonAssocRing.toAddCommGroup.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} B (NonUnitalNonAssocRing.toAddCommGroup.{u3} B (NonAssocRing.toNonUnitalNonAssocRing.{u3} B (Ring.toNonAssocRing.{u3} B (CommRing.toRing.{u3} B _inst_4))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) (Algebra.toModule.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A B (AddCommGroup.toAddCommMonoid.{u2} A (NonUnitalNonAssocRing.toAddCommGroup.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} B (NonUnitalNonAssocRing.toAddCommGroup.{u3} B (NonAssocRing.toNonUnitalNonAssocRing.{u3} B (Ring.toNonAssocRing.{u3} B (CommRing.toRing.{u3} B _inst_4))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) (Algebra.toModule.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_5)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A B (AddCommGroup.toAddCommMonoid.{u2} A (NonUnitalNonAssocRing.toAddCommGroup.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} B (NonUnitalNonAssocRing.toAddCommGroup.{u3} B (NonAssocRing.toNonUnitalNonAssocRing.{u3} B (Ring.toNonAssocRing.{u3} B (CommRing.toRing.{u3} B _inst_4))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) (Algebra.toModule.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_5)) (Semiring.toNonAssocSemiring.{max u2 u3} (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A B (AddCommGroup.toAddCommMonoid.{u2} A (NonUnitalNonAssocRing.toAddCommGroup.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} B (NonUnitalNonAssocRing.toAddCommGroup.{u3} B (NonAssocRing.toNonUnitalNonAssocRing.{u3} B (Ring.toNonAssocRing.{u3} B (CommRing.toRing.{u3} B _inst_4))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) (Algebra.toModule.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_5)) (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3 B (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_5))))))) (Module.toMulActionWithZero.{u3, max u2 u3} B (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A B (AddCommGroup.toAddCommMonoid.{u2} A (NonUnitalNonAssocRing.toAddCommGroup.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} B (NonUnitalNonAssocRing.toAddCommGroup.{u3} B (NonAssocRing.toNonUnitalNonAssocRing.{u3} B (Ring.toNonAssocRing.{u3} B (CommRing.toRing.{u3} B _inst_4))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) (Algebra.toModule.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_5)) (CommSemiring.toSemiring.{u3} B (CommRing.toCommSemiring.{u3} B _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A B (AddCommGroup.toAddCommMonoid.{u2} A (NonUnitalNonAssocRing.toAddCommGroup.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} B (NonUnitalNonAssocRing.toAddCommGroup.{u3} B (NonAssocRing.toNonUnitalNonAssocRing.{u3} B (Ring.toNonAssocRing.{u3} B (CommRing.toRing.{u3} B _inst_4))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) (Algebra.toModule.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_5)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A B (AddCommGroup.toAddCommMonoid.{u2} A (NonUnitalNonAssocRing.toAddCommGroup.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} B (NonUnitalNonAssocRing.toAddCommGroup.{u3} B (NonAssocRing.toNonUnitalNonAssocRing.{u3} B (Ring.toNonAssocRing.{u3} B (CommRing.toRing.{u3} B _inst_4))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) (Algebra.toModule.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_5)) (Semiring.toNonAssocSemiring.{max u2 u3} (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A B (AddCommGroup.toAddCommMonoid.{u2} A (NonUnitalNonAssocRing.toAddCommGroup.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} B (NonUnitalNonAssocRing.toAddCommGroup.{u3} B (NonAssocRing.toNonUnitalNonAssocRing.{u3} B (Ring.toNonAssocRing.{u3} B (CommRing.toRing.{u3} B _inst_4))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) (Algebra.toModule.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_5)) (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3 B (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_5)))) (Algebra.toModule.{u3, max u2 u3} B (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A B (AddCommGroup.toAddCommMonoid.{u2} A (NonUnitalNonAssocRing.toAddCommGroup.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} B (NonUnitalNonAssocRing.toAddCommGroup.{u3} B (NonAssocRing.toNonUnitalNonAssocRing.{u3} B (Ring.toNonAssocRing.{u3} B (CommRing.toRing.{u3} B _inst_4))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) (Algebra.toModule.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_5)) (CommRing.toCommSemiring.{u3} B _inst_4) (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3 B (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_5) (Algebra.TensorProduct.rightAlgebra.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5)))))) (TensorProduct.hasSmul.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A B (AddCommGroup.toAddCommMonoid.{u2} A (NonUnitalNonAssocRing.toAddCommGroup.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} B (NonUnitalNonAssocRing.toAddCommGroup.{u3} B (NonAssocRing.toNonUnitalNonAssocRing.{u3} B (Ring.toNonAssocRing.{u3} B (CommRing.toRing.{u3} B _inst_4))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) (Algebra.toModule.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_5))
-but is expected to have type
- forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {A : Type.{u2}} [_inst_2 : CommRing.{u2} A] [_inst_3 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] {B : Type.{u3}} [_inst_4 : CommRing.{u3} B] [_inst_5 : Algebra.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u3} B (CommRing.toCommSemiring.{u3} B _inst_4))], IsScalarTower.{u1, u3, max u3 u2} R B (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} B (NonAssocRing.toNonUnitalNonAssocRing.{u3} B (Ring.toNonAssocRing.{u3} B (CommRing.toRing.{u3} B _inst_4))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_3) (Algebra.toModule.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u3} B (CommRing.toCommSemiring.{u3} B _inst_4)) _inst_5)) (Algebra.toSMul.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u3} B (CommRing.toCommSemiring.{u3} B _inst_4)) _inst_5) (Algebra.toSMul.{u3, max u2 u3} B (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} B (NonAssocRing.toNonUnitalNonAssocRing.{u3} B (Ring.toNonAssocRing.{u3} B (CommRing.toRing.{u3} B _inst_4))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_3) (Algebra.toModule.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u3} B (CommRing.toCommSemiring.{u3} B _inst_4)) _inst_5)) (CommRing.toCommSemiring.{u3} B _inst_4) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_3 B (CommSemiring.toSemiring.{u3} B (CommRing.toCommSemiring.{u3} B _inst_4)) _inst_5) (Algebra.TensorProduct.rightAlgebra.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5)) (TensorProduct.instSMulTensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} B (NonAssocRing.toNonUnitalNonAssocRing.{u3} B (Ring.toNonAssocRing.{u3} B (CommRing.toRing.{u3} B _inst_4))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_3) (Algebra.toModule.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u3} B (CommRing.toCommSemiring.{u3} B _inst_4)) _inst_5))
+<too large>
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.right_is_scalar_tower Algebra.TensorProduct.right_isScalarTowerₓ'. -/
instance right_isScalarTower : IsScalarTower R B (A ⊗[R] B) :=
IsScalarTower.of_algebraMap_eq fun r => (Algebra.TensorProduct.includeRight.commutes r).symm
@@ -883,10 +805,7 @@ variable {C : Type v₃} [Semiring C] [Algebra R C]
variable {D : Type v₄} [Semiring D] [Algebra R D]
/- warning: algebra.tensor_product.alg_hom_of_linear_map_tensor_product -> Algebra.TensorProduct.algHomOfLinearMapTensorProduct is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {C : Type.{u4}} [_inst_6 : Semiring.{u4} C] [_inst_7 : Algebra.{u1, u4} R C _inst_1 _inst_6] (f : LinearMap.{u1, u1, max u2 u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)), (forall (a₁ : A) (a₂ : A) (b₁ : B) (b₂ : B), Eq.{succ u4} C (coeFn.{max (succ (max u2 u3)) (succ u4), max (succ (max u2 u3)) (succ u4)} (LinearMap.{u1, u1, max u2 u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A 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(Semiring.toNonAssocSemiring.{u4} C _inst_6) (RingHom.instRingHomClassRingHom.{u1, u4} R C (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} C _inst_6))))) (algebraMap.{u1, u4} R C _inst_1 _inst_6 _inst_7) r)) -> (AlgHom.{u1, max u3 u2, u4} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_6 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_7)
+<too large>
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.alg_hom_of_linear_map_tensor_product Algebra.TensorProduct.algHomOfLinearMapTensorProductₓ'. -/
/-- Build an algebra morphism from a linear map out of a tensor product,
and evidence of multiplicativity on pure tensors.
@@ -915,10 +834,7 @@ def algHomOfLinearMapTensorProduct (f : A ⊗[R] B →ₗ[R] C)
#align algebra.tensor_product.alg_hom_of_linear_map_tensor_product Algebra.TensorProduct.algHomOfLinearMapTensorProduct
/- warning: algebra.tensor_product.alg_hom_of_linear_map_tensor_product_apply -> Algebra.TensorProduct.algHomOfLinearMapTensorProduct_apply is a dubious translation:
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(TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5))) (Module.toDistribMulAction.{u1, u4} R C (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, max u2 u3, u4, max (max u2 u3) u4} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_6 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(Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_6 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_7) (AlgHom.algHomClass.{u1, max u2 u3, u4} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B 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_inst_4 _inst_5 C _inst_6 _inst_7 f w₁ w₂) x) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u2) (succ u3), succ u4} (LinearMap.{u1, u1, max u3 u2, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (fun (_x : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => C) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u3, u4} R R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f x)
+<too large>
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.alg_hom_of_linear_map_tensor_product_apply Algebra.TensorProduct.algHomOfLinearMapTensorProduct_applyₓ'. -/
@[simp]
theorem algHomOfLinearMapTensorProduct_apply (f w₁ w₂ x) :
@@ -927,10 +843,7 @@ theorem algHomOfLinearMapTensorProduct_apply (f w₁ w₂ x) :
#align algebra.tensor_product.alg_hom_of_linear_map_tensor_product_apply Algebra.TensorProduct.algHomOfLinearMapTensorProduct_apply
/- warning: algebra.tensor_product.alg_equiv_of_linear_equiv_tensor_product -> Algebra.TensorProduct.algEquivOfLinearEquivTensorProduct is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {C : Type.{u4}} [_inst_6 : Semiring.{u4} C] [_inst_7 : Algebra.{u1, u4} R C _inst_1 _inst_6] (f : LinearEquiv.{u1, u1, max u2 u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Algebra.TensorProduct.algEquivOfLinearEquivTensorProduct._proof_1.{u1} R _inst_1) (Algebra.TensorProduct.algEquivOfLinearEquivTensorProduct._proof_2.{u1} R _inst_1) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B 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Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.alg_equiv_of_linear_equiv_tensor_product Algebra.TensorProduct.algEquivOfLinearEquivTensorProductₓ'. -/
/-- Build an algebra equivalence from a linear equivalence out of a tensor product,
and evidence of multiplicativity on pure tensors.
@@ -942,10 +855,7 @@ def algEquivOfLinearEquivTensorProduct (f : A ⊗[R] B ≃ₗ[R] C)
#align algebra.tensor_product.alg_equiv_of_linear_equiv_tensor_product Algebra.TensorProduct.algEquivOfLinearEquivTensorProduct
/- warning: algebra.tensor_product.alg_equiv_of_linear_equiv_tensor_product_apply -> Algebra.TensorProduct.algEquivOfLinearEquivTensorProduct_apply is a dubious translation:
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_inst_1)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B 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_inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) f x)
+<too large>
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.alg_equiv_of_linear_equiv_tensor_product_apply Algebra.TensorProduct.algEquivOfLinearEquivTensorProduct_applyₓ'. -/
@[simp]
theorem algEquivOfLinearEquivTensorProduct_apply (f w₁ w₂ x) :
@@ -954,10 +864,7 @@ theorem algEquivOfLinearEquivTensorProduct_apply (f w₁ w₂ x) :
#align algebra.tensor_product.alg_equiv_of_linear_equiv_tensor_product_apply Algebra.TensorProduct.algEquivOfLinearEquivTensorProduct_apply
/- warning: algebra.tensor_product.alg_equiv_of_linear_equiv_triple_tensor_product -> Algebra.TensorProduct.algEquivOfLinearEquivTripleTensorProduct is a dubious translation:
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- forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {C : Type.{u4}} [_inst_6 : Semiring.{u4} C] [_inst_7 : Algebra.{u1, u4} R C _inst_1 _inst_6] {D : Type.{u5}} [_inst_8 : Semiring.{u5} D] [_inst_9 : Algebra.{u1, u5} R D _inst_1 _inst_8] (f : LinearEquiv.{u1, u1, max (max u2 u3) u4, u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Algebra.TensorProduct.algEquivOfLinearEquivTripleTensorProduct._proof_1.{u1} R _inst_1) (Algebra.TensorProduct.algEquivOfLinearEquivTripleTensorProduct._proof_2.{u1} R _inst_1) (TensorProduct.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) D (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) 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(Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) => D) (TensorProduct.tmul.{u1, max u2 u3, 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TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) => D) (TensorProduct.tmul.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a₂ b₂) c₂)) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) => D) (TensorProduct.tmul.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a₁ b₁) c₁)) (instHMul.{u5} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) => D) (TensorProduct.tmul.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a₁ b₁) c₁)) (NonUnitalNonAssocSemiring.toMul.{u5} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) 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_inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) D _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) 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+<too large>
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.alg_equiv_of_linear_equiv_triple_tensor_product Algebra.TensorProduct.algEquivOfLinearEquivTripleTensorProductₓ'. -/
/-- Build an algebra equivalence from a linear equivalence out of a triple tensor product,
and evidence of multiplicativity on pure tensors.
@@ -998,10 +905,7 @@ def algEquivOfLinearEquivTripleTensorProduct (f : (A ⊗[R] B) ⊗[R] C ≃ₗ[R
#align algebra.tensor_product.alg_equiv_of_linear_equiv_triple_tensor_product Algebra.TensorProduct.algEquivOfLinearEquivTripleTensorProduct
/- warning: algebra.tensor_product.alg_equiv_of_linear_equiv_triple_tensor_product_apply -> Algebra.TensorProduct.algEquivOfLinearEquivTripleTensorProduct_apply is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {C : Type.{u4}} [_inst_6 : Semiring.{u4} C] [_inst_7 : Algebra.{u1, u4} R C _inst_1 _inst_6] {D : Type.{u5}} [_inst_8 : Semiring.{u5} D] [_inst_9 : Algebra.{u1, u5} R D _inst_1 _inst_8] (f : LinearEquiv.{u1, u1, max (max u2 u3) u4, u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Algebra.TensorProduct.algEquivOfLinearEquivTripleTensorProduct._proof_1.{u1} R _inst_1) (Algebra.TensorProduct.algEquivOfLinearEquivTripleTensorProduct._proof_2.{u1} R _inst_1) (TensorProduct.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) D (TensorProduct.addCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) 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_inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u5} R D _inst_1 _inst_8 _inst_9)) (fun (_x : LinearEquiv.{u1, u1, max (max u2 u3) u4, u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Algebra.TensorProduct.algEquivOfLinearEquivTripleTensorProduct._proof_3.{u1} R _inst_1) (Algebra.TensorProduct.algEquivOfLinearEquivTripleTensorProduct._proof_4.{u1} R _inst_1) (TensorProduct.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) D (TensorProduct.addCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B 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(Algebra.toModule.{u1, u5} R D _inst_1 _inst_8 _inst_9)) => (TensorProduct.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) -> D) (LinearEquiv.hasCoeToFun.{u1, u1, max (max u2 u3) u4, u5} R R (TensorProduct.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) D (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} D (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} D (Semiring.toNonAssocSemiring.{u5} D _inst_8))) (TensorProduct.module.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) 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TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) => D) (TensorProduct.tmul.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a₂ b₂) c₂)) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) => D) (TensorProduct.tmul.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a₁ b₁) c₁)) (instHMul.{u5} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) => D) (TensorProduct.tmul.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a₁ b₁) c₁)) (NonUnitalNonAssocSemiring.toMul.{u5} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) => D) (TensorProduct.tmul.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) 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+<too large>
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.alg_equiv_of_linear_equiv_triple_tensor_product_apply Algebra.TensorProduct.algEquivOfLinearEquivTripleTensorProduct_applyₓ'. -/
@[simp]
theorem algEquivOfLinearEquivTripleTensorProduct_apply (f w₁ w₂ x) :
@@ -1039,10 +943,7 @@ protected def lid : R ⊗[R] A ≃ₐ[R] A :=
#align algebra.tensor_product.lid Algebra.TensorProduct.lid
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+<too large>
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.lid_tmul Algebra.TensorProduct.lid_tmulₓ'. -/
@[simp]
theorem lid_tmul (r : R) (a : A) : (TensorProduct.lid R A : R ⊗ A → A) (r ⊗ₜ a) = r • a := by
@@ -1063,10 +964,7 @@ protected def rid : A ⊗[R] R ≃ₐ[R] A :=
#align algebra.tensor_product.rid Algebra.TensorProduct.rid
/- warning: algebra.tensor_product.rid_tmul -> Algebra.TensorProduct.rid_tmul is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.rid_tmul Algebra.TensorProduct.rid_tmulₓ'. -/
@[simp]
theorem rid_tmul (r : R) (a : A) : (TensorProduct.rid R A : A ⊗ R → A) (a ⊗ₜ r) = r • a := by
@@ -1095,10 +993,7 @@ protected def comm : A ⊗[R] B ≃ₐ[R] B ⊗[R] A :=
#align algebra.tensor_product.comm Algebra.TensorProduct.comm
/- warning: algebra.tensor_product.comm_tmul -> Algebra.TensorProduct.comm_tmul is a dubious translation:
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_inst_5) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u3, u2} R _inst_1 B _inst_4 _inst_5 A _inst_2 _inst_3)))) (Algebra.toModule.{u1, max u2 u3} R (TensorProduct.{u1, u3, u2} R _inst_1 B A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u3, u2} R _inst_1 B _inst_4 _inst_5 A _inst_2 _inst_3) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u3, u2} R _inst_1 B _inst_4 _inst_5 A _inst_2 _inst_3))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, max u2 u3, max u2 u3, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.{u1, u3, u2} R _inst_1 B A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u3, u2} R _inst_1 B _inst_4 _inst_5 A _inst_2 _inst_3) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u3, u2} R _inst_1 B _inst_4 _inst_5 A _inst_2 _inst_3) (AlgEquiv.{u1, max u3 u2, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.{u1, u3, u2} R _inst_1 B A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B 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(Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u3, u2} R _inst_1 B _inst_4 _inst_5 A _inst_2 _inst_3)) (AlgEquivClass.toAlgHomClass.{max u2 u3, u1, max u2 u3, max u2 u3} (AlgEquiv.{u1, max u3 u2, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.{u1, u3, u2} R _inst_1 B A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _inst_1 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+<too large>
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.comm_tmul Algebra.TensorProduct.comm_tmulₓ'. -/
@[simp]
theorem comm_tmul (a : A) (b : B) :
@@ -1107,10 +1002,7 @@ theorem comm_tmul (a : A) (b : B) :
#align algebra.tensor_product.comm_tmul Algebra.TensorProduct.comm_tmul
/- warning: algebra.tensor_product.adjoin_tmul_eq_top -> Algebra.TensorProduct.adjoin_tmul_eq_top is a dubious translation:
-lean 3 declaration is
- forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (A : Type.{u2}) [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (B : Type.{u3}) [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4], Eq.{succ (max u2 u3)} (Subalgebra.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) _inst_1 (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (Algebra.TensorProduct.TensorProduct.algebra.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5)) (Algebra.adjoin.{u1, max u2 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+<too large>
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.adjoin_tmul_eq_top Algebra.TensorProduct.adjoin_tmul_eq_topₓ'. -/
theorem adjoin_tmul_eq_top : adjoin R { t : A ⊗[R] B | ∃ a b, a ⊗ₜ[R] b = t } = ⊤ :=
top_le_iff.mp <| (top_le_iff.mpr <| span_tmul_eq_top R A B).trans (span_le_adjoin R _)
@@ -1123,10 +1015,7 @@ section
variable {R A B C}
/- warning: algebra.tensor_product.assoc_aux_1 -> Algebra.TensorProduct.assoc_aux_1 is a dubious translation:
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u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (TensorProduct.module.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B 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_inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (TensorProduct.addCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (TensorProduct.addCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C 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_inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (Module.toDistribMulAction.{u1, max (max u2 u3) u4} R (TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) => TensorProduct.{u1, u2, max u4 u3} R _inst_1 A (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (TensorProduct.tmul.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) 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(Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a₁ b₁) c₁)) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (TensorProduct.tmul.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a₂ b₂) c₂)) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) => TensorProduct.{u1, u2, max u4 u3} R _inst_1 A (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (TensorProduct.tmul.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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_inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (AddMonoid.toAddZeroClass.{max (max u2 u3) u4} (TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (Module.toDistribMulAction.{u1, max (max u2 u3) u4} R (TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)))) (DistribSMul.toSMulZeroClass.{u1, max (max u2 u3) u4} R (TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) 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+<too large>
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.assoc_aux_1 Algebra.TensorProduct.assoc_aux_1ₓ'. -/
theorem assoc_aux_1 (a₁ a₂ : A) (b₁ b₂ : B) (c₁ c₂ : C) :
(TensorProduct.assoc R A B C) (((a₁ * a₂) ⊗ₜ[R] (b₁ * b₂)) ⊗ₜ[R] (c₁ * c₂)) =
@@ -1136,10 +1025,7 @@ theorem assoc_aux_1 (a₁ a₂ : A) (b₁ b₂ : B) (c₁ c₂ : C) :
#align algebra.tensor_product.assoc_aux_1 Algebra.TensorProduct.assoc_aux_1
/- warning: algebra.tensor_product.assoc_aux_2 -> Algebra.TensorProduct.assoc_aux_2 is a dubious translation:
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- forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {C : Type.{u4}} [_inst_6 : Semiring.{u4} C] [_inst_7 : Algebra.{u1, u4} R C _inst_1 _inst_6] (r : R), Eq.{succ (max u2 u3 u4)} (TensorProduct.{u1, u2, max u3 u4} R _inst_1 A (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (TensorProduct.module.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (coeFn.{max (succ (max (max u2 u3) u4)) (succ (max u2 u3 u4)), max (succ (max (max u2 u3) u4)) (succ (max u2 u3 u4))} (LinearEquiv.{u1, u1, max (max u2 u3) u4, max u2 u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.assoc._proof_1.{u1} R _inst_1) (TensorProduct.assoc._proof_2.{u1} R _inst_1) (TensorProduct.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A 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(TensorProduct.module.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (TensorProduct.addCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A 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u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (TensorProduct.addCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (AddMonoid.toAddZeroClass.{max (max u2 u3) u4} (TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u4} (TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (TensorProduct.addCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C 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_inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (TensorProduct.addCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A 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_inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (TensorProduct.addCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A 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+<too large>
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.assoc_aux_2 Algebra.TensorProduct.assoc_aux_2ₓ'. -/
theorem assoc_aux_2 (r : R) :
(TensorProduct.assoc R A B C) (((algebraMap R A) r ⊗ₜ[R] 1) ⊗ₜ[R] 1) =
@@ -1150,10 +1036,7 @@ theorem assoc_aux_2 (r : R) :
variable (R A B C)
/- warning: algebra.tensor_product.assoc -> Algebra.TensorProduct.assoc is a dubious translation:
-lean 3 declaration is
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+<too large>
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.assoc Algebra.TensorProduct.assocₓ'. -/
/-- The associator for tensor product of R-algebras, as an algebra isomorphism. -/
protected def assoc : (A ⊗[R] B) ⊗[R] C ≃ₐ[R] A ⊗[R] B ⊗[R] C :=
@@ -1166,10 +1049,7 @@ protected def assoc : (A ⊗[R] B) ⊗[R] C ≃ₐ[R] A ⊗[R] B ⊗[R] C :=
variable {R A B C}
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (TensorProduct.addCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C 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_inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (TensorProduct.addCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A 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_inst_6 _inst_7) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a b) c)) (TensorProduct.tmul.{u1, u2, max u4 u3} R _inst_1 A (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) a (TensorProduct.tmul.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) b c))
+<too large>
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.assoc_tmul Algebra.TensorProduct.assoc_tmulₓ'. -/
@[simp]
theorem assoc_tmul (a : A) (b : B) (c : C) :
@@ -1183,10 +1063,7 @@ end
variable {R A B C D}
/- warning: algebra.tensor_product.map -> Algebra.TensorProduct.map is a dubious translation:
-lean 3 declaration is
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Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.map Algebra.TensorProduct.mapₓ'. -/
/-- The tensor product of a pair of algebra morphisms. -/
def map (f : A →ₐ[R] B) (g : C →ₐ[R] D) : A ⊗[R] C →ₐ[R] B ⊗[R] D :=
@@ -1202,10 +1079,7 @@ theorem map_tmul (f : A →ₐ[R] B) (g : C →ₐ[R] D) (a : A) (c : C) : map f
-/
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Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.map_comp_include_left Algebra.TensorProduct.map_comp_includeLeftₓ'. -/
@[simp]
theorem map_comp_includeLeft (f : A →ₐ[R] B) (g : C →ₐ[R] D) :
@@ -1214,10 +1088,7 @@ theorem map_comp_includeLeft (f : A →ₐ[R] B) (g : C →ₐ[R] D) :
#align algebra.tensor_product.map_comp_include_left Algebra.TensorProduct.map_comp_includeLeft
/- warning: algebra.tensor_product.map_comp_include_right -> Algebra.TensorProduct.map_comp_includeRight is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.map_comp_include_right Algebra.TensorProduct.map_comp_includeRightₓ'. -/
@[simp]
theorem map_comp_includeRight (f : A →ₐ[R] B) (g : C →ₐ[R] D) :
@@ -1226,10 +1097,7 @@ theorem map_comp_includeRight (f : A →ₐ[R] B) (g : C →ₐ[R] D) :
#align algebra.tensor_product.map_comp_include_right Algebra.TensorProduct.map_comp_includeRight
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g)))
+<too large>
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.map_range Algebra.TensorProduct.map_rangeₓ'. -/
theorem map_range (f : A →ₐ[R] B) (g : C →ₐ[R] D) :
(map f g).range = (includeLeft.comp f).range ⊔ (includeRight.comp g).range :=
@@ -1244,10 +1112,7 @@ theorem map_range (f : A →ₐ[R] B) (g : C →ₐ[R] D) :
#align algebra.tensor_product.map_range Algebra.TensorProduct.map_range
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Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.congr Algebra.TensorProduct.congrₓ'. -/
/-- Construct an isomorphism between tensor products of R-algebras
from isomorphisms between the tensor factors.
@@ -1257,10 +1122,7 @@ def congr (f : A ≃ₐ[R] B) (g : C ≃ₐ[R] D) : A ⊗[R] C ≃ₐ[R] B ⊗[R
#align algebra.tensor_product.congr Algebra.TensorProduct.congr
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+<too large>
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.congr_apply Algebra.TensorProduct.congr_applyₓ'. -/
@[simp]
theorem congr_apply (f : A ≃ₐ[R] B) (g : C ≃ₐ[R] D) (x) :
@@ -1269,10 +1131,7 @@ theorem congr_apply (f : A ≃ₐ[R] B) (g : C ≃ₐ[R] D) (x) :
#align algebra.tensor_product.congr_apply Algebra.TensorProduct.congr_apply
/- warning: algebra.tensor_product.congr_symm_apply -> Algebra.TensorProduct.congr_symm_apply is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {C : Type.{u4}} [_inst_6 : Semiring.{u4} C] [_inst_7 : Algebra.{u1, u4} R C _inst_1 _inst_6] {D : Type.{u5}} [_inst_8 : Semiring.{u5} D] [_inst_9 : Algebra.{u1, u5} R D _inst_1 _inst_8] (f : AlgEquiv.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (g : AlgEquiv.{u1, u4, u5} R C D _inst_1 _inst_6 _inst_8 _inst_7 _inst_9) (x : TensorProduct.{u1, u3, u5} R _inst_1 B D (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} D (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} D (Semiring.toNonAssocSemiring.{u5} D _inst_8))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) 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_inst_9)))))) (DistribMulAction.toDistribSMul.{u1, max u3 u5} R (TensorProduct.{u1, u3, u5} R _inst_1 B D (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} D (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} D (Semiring.toNonAssocSemiring.{u5} D _inst_8))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u5} R D _inst_1 _inst_8 _inst_9)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u5} (TensorProduct.{u1, u3, u5} R _inst_1 B D (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} D (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} D (Semiring.toNonAssocSemiring.{u5} D 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(Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u4} R _inst_1 A _inst_2 _inst_3 C _inst_6 _inst_7) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u4} R _inst_1 A _inst_2 _inst_3 C _inst_6 _inst_7))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, max u3 u5, max u2 u4, max (max (max u2 u3) u4) u5} R (TensorProduct.{u1, u3, u5} R _inst_1 B D 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B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f)) (AlgHomClass.toAlgHom.{u1, u5, u4, max u4 u5} R D C _inst_1 _inst_8 _inst_6 _inst_9 _inst_7 (AlgEquiv.{u1, u5, u4} R D C _inst_1 _inst_8 _inst_6 _inst_9 _inst_7) (AlgEquivClass.toAlgHomClass.{max u4 u5, u1, u5, u4} (AlgEquiv.{u1, u5, u4} R D C _inst_1 _inst_8 _inst_6 _inst_9 _inst_7) R D C _inst_1 _inst_8 _inst_6 _inst_9 _inst_7 (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u5, u4} R D C _inst_1 _inst_8 _inst_6 _inst_9 _inst_7)) (AlgEquiv.symm.{u1, u4, u5} R C D _inst_1 _inst_6 _inst_8 _inst_7 _inst_9 g))) x)
+<too large>
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.congr_symm_apply Algebra.TensorProduct.congr_symm_applyₓ'. -/
@[simp]
theorem congr_symm_apply (f : A ≃ₐ[R] B) (g : C ≃ₐ[R] D) (x) :
@@ -1310,10 +1169,7 @@ def lmul' : S ⊗[R] S →ₐ[R] S :=
variable {R}
/- warning: algebra.tensor_product.lmul'_to_linear_map -> Algebra.TensorProduct.lmul'_toLinearMap is a dubious translation:
-lean 3 declaration is
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+<too large>
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.lmul'_to_linear_map Algebra.TensorProduct.lmul'_toLinearMapₓ'. -/
theorem lmul'_toLinearMap : (lmul' R : _ →ₐ[R] S).toLinearMap = LinearMap.mul' R S :=
rfl
@@ -1354,10 +1210,7 @@ def productMap : A ⊗[R] B →ₐ[R] S :=
#align algebra.tensor_product.product_map Algebra.TensorProduct.productMap
/- warning: algebra.tensor_product.product_map_apply_tmul -> Algebra.TensorProduct.productMap_apply_tmul is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.product_map_apply_tmul Algebra.TensorProduct.productMap_apply_tmulₓ'. -/
@[simp]
theorem productMap_apply_tmul (a : A) (b : B) : productMap f g (a ⊗ₜ b) = f a * g b :=
@@ -1367,20 +1220,14 @@ theorem productMap_apply_tmul (a : A) (b : B) : productMap f g (a ⊗ₜ b) = f
#align algebra.tensor_product.product_map_apply_tmul Algebra.TensorProduct.productMap_apply_tmul
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Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.product_map_left_apply Algebra.TensorProduct.productMap_left_applyₓ'. -/
theorem productMap_left_apply (a : A) : productMap f g ((includeLeft : A →ₐ[R] A ⊗ B) a) = f a := by
simp
#align algebra.tensor_product.product_map_left_apply Algebra.TensorProduct.productMap_left_apply
/- warning: algebra.tensor_product.product_map_left -> Algebra.TensorProduct.productMap_left is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.product_map_left Algebra.TensorProduct.productMap_leftₓ'. -/
@[simp]
theorem productMap_left : (productMap f g).comp includeLeft = f :=
@@ -1388,19 +1235,13 @@ theorem productMap_left : (productMap f g).comp includeLeft = f :=
#align algebra.tensor_product.product_map_left Algebra.TensorProduct.productMap_left
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(Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6)))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u3, u1, max u1 u2} (AlgHom.{u3, u1, max u1 u2} R B (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) _inst_1 _inst_3 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(Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6)))))) (DistribSMul.toSMulZeroClass.{u3, max u2 u1} R (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (AddMonoid.toAddZeroClass.{max u2 u1} (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (AddCommMonoid.toAddMonoid.{max u2 u1} (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A 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_inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u1} (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6))))) (Module.toDistribMulAction.{u3, max u2 u1} R (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 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_inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (Semiring.toNonAssocSemiring.{max u2 u1} (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6)))) (Algebra.toModule.{u3, max u2 u1} R (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6)))))) (SMulZeroClass.toSMul.{u3, u4} R S (AddMonoid.toZero.{u4} S (AddCommMonoid.toAddMonoid.{u4} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4)))))) (DistribSMul.toSMulZeroClass.{u3, u4} R S (AddMonoid.toAddZeroClass.{u4} S (AddCommMonoid.toAddMonoid.{u4} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4)))))) (DistribMulAction.toDistribSMul.{u3, u4} R S (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u4} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4))))) 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Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.product_map_right_apply Algebra.TensorProduct.productMap_right_applyₓ'. -/
theorem productMap_right_apply (b : B) : productMap f g (includeRight b) = g b := by simp
#align algebra.tensor_product.product_map_right_apply Algebra.TensorProduct.productMap_right_apply
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Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.product_map_right Algebra.TensorProduct.productMap_rightₓ'. -/
@[simp]
theorem productMap_right : (productMap f g).comp includeRight = g :=
@@ -1408,10 +1249,7 @@ theorem productMap_right : (productMap f g).comp includeRight = g :=
#align algebra.tensor_product.product_map_right Algebra.TensorProduct.productMap_right
/- warning: algebra.tensor_product.product_map_range -> Algebra.TensorProduct.productMap_range is a dubious translation:
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- forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} {S : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Semiring.{u3} B] [_inst_4 : CommSemiring.{u4} S] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_6 : Algebra.{u1, u3} R B _inst_1 _inst_3] [_inst_7 : Algebra.{u1, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_4)] (f : AlgHom.{u1, u2, u4} R A S _inst_1 _inst_2 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_5 _inst_7) (g : AlgHom.{u1, u3, u4} R B S _inst_1 _inst_3 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_6 _inst_7), Eq.{succ u4} (Subalgebra.{u1, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_7) (AlgHom.range.{u1, max u2 u3, u4} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_3 _inst_6)) S _inst_1 (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u3} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) (Algebra.TensorProduct.TensorProduct.algebra.{u1, u2, u3} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) (CommSemiring.toSemiring.{u4} S _inst_4) _inst_7 (Algebra.TensorProduct.productMap.{u1, u2, u3, u4} R A B S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f g)) (Sup.sup.{u4} (Subalgebra.{u1, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_7) (SemilatticeSup.toHasSup.{u4} (Subalgebra.{u1, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_7) (Lattice.toSemilatticeSup.{u4} (Subalgebra.{u1, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_7) (ConditionallyCompleteLattice.toLattice.{u4} (Subalgebra.{u1, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{u4} (Subalgebra.{u1, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_7) (Algebra.Subalgebra.completeLattice.{u1, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_7))))) (AlgHom.range.{u1, u2, u4} R A S _inst_1 _inst_2 _inst_5 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_7 f) (AlgHom.range.{u1, u3, u4} R B S _inst_1 _inst_3 _inst_6 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_7 g))
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+<too large>
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.product_map_range Algebra.TensorProduct.productMap_rangeₓ'. -/
theorem productMap_range : (productMap f g).range = f.range ⊔ g.range := by
rw [product_map, AlgHom.range_comp, map_range, map_sup, ← AlgHom.range_comp, ← AlgHom.range_comp,
@@ -1432,10 +1270,7 @@ variable [Algebra R A] [Algebra R A'] [Algebra A A'] [IsScalarTower R A A'] [Alg
variable [Algebra R S] [Algebra A S] [IsScalarTower R A S]
/- warning: algebra.tensor_product.product_left_alg_hom -> Algebra.TensorProduct.productLeftAlgHom is a dubious translation:
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(CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_6))))) (SMulZeroClass.toHasSmul.{u2, u3} A A' (AddZeroClass.toHasZero.{u3} A' (AddMonoid.toAddZeroClass.{u3} A' (AddCommMonoid.toAddMonoid.{u3} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} A A' (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) (AddZeroClass.toHasZero.{u3} A' (AddMonoid.toAddZeroClass.{u3} A' (AddCommMonoid.toAddMonoid.{u3} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} A A' (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (AddZeroClass.toHasZero.{u3} A' (AddMonoid.toAddZeroClass.{u3} A' (AddCommMonoid.toAddMonoid.{u3} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} A A' (CommSemiring.toSemiring.{u2} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_3))) (Algebra.toModule.{u2, u3} A A' _inst_2 _inst_3 _inst_8))))) (SMulZeroClass.toHasSmul.{u1, u3} R A' (AddZeroClass.toHasZero.{u3} A' (AddMonoid.toAddZeroClass.{u3} A' (AddCommMonoid.toAddMonoid.{u3} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A' (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A' (AddMonoid.toAddZeroClass.{u3} A' (AddCommMonoid.toAddMonoid.{u3} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A' (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} A' (AddMonoid.toAddZeroClass.{u3} A' (AddCommMonoid.toAddMonoid.{u3} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_3))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_3 _inst_7)))))] [_inst_10 : Algebra.{u1, u4} R B _inst_1 _inst_4] [_inst_11 : Algebra.{u1, u5} R S _inst_1 (CommSemiring.toSemiring.{u5} S _inst_5)] [_inst_12 : Algebra.{u2, u5} A S _inst_2 (CommSemiring.toSemiring.{u5} S _inst_5)] [_inst_13 : IsScalarTower.{u1, u2, u5} R A S (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_6))))) (SMulZeroClass.toHasSmul.{u2, u5} A S (AddZeroClass.toHasZero.{u5} S (AddMonoid.toAddZeroClass.{u5} S (AddCommMonoid.toAddMonoid.{u5} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} S (Semiring.toNonAssocSemiring.{u5} S (CommSemiring.toSemiring.{u5} S _inst_5))))))) (SMulWithZero.toSmulZeroClass.{u2, u5} A S (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) (AddZeroClass.toHasZero.{u5} S (AddMonoid.toAddZeroClass.{u5} S (AddCommMonoid.toAddMonoid.{u5} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} S (Semiring.toNonAssocSemiring.{u5} S (CommSemiring.toSemiring.{u5} S _inst_5))))))) (MulActionWithZero.toSMulWithZero.{u2, u5} A S (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (AddZeroClass.toHasZero.{u5} S (AddMonoid.toAddZeroClass.{u5} S (AddCommMonoid.toAddMonoid.{u5} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} S (Semiring.toNonAssocSemiring.{u5} S (CommSemiring.toSemiring.{u5} S _inst_5))))))) (Module.toMulActionWithZero.{u2, u5} A S (CommSemiring.toSemiring.{u2} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} S (Semiring.toNonAssocSemiring.{u5} S (CommSemiring.toSemiring.{u5} S _inst_5)))) (Algebra.toModule.{u2, u5} A S _inst_2 (CommSemiring.toSemiring.{u5} S _inst_5) _inst_12))))) (SMulZeroClass.toHasSmul.{u1, u5} R S (AddZeroClass.toHasZero.{u5} S (AddMonoid.toAddZeroClass.{u5} S (AddCommMonoid.toAddMonoid.{u5} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} S (Semiring.toNonAssocSemiring.{u5} S (CommSemiring.toSemiring.{u5} S _inst_5))))))) (SMulWithZero.toSmulZeroClass.{u1, u5} R S (MulZeroClass.toHasZero.{u1} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} S (Semiring.toNonAssocSemiring.{u5} S (CommSemiring.toSemiring.{u5} S _inst_5)))) (Algebra.toModule.{u1, u5} R S _inst_1 (CommSemiring.toSemiring.{u5} S _inst_5) _inst_11)))))], (AlgHom.{u2, u3, u5} A A' S _inst_2 _inst_3 (CommSemiring.toSemiring.{u5} S _inst_5) _inst_8 _inst_12) -> (AlgHom.{u1, u4, u5} R B S _inst_1 _inst_4 (CommSemiring.toSemiring.{u5} S _inst_5) _inst_10 _inst_11) -> (AlgHom.{u2, max u3 u4, u5} A (TensorProduct.{u1, u3, u4} R _inst_1 A' B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_3 _inst_7) (Algebra.toModule.{u1, u4} R B _inst_1 _inst_4 _inst_10)) S _inst_2 (Algebra.TensorProduct.TensorProduct.semiring.{u1, u3, u4} R _inst_1 A' _inst_3 _inst_7 B _inst_4 _inst_10) (CommSemiring.toSemiring.{u5} S _inst_5) (Algebra.TensorProduct.leftAlgebra.{u1, u3, u4, u2} R _inst_1 A' _inst_3 _inst_7 B _inst_4 _inst_10 A _inst_2 _inst_6 _inst_8 _inst_9) _inst_12)
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- forall {R : Type.{u1}} {A : Type.{u2}} {A' : Type.{u3}} {B : Type.{u4}} {S : Type.{u5}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Semiring.{u3} A'] [_inst_4 : Semiring.{u4} B] [_inst_5 : CommSemiring.{u5} S] [_inst_6 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] [_inst_7 : Algebra.{u1, u3} R A' _inst_1 _inst_3] [_inst_8 : Algebra.{u2, u3} A A' _inst_2 _inst_3] [_inst_9 : IsScalarTower.{u1, u2, u3} R A A' (Algebra.toSMul.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_6) (Algebra.toSMul.{u2, u3} A A' _inst_2 _inst_3 _inst_8) (Algebra.toSMul.{u1, u3} R A' _inst_1 _inst_3 _inst_7)] [_inst_10 : Algebra.{u1, u4} R B _inst_1 _inst_4] [_inst_11 : Algebra.{u1, u5} R S _inst_1 (CommSemiring.toSemiring.{u5} S _inst_5)] [_inst_12 : Algebra.{u2, u5} A S _inst_2 (CommSemiring.toSemiring.{u5} S _inst_5)] [_inst_13 : IsScalarTower.{u1, u2, u5} R A S (Algebra.toSMul.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_6) (Algebra.toSMul.{u2, u5} A S _inst_2 (CommSemiring.toSemiring.{u5} S _inst_5) _inst_12) (Algebra.toSMul.{u1, u5} R S _inst_1 (CommSemiring.toSemiring.{u5} S _inst_5) _inst_11)], (AlgHom.{u2, u3, u5} A A' S _inst_2 _inst_3 (CommSemiring.toSemiring.{u5} S _inst_5) _inst_8 _inst_12) -> (AlgHom.{u1, u4, u5} R B S _inst_1 _inst_4 (CommSemiring.toSemiring.{u5} S _inst_5) _inst_10 _inst_11) -> (AlgHom.{u2, max u4 u3, u5} A (TensorProduct.{u1, u3, u4} R _inst_1 A' B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_3 _inst_7) (Algebra.toModule.{u1, u4} R B _inst_1 _inst_4 _inst_10)) S _inst_2 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u3, u4} R _inst_1 A' _inst_3 _inst_7 B _inst_4 _inst_10) (CommSemiring.toSemiring.{u5} S _inst_5) (Algebra.TensorProduct.leftAlgebra.{u1, u3, u4, u2} R _inst_1 A' _inst_3 _inst_7 B _inst_4 _inst_10 A _inst_2 _inst_6 _inst_8 _inst_9) _inst_12)
+<too large>
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.product_left_alg_hom Algebra.TensorProduct.productLeftAlgHomₓ'. -/
/-- If `A`, `B` are `R`-algebras, `A'` is an `A`-algebra, then the product map of `f : A' →ₐ[A] S`
and `g : B →ₐ[R] S` is an `A`-algebra homomorphism. -/
@@ -1471,10 +1306,7 @@ noncomputable def basisAux : R ⊗[k] M ≃ₗ[k] ι →₀ R :=
variable {R}
/- warning: algebra.tensor_product.basis_aux_tmul -> Algebra.TensorProduct.basisAux_tmul is a dubious translation:
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_inst_1)) (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (Algebra.TensorProduct.basisAux._proof_1.{u_1} k _inst_1) (Algebra.TensorProduct.basisAux._proof_2.{u_1} k _inst_1) (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))))) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.module.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3))) (fun (_x : LinearEquiv.{u_1, u_1, max u_2 u_3, max u_4 u_2} k k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (Algebra.TensorProduct.basisAux._proof_1.{u_1} k _inst_1) 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(CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) => Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) _x) (SMulHomClass.toFunLike.{max (max u_1 u_4) u_2, u_3, max u_1 u_4, max u_1 u_2} (LinearEquiv.{u_3, u_3, max u_4 u_1, max u_1 u_2} k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_2, u_1, u_3} ι R k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3))) k (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (SMulZeroClass.toSMul.{u_3, max u_1 u_4} k (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (AddMonoid.toZero.{max u_1 u_4} (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (AddCommMonoid.toAddMonoid.{max u_1 u_4} (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5))) (DistribSMul.toSMulZeroClass.{u_3, max u_1 u_4} k (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (AddMonoid.toAddZeroClass.{max u_1 u_4} (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (AddCommMonoid.toAddMonoid.{max u_1 u_4} (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5))) (DistribMulAction.toDistribSMul.{u_3, max u_1 u_4} k (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (MonoidWithZero.toMonoid.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (AddCommMonoid.toAddMonoid.{max u_1 u_4} (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5)) (Module.toDistribMulAction.{u_3, max u_1 u_4} k (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5))))) (SMulZeroClass.toSMul.{u_3, max u_1 u_2} k (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (AddMonoid.toZero.{max u_1 u_2} (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2))))))) (DistribSMul.toSMulZeroClass.{u_3, max u_1 u_2} k (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (AddMonoid.toAddZeroClass.{max u_1 u_2} (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2))))))) (DistribMulAction.toDistribSMul.{u_3, max u_1 u_2} k (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (MonoidWithZero.toMonoid.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))))) (Module.toDistribMulAction.{u_3, max u_1 u_2} k (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2))))) (Finsupp.module.{u_2, u_1, u_3} ι R k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u_1 u_4) u_2, u_3, max u_1 u_4, max u_1 u_2} (LinearEquiv.{u_3, u_3, max u_4 u_1, max u_1 u_2} k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_2, u_1, u_3} ι R k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3))) k (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (MonoidWithZero.toMonoid.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (AddCommMonoid.toAddMonoid.{max u_1 u_4} (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5)) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))))) (Module.toDistribMulAction.{u_3, max u_1 u_4} k (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5)) (Module.toDistribMulAction.{u_3, max u_1 u_2} k (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2))))) (Finsupp.module.{u_2, u_1, u_3} ι R k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3))) (SemilinearMapClass.distribMulActionHomClass.{u_3, max u_1 u_4, max u_1 u_2, max (max u_1 u_4) u_2} k (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (LinearEquiv.{u_3, u_3, max u_4 u_1, max u_1 u_2} k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_2, u_1, u_3} ι R k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3))) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_2, u_1, u_3} ι R k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3)) (SemilinearEquivClass.instSemilinearMapClass.{u_3, u_3, max u_1 u_4, max u_1 u_2, max (max u_1 u_4) u_2} k k (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (LinearEquiv.{u_3, u_3, max u_4 u_1, max u_1 u_2} k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_2, u_1, u_3} ι R k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3))) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_2, u_1, u_3} ι R k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3)) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u_3, u_3, max u_1 u_4, max u_1 u_2} k k (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) 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(Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_2, u_1, u_3} ι R k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3)) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))))) (Algebra.TensorProduct.basisAux.{u_6, u_3, u_1, u_4, u_2} k _inst_1 R _inst_2 _inst_3 M _inst_4 _inst_5 ι b) (TensorProduct.tmul.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5 r m)) (HSMul.hSMul.{u_1, max u_1 u_2, max u_1 u_2} R (Finsupp.{u_2, u_1} ι R (MulZeroOneClass.toZero.{u_1} R (NonAssocSemiring.toMulZeroOneClass.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))))) (Finsupp.{u_2, u_1} ι R (MulZeroOneClass.toZero.{u_1} R (NonAssocSemiring.toMulZeroOneClass.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))))) (instHSMul.{u_1, max u_1 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u_3 u_1, u_3, u_1} (RingHom.{u_3, u_1} k R (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) k R (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (RingHom.instRingHomClassRingHom.{u_3, u_1} k R (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))))) 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))) _inst_5 (Finsupp.module.{u_2, u_3, u_3} ι k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Semiring.toModule.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) k M (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (SMulZeroClass.toSMul.{u_3, u_4} k M (AddMonoid.toZero.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M _inst_4)) (DistribSMul.toSMulZeroClass.{u_3, u_4} k M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M _inst_4)) (DistribMulAction.toDistribSMul.{u_3, u_4} k M (MonoidWithZero.toMonoid.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (AddCommMonoid.toAddMonoid.{u_4} M _inst_4) (Module.toDistribMulAction.{u_3, u_4} k M (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) _inst_4 _inst_5)))) (SMulZeroClass.toSMul.{u_3, max u_3 u_2} k (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (AddMonoid.toZero.{max u_3 u_2} (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (AddCommMonoid.toAddMonoid.{max u_3 u_2} (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u_3, max u_3 u_2} k (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (AddMonoid.toAddZeroClass.{max u_3 u_2} (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (AddCommMonoid.toAddMonoid.{max u_3 u_2} (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))))) (DistribMulAction.toDistribSMul.{u_3, max u_3 u_2} k (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (MonoidWithZero.toMonoid.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (AddCommMonoid.toAddMonoid.{max u_3 u_2} (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))))) (Module.toDistribMulAction.{u_3, max u_3 u_2} k (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))) (Finsupp.module.{u_2, u_3, u_3} ι k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Semiring.toModule.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u_3 u_4) u_2, u_3, u_4, max u_3 u_2} (LinearEquiv.{u_3, u_3, u_4, max u_3 u_2} k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) M (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) _inst_4 (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))) _inst_5 (Finsupp.module.{u_2, u_3, u_3} ι k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Semiring.toModule.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) k M (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (MonoidWithZero.toMonoid.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (AddCommMonoid.toAddMonoid.{u_4} M _inst_4) (AddCommMonoid.toAddMonoid.{max u_3 u_2} (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))))) (Module.toDistribMulAction.{u_3, u_4} k M (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) _inst_4 _inst_5) (Module.toDistribMulAction.{u_3, max u_3 u_2} k (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))) (Finsupp.module.{u_2, u_3, u_3} ι k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Semiring.toModule.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u_3, u_4, max u_3 u_2, max (max u_3 u_4) u_2} k M (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (LinearEquiv.{u_3, u_3, u_4, max u_3 u_2} k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) M (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) _inst_4 (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))) _inst_5 (Finsupp.module.{u_2, u_3, u_3} ι k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Semiring.toModule.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) _inst_4 (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))) _inst_5 (Finsupp.module.{u_2, u_3, u_3} ι k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Semiring.toModule.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (SemilinearEquivClass.instSemilinearMapClass.{u_3, u_3, u_4, max u_3 u_2, max (max u_3 u_4) u_2} k k M (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (LinearEquiv.{u_3, u_3, u_4, max u_3 u_2} k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) M (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) _inst_4 (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))) _inst_5 (Finsupp.module.{u_2, u_3, u_3} ι k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Semiring.toModule.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) _inst_4 (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))) _inst_5 (Finsupp.module.{u_2, u_3, u_3} ι k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Semiring.toModule.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u_3, u_3, u_4, max u_3 u_2} k k M (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) _inst_4 (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))) _inst_5 (Finsupp.module.{u_2, u_3, u_3} ι k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Semiring.toModule.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))))) (Basis.repr.{u_2, u_3, u_4} ι k M (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) _inst_4 _inst_5 b) m)))
+<too large>
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.basis_aux_tmul Algebra.TensorProduct.basisAux_tmulₓ'. -/
theorem basisAux_tmul (r : R) (m : M) :
basisAux R b (r ⊗ₜ m) = r • Finsupp.mapRange (algebraMap k R) (map_zero _) (b.repr m) :=
@@ -1484,10 +1316,7 @@ theorem basisAux_tmul (r : R) (m : M) :
#align algebra.tensor_product.basis_aux_tmul Algebra.TensorProduct.basisAux_tmul
/- warning: algebra.tensor_product.basis_aux_map_smul -> Algebra.TensorProduct.basisAux_map_smul is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u_1}} [_inst_1 : CommRing.{u_1} k] {R : Type.{u_2}} [_inst_2 : Ring.{u_2} R] [_inst_3 : Algebra.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2)] {M : Type.{u_3}} [_inst_4 : AddCommMonoid.{u_3} M] [_inst_5 : Module.{u_1, u_3} k M (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) _inst_4] {ι : Type.{u_4}} (b : Basis.{u_4, u_1, u_3} ι k M (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) _inst_4 _inst_5) (r : R) (x : TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5), Eq.{max (succ u_4) (succ u_2)} (Finsupp.{u_4, u_2} ι R (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))))) (coeFn.{max (succ (max u_2 u_3)) (succ (max u_4 u_2)), max (succ (max u_2 u_3)) (succ (max u_4 u_2))} (LinearEquiv.{u_1, u_1, max u_2 u_3, max u_4 u_2} k k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (Algebra.TensorProduct.basisAux._proof_1.{u_1} k _inst_1) (Algebra.TensorProduct.basisAux._proof_2.{u_1} k _inst_1) (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))))) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.module.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3))) (fun (_x : LinearEquiv.{u_1, u_1, max u_2 u_3, max u_4 u_2} k k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (Algebra.TensorProduct.basisAux._proof_1.{u_1} k _inst_1) (Algebra.TensorProduct.basisAux._proof_2.{u_1} k _inst_1) (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))))) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.module.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3))) => (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) -> (Finsupp.{u_4, u_2} ι R (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))))) (LinearEquiv.hasCoeToFun.{u_1, u_1, max u_2 u_3, max u_4 u_2} k k (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))))) (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.module.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) 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(AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (TensorProduct.leftHasSMul.{u_1, u_2, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R (Ring.toMonoid.{u_2} R _inst_2) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5 (Module.toDistribMulAction.{u_2, u_2} R R (Ring.toSemiring.{u_2} R _inst_2) (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Semiring.toModule.{u_2} R (Ring.toSemiring.{u_2} R _inst_2))) (Algebra.to_smulCommClass.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3)) r x)) (SMul.smul.{u_2, max u_4 u_2} R (Finsupp.{u_4, u_2} ι R (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))))) (SMulZeroClass.toHasSmul.{u_2, max u_4 u_2} R (Finsupp.{u_4, u_2} ι R (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))))) (Finsupp.zero.{u_4, u_2} ι R (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))))) (Finsupp.smulZeroClass.{u_4, u_2, u_2} ι R R (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (SMulWithZero.toSmulZeroClass.{u_2, u_2} R R (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (MulZeroClass.toSMulWithZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))))))) r (coeFn.{max (succ (max u_2 u_3)) (succ (max u_4 u_2)), max (succ (max u_2 u_3)) (succ (max u_4 u_2))} (LinearEquiv.{u_1, u_1, max u_2 u_3, max u_4 u_2} k k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (Algebra.TensorProduct.basisAux._proof_1.{u_1} k _inst_1) (Algebra.TensorProduct.basisAux._proof_2.{u_1} k _inst_1) (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 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(NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (fun (_x : TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) => Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) _x) (SMulHomClass.toFunLike.{max (max u_2 u_3) u_4, u_1, max u_2 u_3, max u_2 u_4} (LinearEquiv.{u_1, u_1, max u_3 u_2, max u_2 u_4} k k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3))) k (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (SMulZeroClass.toSMul.{u_1, max u_2 u_3} k (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (AddMonoid.toZero.{max u_2 u_3} (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5))) (DistribSMul.toSMulZeroClass.{u_1, max u_2 u_3} k (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (AddMonoid.toAddZeroClass.{max u_2 u_3} (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5))) (DistribMulAction.toDistribSMul.{u_1, max u_2 u_3} k (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (MonoidWithZero.toMonoid.{u_1} k (Semiring.toMonoidWithZero.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5)) (Module.toDistribMulAction.{u_1, max u_2 u_3} k (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5))))) (SMulZeroClass.toSMul.{u_1, max u_2 u_4} k (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (AddMonoid.toZero.{max u_2 u_4} (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (AddCommMonoid.toAddMonoid.{max u_2 u_4} (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))))) (DistribSMul.toSMulZeroClass.{u_1, max u_2 u_4} k (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (AddMonoid.toAddZeroClass.{max u_2 u_4} (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (AddCommMonoid.toAddMonoid.{max u_2 u_4} (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))))) (DistribMulAction.toDistribSMul.{u_1, max u_2 u_4} k (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (MonoidWithZero.toMonoid.{u_1} k (Semiring.toMonoidWithZero.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (AddCommMonoid.toAddMonoid.{max u_2 u_4} (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))))) (Module.toDistribMulAction.{u_1, max u_2 u_4} k (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (Finsupp.module.{u_4, u_2, u_1} ι R k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u_2 u_3) u_4, u_1, max u_2 u_3, max u_2 u_4} (LinearEquiv.{u_1, u_1, max u_3 u_2, max u_2 u_4} k k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3))) k (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (MonoidWithZero.toMonoid.{u_1} k (Semiring.toMonoidWithZero.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5)) (AddCommMonoid.toAddMonoid.{max u_2 u_4} (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))))) (Module.toDistribMulAction.{u_1, max u_2 u_3} k (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5)) (Module.toDistribMulAction.{u_1, max u_2 u_4} k (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (Finsupp.module.{u_4, u_2, u_1} ι R k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3))) (SemilinearMapClass.distribMulActionHomClass.{u_1, max u_2 u_3, max u_2 u_4, max (max u_2 u_3) u_4} k (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (LinearEquiv.{u_1, u_1, max u_3 u_2, max u_2 u_4} k k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3))) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3)) (SemilinearEquivClass.instSemilinearMapClass.{u_1, u_1, max u_2 u_3, max u_2 u_4, max (max u_2 u_3) u_4} k k (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (LinearEquiv.{u_1, u_1, max u_3 u_2, max u_2 u_4} k k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3))) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3)) (RingHom.id.{u_1} k 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_inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) => Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) _x) (SMulHomClass.toFunLike.{max (max u_2 u_3) u_4, u_1, max u_2 u_3, max u_2 u_4} (LinearEquiv.{u_1, u_1, max u_3 u_2, max u_2 u_4} k k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3))) k (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (SMulZeroClass.toSMul.{u_1, max u_2 u_3} k (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (AddMonoid.toZero.{max u_2 u_3} (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5))) (DistribSMul.toSMulZeroClass.{u_1, max u_2 u_3} k (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (AddMonoid.toAddZeroClass.{max u_2 u_3} (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5))) (DistribMulAction.toDistribSMul.{u_1, max u_2 u_3} k (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (MonoidWithZero.toMonoid.{u_1} k (Semiring.toMonoidWithZero.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5)) (Module.toDistribMulAction.{u_1, max u_2 u_3} k (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5))))) (SMulZeroClass.toSMul.{u_1, max u_2 u_4} k (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (AddMonoid.toZero.{max u_2 u_4} (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (AddCommMonoid.toAddMonoid.{max u_2 u_4} (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))))) (DistribSMul.toSMulZeroClass.{u_1, max u_2 u_4} k (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (AddMonoid.toAddZeroClass.{max u_2 u_4} (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (AddCommMonoid.toAddMonoid.{max u_2 u_4} (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))))) (DistribMulAction.toDistribSMul.{u_1, max u_2 u_4} k (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (MonoidWithZero.toMonoid.{u_1} k (Semiring.toMonoidWithZero.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (AddCommMonoid.toAddMonoid.{max u_2 u_4} (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))))) (Module.toDistribMulAction.{u_1, max u_2 u_4} k (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (Finsupp.module.{u_4, u_2, u_1} ι R k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u_2 u_3) u_4, u_1, max u_2 u_3, max u_2 u_4} (LinearEquiv.{u_1, u_1, max u_3 u_2, max u_2 u_4} k k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3))) k (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (MonoidWithZero.toMonoid.{u_1} k (Semiring.toMonoidWithZero.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5)) (AddCommMonoid.toAddMonoid.{max u_2 u_4} (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))))) (Module.toDistribMulAction.{u_1, max u_2 u_3} k (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5)) (Module.toDistribMulAction.{u_1, max u_2 u_4} k (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (Finsupp.module.{u_4, u_2, u_1} ι R k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3))) (SemilinearMapClass.distribMulActionHomClass.{u_1, max u_2 u_3, max u_2 u_4, max (max u_2 u_3) u_4} k (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (LinearEquiv.{u_1, u_1, max u_3 u_2, max u_2 u_4} k k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3))) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3)) (SemilinearEquivClass.instSemilinearMapClass.{u_1, u_1, max u_2 u_3, max u_2 u_4, max (max u_2 u_3) u_4} k k (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (LinearEquiv.{u_1, u_1, max u_3 u_2, max u_2 u_4} k k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3))) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3)) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u_1, u_1, max u_2 u_3, max u_2 u_4} k k (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3)) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))))))) (Algebra.TensorProduct.basisAux.{u_7, u_1, u_2, u_3, u_4} k _inst_1 R _inst_2 _inst_3 M _inst_4 _inst_5 ι b) x))
+<too large>
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.basis_aux_map_smul Algebra.TensorProduct.basisAux_map_smulₓ'. -/
theorem basisAux_map_smul (r : R) (x : R ⊗[k] M) : basisAux R b (r • x) = r • basisAux R b x :=
TensorProduct.induction_on x (by simp)
@@ -1511,10 +1340,7 @@ noncomputable def basis : Basis ι R (R ⊗[k] M)
variable {R}
/- warning: algebra.tensor_product.basis_repr_tmul -> Algebra.TensorProduct.basis_repr_tmul is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u_1}} [_inst_1 : CommRing.{u_1} k] {R : Type.{u_2}} [_inst_2 : Ring.{u_2} R] [_inst_3 : Algebra.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2)] {M : Type.{u_3}} [_inst_4 : AddCommMonoid.{u_3} M] [_inst_5 : Module.{u_1, u_3} k M (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) _inst_4] {ι : Type.{u_4}} (b : Basis.{u_4, u_1, u_3} ι k M (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) _inst_4 _inst_5) (r : R) (m : M), Eq.{max (succ u_4) (succ u_2)} (Finsupp.{u_4, u_2} ι R (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))))) (coeFn.{max (succ (max u_2 u_3)) (succ (max u_4 u_2)), max (succ (max u_2 u_3)) (succ (max u_4 u_2))} (LinearEquiv.{u_2, u_2, max u_2 u_3, max u_4 u_2} R R (Ring.toSemiring.{u_2} R _inst_2) (Ring.toSemiring.{u_2} R _inst_2) 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_inst_5 (Semiring.toModule.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)) (Algebra.TensorProduct.basis._proof_1.{u_1, u_2} k _inst_1 R _inst_2 _inst_3)) (Finsupp.module.{u_4, u_2, u_2} ι R R (Ring.toSemiring.{u_2} R _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (Semiring.toModule.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (fun (_x : LinearEquiv.{u_2, u_2, max u_2 u_3, max u_4 u_2} R R (Ring.toSemiring.{u_2} R _inst_2) (Ring.toSemiring.{u_2} R _inst_2) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R _inst_2))) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R _inst_2))) (RingHomInvPair.ids.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)) (RingHomInvPair.ids.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)) (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))))) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R 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_inst_2)))) (Semiring.toModule.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) => (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) -> (Finsupp.{u_4, u_2} ι R (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R _inst_2))))))) (LinearEquiv.hasCoeToFun.{u_2, u_2, max u_2 u_3, max u_4 u_2} R R (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R _inst_2))))) (TensorProduct.leftModule.{u_1, u_2, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R (Ring.toSemiring.{u_2} R _inst_2) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5 (Semiring.toModule.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)) (Algebra.TensorProduct.basis._proof_1.{u_1, u_2} k _inst_1 R _inst_2 _inst_3)) (Finsupp.module.{u_4, u_2, u_2} ι R R (Ring.toSemiring.{u_2} R _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (Semiring.toModule.{u_2} R 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(CommRing.toRing.{u_1} k _inst_1)))))))) (LinearEquiv.hasCoeToFun.{u_1, u_1, u_3, max u_4 u_1} k k M (Finsupp.{u_4, u_1} ι k (MulZeroClass.toHasZero.{u_1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u_1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1))))))) (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) _inst_4 (Finsupp.addCommMonoid.{u_4, u_1} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))))) _inst_5 (Finsupp.module.{u_4, u_1, u_1} ι k k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1))))) (Semiring.toModule.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (RingHomInvPair.ids.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1))) (RingHomInvPair.ids.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (Basis.repr.{u_4, u_1, u_3} ι k M (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) _inst_4 _inst_5 b) m)))
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(Ring.toSemiring.{u_1} R _inst_2))) (RingHomInvPair.ids.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (RingHomInvPair.ids.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))))) (TensorProduct.leftModule.{u_3, u_1, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R (Ring.toSemiring.{u_1} R _inst_2) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5 (Semiring.toModule.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (Algebra.to_smulCommClass.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3)) (Finsupp.module.{u_2, u_1, u_1} ι R R (Ring.toSemiring.{u_1} R _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Semiring.toModule.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (fun (_x : TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) => Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) _x) (SMulHomClass.toFunLike.{max (max u_1 u_4) u_2, u_1, max u_1 u_4, max u_1 u_2} (LinearEquiv.{u_1, u_1, max u_1 u_4, max u_1 u_2} R R (Ring.toSemiring.{u_1} R _inst_2) (Ring.toSemiring.{u_1} R _inst_2) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (RingHomInvPair.ids.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (RingHomInvPair.ids.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))))) (TensorProduct.leftModule.{u_3, u_1, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R (Ring.toSemiring.{u_1} R _inst_2) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5 (Semiring.toModule.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (Algebra.to_smulCommClass.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3)) (Finsupp.module.{u_2, u_1, u_1} ι R R (Ring.toSemiring.{u_1} R _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Semiring.toModule.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) R (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (SMulZeroClass.toSMul.{u_1, max u_1 u_4} R (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (AddMonoid.toZero.{max u_1 u_4} (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (AddCommMonoid.toAddMonoid.{max u_1 u_4} (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5))) (DistribSMul.toSMulZeroClass.{u_1, max u_1 u_4} R (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (AddMonoid.toAddZeroClass.{max u_1 u_4} (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (AddCommMonoid.toAddMonoid.{max u_1 u_4} (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5))) (DistribMulAction.toDistribSMul.{u_1, max u_1 u_4} R (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (AddCommMonoid.toAddMonoid.{max u_1 u_4} (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5)) (Module.toDistribMulAction.{u_1, max u_1 u_4} R (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Ring.toSemiring.{u_1} R _inst_2) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (TensorProduct.leftModule.{u_3, u_1, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R (Ring.toSemiring.{u_1} R _inst_2) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5 (Semiring.toModule.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (Algebra.to_smulCommClass.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3)))))) (SMulZeroClass.toSMul.{u_1, max u_1 u_2} R (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (AddMonoid.toZero.{max u_1 u_2} (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))))))) (DistribSMul.toSMulZeroClass.{u_1, max u_1 u_2} R (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (AddMonoid.toAddZeroClass.{max u_1 u_2} (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))))))) (DistribMulAction.toDistribSMul.{u_1, max u_1 u_2} R (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))))) (Module.toDistribMulAction.{u_1, max u_1 u_2} R (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Ring.toSemiring.{u_1} R _inst_2) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))))) (Finsupp.module.{u_2, u_1, u_1} ι R R (Ring.toSemiring.{u_1} R _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Semiring.toModule.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u_1 u_4) u_2, u_1, max u_1 u_4, max u_1 u_2} (LinearEquiv.{u_1, u_1, max u_1 u_4, max u_1 u_2} R R (Ring.toSemiring.{u_1} R _inst_2) (Ring.toSemiring.{u_1} R _inst_2) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (RingHomInvPair.ids.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (RingHomInvPair.ids.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))))) (TensorProduct.leftModule.{u_3, u_1, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R (Ring.toSemiring.{u_1} R _inst_2) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5 (Semiring.toModule.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (Algebra.to_smulCommClass.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3)) (Finsupp.module.{u_2, u_1, u_1} ι R R (Ring.toSemiring.{u_1} R _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Semiring.toModule.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) R (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (AddCommMonoid.toAddMonoid.{max u_1 u_4} (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5)) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))))) (Module.toDistribMulAction.{u_1, max u_1 u_4} R (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Ring.toSemiring.{u_1} R _inst_2) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (TensorProduct.leftModule.{u_3, u_1, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R (Ring.toSemiring.{u_1} R _inst_2) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5 (Semiring.toModule.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (Algebra.to_smulCommClass.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3))) (Module.toDistribMulAction.{u_1, max u_1 u_2} R (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Ring.toSemiring.{u_1} R _inst_2) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))))) (Finsupp.module.{u_2, u_1, u_1} ι R R (Ring.toSemiring.{u_1} R _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Semiring.toModule.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (SemilinearMapClass.distribMulActionHomClass.{u_1, max u_1 u_4, max u_1 u_2, max (max u_1 u_4) u_2} R (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (LinearEquiv.{u_1, u_1, max u_1 u_4, max u_1 u_2} R R (Ring.toSemiring.{u_1} R _inst_2) (Ring.toSemiring.{u_1} R _inst_2) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (RingHomInvPair.ids.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (RingHomInvPair.ids.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))))) (TensorProduct.leftModule.{u_3, u_1, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R (Ring.toSemiring.{u_1} R _inst_2) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5 (Semiring.toModule.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (Algebra.to_smulCommClass.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3)) (Finsupp.module.{u_2, u_1, u_1} ι R R (Ring.toSemiring.{u_1} R _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Semiring.toModule.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Ring.toSemiring.{u_1} R _inst_2) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))))) (TensorProduct.leftModule.{u_3, u_1, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R (Ring.toSemiring.{u_1} R _inst_2) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5 (Semiring.toModule.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (Algebra.to_smulCommClass.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3)) (Finsupp.module.{u_2, u_1, u_1} ι R R (Ring.toSemiring.{u_1} R _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Semiring.toModule.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (SemilinearEquivClass.instSemilinearMapClass.{u_1, u_1, max u_1 u_4, max u_1 u_2, max (max u_1 u_4) u_2} R R (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (LinearEquiv.{u_1, u_1, max u_1 u_4, max u_1 u_2} R R (Ring.toSemiring.{u_1} R _inst_2) (Ring.toSemiring.{u_1} R _inst_2) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (RingHomInvPair.ids.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (RingHomInvPair.ids.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))))) (TensorProduct.leftModule.{u_3, u_1, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R (Ring.toSemiring.{u_1} R _inst_2) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5 (Semiring.toModule.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (Algebra.to_smulCommClass.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3)) (Finsupp.module.{u_2, u_1, u_1} ι R R (Ring.toSemiring.{u_1} R _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Semiring.toModule.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Ring.toSemiring.{u_1} R _inst_2) (Ring.toSemiring.{u_1} R _inst_2) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))))) (TensorProduct.leftModule.{u_3, u_1, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R (Ring.toSemiring.{u_1} R _inst_2) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5 (Semiring.toModule.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (Algebra.to_smulCommClass.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3)) (Finsupp.module.{u_2, u_1, u_1} ι R R (Ring.toSemiring.{u_1} R _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Semiring.toModule.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (RingHomInvPair.ids.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (RingHomInvPair.ids.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u_1, u_1, max u_1 u_4, max u_1 u_2} R R (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Ring.toSemiring.{u_1} R _inst_2) (Ring.toSemiring.{u_1} R _inst_2) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))))) (TensorProduct.leftModule.{u_3, u_1, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R (Ring.toSemiring.{u_1} R _inst_2) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5 (Semiring.toModule.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (Algebra.to_smulCommClass.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3)) (Finsupp.module.{u_2, u_1, u_1} ι R R (Ring.toSemiring.{u_1} R _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Semiring.toModule.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (RingHomInvPair.ids.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (RingHomInvPair.ids.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))))))) (Basis.repr.{u_2, u_1, max u_1 u_4} ι R (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Ring.toSemiring.{u_1} R _inst_2) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (TensorProduct.leftModule.{u_3, u_1, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R (Ring.toSemiring.{u_1} R _inst_2) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5 (Semiring.toModule.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (Algebra.to_smulCommClass.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3)) (Algebra.TensorProduct.basis.{u_6, u_3, u_1, u_4, u_2} k _inst_1 R _inst_2 _inst_3 M _inst_4 _inst_5 ι b)) (TensorProduct.tmul.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5 r m)) (HSMul.hSMul.{u_1, max u_1 u_2, max u_1 u_2} R (Finsupp.{u_2, u_1} ι R (MulZeroOneClass.toZero.{u_1} R (NonAssocSemiring.toMulZeroOneClass.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))))) (Finsupp.{u_2, u_1} ι R (MulZeroOneClass.toZero.{u_1} R (NonAssocSemiring.toMulZeroOneClass.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))))) (instHSMul.{u_1, max u_1 u_2} R (Finsupp.{u_2, u_1} ι R (MulZeroOneClass.toZero.{u_1} R (NonAssocSemiring.toMulZeroOneClass.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))))) (SMulZeroClass.toSMul.{u_1, max u_1 u_2} R (Finsupp.{u_2, u_1} ι R (MulZeroOneClass.toZero.{u_1} R (NonAssocSemiring.toMulZeroOneClass.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))))) (Finsupp.zero.{u_2, u_1} ι R (MulZeroOneClass.toZero.{u_1} R (NonAssocSemiring.toMulZeroOneClass.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))))) (Finsupp.smulZeroClass.{u_2, u_1, u_1} ι R R (MulZeroOneClass.toZero.{u_1} R (NonAssocSemiring.toMulZeroOneClass.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (SMulWithZero.toSMulZeroClass.{u_1, u_1} R R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (MulZeroOneClass.toZero.{u_1} R (NonAssocSemiring.toMulZeroOneClass.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (MulZeroClass.toSMulWithZero.{u_1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2))))))))) r (Finsupp.mapRange.{u_2, u_3, u_1} ι k R (MulZeroOneClass.toZero.{u_3} k (NonAssocSemiring.toMulZeroOneClass.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (MulZeroOneClass.toZero.{u_1} R (NonAssocSemiring.toMulZeroOneClass.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (FunLike.coe.{max (succ u_3) (succ u_1), succ u_3, succ u_1} (RingHom.{u_3, u_1} k R (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) k (fun (_x : k) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : k) => R) _x) (MulHomClass.toFunLike.{max u_3 u_1, u_3, u_1} (RingHom.{u_3, u_1} k R (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) k R (NonUnitalNonAssocSemiring.toMul.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u_3 u_1, u_3, u_1} (RingHom.{u_3, u_1} k R (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) k R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u_3 u_1, u_3, u_1} (RingHom.{u_3, u_1} k R (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) k R (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (RingHom.instRingHomClassRingHom.{u_3, u_1} k R (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))))) (algebraMap.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3)) (map_zero.{u_1, u_3, max u_3 u_1} k R (RingHom.{u_3, u_1} k R (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (MulZeroOneClass.toZero.{u_3} k (NonAssocSemiring.toMulZeroOneClass.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (MulZeroOneClass.toZero.{u_1} R (NonAssocSemiring.toMulZeroOneClass.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (MonoidWithZeroHomClass.toZeroHomClass.{max u_3 u_1, u_3, u_1} (RingHom.{u_3, u_1} k R (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) k R (NonAssocSemiring.toMulZeroOneClass.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (RingHomClass.toMonoidWithZeroHomClass.{max u_3 u_1, u_3, u_1} (RingHom.{u_3, u_1} k R (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) k R (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (RingHom.instRingHomClassRingHom.{u_3, u_1} k R (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))))) (algebraMap.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3)) (FunLike.coe.{max (max (succ u_3) (succ u_4)) (succ u_2), succ u_4, max (succ u_3) (succ u_2)} (LinearEquiv.{u_3, u_3, u_4, max u_3 u_2} k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) M (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) _inst_4 (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))) _inst_5 (Finsupp.module.{u_2, u_3, u_3} ι k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Semiring.toModule.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : M) => Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) _x) (SMulHomClass.toFunLike.{max (max u_3 u_4) u_2, u_3, u_4, max u_3 u_2} (LinearEquiv.{u_3, u_3, u_4, max u_3 u_2} k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) M (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) _inst_4 (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))) _inst_5 (Finsupp.module.{u_2, u_3, u_3} ι k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Semiring.toModule.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) k M (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (SMulZeroClass.toSMul.{u_3, u_4} k M (AddMonoid.toZero.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M _inst_4)) (DistribSMul.toSMulZeroClass.{u_3, u_4} k M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M _inst_4)) (DistribMulAction.toDistribSMul.{u_3, u_4} k M (MonoidWithZero.toMonoid.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (AddCommMonoid.toAddMonoid.{u_4} M _inst_4) (Module.toDistribMulAction.{u_3, u_4} k M (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) _inst_4 _inst_5)))) (SMulZeroClass.toSMul.{u_3, max u_3 u_2} k (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (AddMonoid.toZero.{max u_3 u_2} (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (AddCommMonoid.toAddMonoid.{max u_3 u_2} (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u_3, max u_3 u_2} k (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (AddMonoid.toAddZeroClass.{max u_3 u_2} (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (AddCommMonoid.toAddMonoid.{max u_3 u_2} (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))))) (DistribMulAction.toDistribSMul.{u_3, max u_3 u_2} k (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (MonoidWithZero.toMonoid.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (AddCommMonoid.toAddMonoid.{max u_3 u_2} (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))))) (Module.toDistribMulAction.{u_3, max u_3 u_2} k (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))) (Finsupp.module.{u_2, u_3, u_3} ι k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Semiring.toModule.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u_3 u_4) u_2, u_3, u_4, max u_3 u_2} (LinearEquiv.{u_3, u_3, u_4, max u_3 u_2} k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) M (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) _inst_4 (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))) _inst_5 (Finsupp.module.{u_2, u_3, u_3} ι k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Semiring.toModule.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) k M (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (MonoidWithZero.toMonoid.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (AddCommMonoid.toAddMonoid.{u_4} M _inst_4) (AddCommMonoid.toAddMonoid.{max u_3 u_2} (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))))) (Module.toDistribMulAction.{u_3, u_4} k M (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) _inst_4 _inst_5) (Module.toDistribMulAction.{u_3, max u_3 u_2} k (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))) (Finsupp.module.{u_2, u_3, u_3} ι k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Semiring.toModule.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u_3, u_4, max u_3 u_2, max (max u_3 u_4) u_2} k M (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (LinearEquiv.{u_3, u_3, u_4, max u_3 u_2} k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) M (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) _inst_4 (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))) _inst_5 (Finsupp.module.{u_2, u_3, u_3} ι k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Semiring.toModule.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) _inst_4 (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))) _inst_5 (Finsupp.module.{u_2, u_3, u_3} ι k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Semiring.toModule.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (SemilinearEquivClass.instSemilinearMapClass.{u_3, u_3, u_4, max u_3 u_2, max (max u_3 u_4) u_2} k k M (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (LinearEquiv.{u_3, u_3, u_4, max u_3 u_2} k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) M (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) _inst_4 (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))) _inst_5 (Finsupp.module.{u_2, u_3, u_3} ι k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Semiring.toModule.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) _inst_4 (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))) _inst_5 (Finsupp.module.{u_2, u_3, u_3} ι k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Semiring.toModule.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u_3, u_3, u_4, max u_3 u_2} k k M (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) _inst_4 (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))) _inst_5 (Finsupp.module.{u_2, u_3, u_3} ι k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Semiring.toModule.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))))) (Basis.repr.{u_2, u_3, u_4} ι k M (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) _inst_4 _inst_5 b) m)))
+<too large>
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.basis_repr_tmul Algebra.TensorProduct.basis_repr_tmulₓ'. -/
@[simp]
theorem basis_repr_tmul (r : R) (m : M) :
@@ -1523,10 +1349,7 @@ theorem basis_repr_tmul (r : R) (m : M) :
#align algebra.tensor_product.basis_repr_tmul Algebra.TensorProduct.basis_repr_tmul
/- warning: algebra.tensor_product.basis_repr_symm_apply -> Algebra.TensorProduct.basis_repr_symm_apply is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u_1}} [_inst_1 : CommRing.{u_1} k] {R : Type.{u_2}} [_inst_2 : Ring.{u_2} R] [_inst_3 : Algebra.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2)] {M : Type.{u_3}} [_inst_4 : AddCommMonoid.{u_3} M] [_inst_5 : Module.{u_1, u_3} k M (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) _inst_4] {ι : Type.{u_4}} (b : Basis.{u_4, u_1, u_3} ι k M (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) _inst_4 _inst_5) (r : R) (i : ι), Eq.{succ (max u_2 u_3)} (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (coeFn.{max (succ (max u_4 u_2)) (succ (max u_2 u_3)), max (succ (max u_4 u_2)) (succ (max u_2 u_3))} (LinearEquiv.{u_2, u_2, max u_4 u_2, max u_2 u_3} R R (Ring.toSemiring.{u_2} R _inst_2) (Ring.toSemiring.{u_2} R _inst_2) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R _inst_2))) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R _inst_2))) (RingHomInvPair.ids.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)) (RingHomInvPair.ids.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)) (Finsupp.{u_4, u_2} ι R (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))))) (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R _inst_2))))) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_2} ι R R (Ring.toSemiring.{u_2} R _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (Semiring.toModule.{u_2} R (Ring.toSemiring.{u_2} R _inst_2))) (TensorProduct.leftModule.{u_1, u_2, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R (Ring.toSemiring.{u_2} R _inst_2) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5 (Semiring.toModule.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)) (Algebra.TensorProduct.basis._proof_1.{u_1, u_2} k _inst_1 R _inst_2 _inst_3))) (fun (_x : LinearEquiv.{u_2, u_2, max u_4 u_2, max u_2 u_3} R R (Ring.toSemiring.{u_2} R _inst_2) (Ring.toSemiring.{u_2} R _inst_2) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R _inst_2))) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R _inst_2))) (RingHomInvPair.ids.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)) (RingHomInvPair.ids.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)) (Finsupp.{u_4, u_2} ι R (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))))) (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R _inst_2))))) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_2} ι R R (Ring.toSemiring.{u_2} R _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (Semiring.toModule.{u_2} R (Ring.toSemiring.{u_2} R _inst_2))) (TensorProduct.leftModule.{u_1, u_2, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R (Ring.toSemiring.{u_2} R _inst_2) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5 (Semiring.toModule.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)) (Algebra.TensorProduct.basis._proof_1.{u_1, u_2} k _inst_1 R _inst_2 _inst_3))) => (Finsupp.{u_4, u_2} ι R (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))))) -> (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5)) (LinearEquiv.hasCoeToFun.{u_2, u_2, max u_4 u_2, max u_2 u_3} R R (Finsupp.{u_4, u_2} ι R (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))))) (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Ring.toSemiring.{u_2} R _inst_2) (Ring.toSemiring.{u_2} R _inst_2) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R _inst_2))))) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_2} ι R R (Ring.toSemiring.{u_2} R _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (Semiring.toModule.{u_2} R (Ring.toSemiring.{u_2} R _inst_2))) (TensorProduct.leftModule.{u_1, u_2, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R (Ring.toSemiring.{u_2} R _inst_2) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5 (Semiring.toModule.{u_2} R 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- forall {k : Type.{u_4}} [_inst_1 : CommRing.{u_4} k] {R : Type.{u_1}} [_inst_2 : Ring.{u_1} R] [_inst_3 : Algebra.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2)] {M : Type.{u_2}} [_inst_4 : AddCommMonoid.{u_2} M] [_inst_5 : Module.{u_4, u_2} k M (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)) _inst_4] {ι : Type.{u_3}} (b : Basis.{u_3, u_4, u_2} ι k M (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)) _inst_4 _inst_5) (r : R) (i : ι), Eq.{max (succ u_1) (succ u_2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Finsupp.{u_3, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) => TensorProduct.{u_4, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.single.{u_3, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) i r)) (FunLike.coe.{max (max (succ u_1) (succ u_2)) (succ u_3), max (succ u_1) (succ u_3), max (succ u_1) (succ u_2)} (LinearEquiv.{u_1, u_1, max u_1 u_3, max u_1 u_2} R R (Ring.toSemiring.{u_1} R _inst_2) (Ring.toSemiring.{u_1} R _inst_2) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (RingHomInvPair.ids.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (RingHomInvPair.ids.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (Finsupp.{u_3, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (TensorProduct.{u_4, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_3, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))))) (TensorProduct.addCommMonoid.{u_4, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_3, u_1, u_1} ι R R (Ring.toSemiring.{u_1} R _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Semiring.toModule.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (TensorProduct.leftModule.{u_4, u_1, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R (Ring.toSemiring.{u_1} R _inst_2) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5 (Semiring.toModule.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (Algebra.to_smulCommClass.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3))) (Finsupp.{u_3, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (fun (_x : Finsupp.{u_3, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Finsupp.{u_3, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) => TensorProduct.{u_4, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) _x) (SMulHomClass.toFunLike.{max (max u_1 u_2) u_3, u_1, max u_1 u_3, max u_1 u_2} (LinearEquiv.{u_1, u_1, max u_1 u_3, max u_1 u_2} R R (Ring.toSemiring.{u_1} R _inst_2) (Ring.toSemiring.{u_1} R _inst_2) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (RingHomInvPair.ids.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (RingHomInvPair.ids.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (Finsupp.{u_3, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (TensorProduct.{u_4, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_3, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))))) (TensorProduct.addCommMonoid.{u_4, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_3, u_1, u_1} ι R R (Ring.toSemiring.{u_1} R _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Semiring.toModule.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (TensorProduct.leftModule.{u_4, u_1, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R (Ring.toSemiring.{u_1} R _inst_2) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5 (Semiring.toModule.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (Algebra.to_smulCommClass.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3))) R (Finsupp.{u_3, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (TensorProduct.{u_4, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (SMulZeroClass.toSMul.{u_1, max u_1 u_3} R (Finsupp.{u_3, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (AddMonoid.toZero.{max u_1 u_3} (Finsupp.{u_3, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (AddCommMonoid.toAddMonoid.{max u_1 u_3} (Finsupp.{u_3, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Finsupp.addCommMonoid.{u_3, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))))))) (DistribSMul.toSMulZeroClass.{u_1, max u_1 u_3} R (Finsupp.{u_3, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (AddMonoid.toAddZeroClass.{max u_1 u_3} (Finsupp.{u_3, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (AddCommMonoid.toAddMonoid.{max u_1 u_3} (Finsupp.{u_3, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Finsupp.addCommMonoid.{u_3, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))))))) (DistribMulAction.toDistribSMul.{u_1, max u_1 u_3} R (Finsupp.{u_3, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (AddCommMonoid.toAddMonoid.{max u_1 u_3} (Finsupp.{u_3, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Finsupp.addCommMonoid.{u_3, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))))) (Module.toDistribMulAction.{u_1, max u_1 u_3} R (Finsupp.{u_3, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Ring.toSemiring.{u_1} R _inst_2) (Finsupp.addCommMonoid.{u_3, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))))) (Finsupp.module.{u_3, u_1, u_1} ι R R (Ring.toSemiring.{u_1} R _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Semiring.toModule.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))))))) (SMulZeroClass.toSMul.{u_1, max u_1 u_2} R (TensorProduct.{u_4, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (AddMonoid.toZero.{max u_1 u_2} (TensorProduct.{u_4, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (TensorProduct.{u_4, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (TensorProduct.addCommMonoid.{u_4, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5))) (DistribSMul.toSMulZeroClass.{u_1, max u_1 u_2} R (TensorProduct.{u_4, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (AddMonoid.toAddZeroClass.{max u_1 u_2} (TensorProduct.{u_4, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (TensorProduct.{u_4, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (TensorProduct.addCommMonoid.{u_4, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5))) (DistribMulAction.toDistribSMul.{u_1, max u_1 u_2} R (TensorProduct.{u_4, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (TensorProduct.{u_4, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (TensorProduct.addCommMonoid.{u_4, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5)) (Module.toDistribMulAction.{u_1, max u_1 u_2} R (TensorProduct.{u_4, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Ring.toSemiring.{u_1} R _inst_2) (TensorProduct.addCommMonoid.{u_4, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (TensorProduct.leftModule.{u_4, u_1, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R (Ring.toSemiring.{u_1} R _inst_2) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5 (Semiring.toModule.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (Algebra.to_smulCommClass.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u_1 u_2) u_3, u_1, max u_1 u_3, max u_1 u_2} (LinearEquiv.{u_1, u_1, max u_1 u_3, max u_1 u_2} R R (Ring.toSemiring.{u_1} R _inst_2) (Ring.toSemiring.{u_1} R _inst_2) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (RingHomInvPair.ids.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (RingHomInvPair.ids.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (Finsupp.{u_3, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (TensorProduct.{u_4, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_3, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))))) (TensorProduct.addCommMonoid.{u_4, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_3, u_1, u_1} ι R R (Ring.toSemiring.{u_1} R _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Semiring.toModule.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (TensorProduct.leftModule.{u_4, u_1, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R (Ring.toSemiring.{u_1} R _inst_2) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5 (Semiring.toModule.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (Algebra.to_smulCommClass.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3))) R (Finsupp.{u_3, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (TensorProduct.{u_4, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (AddCommMonoid.toAddMonoid.{max u_1 u_3} (Finsupp.{u_3, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Finsupp.addCommMonoid.{u_3, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))))) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (TensorProduct.{u_4, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (TensorProduct.addCommMonoid.{u_4, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5)) (Module.toDistribMulAction.{u_1, max u_1 u_3} R (Finsupp.{u_3, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Ring.toSemiring.{u_1} R _inst_2) (Finsupp.addCommMonoid.{u_3, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))))) (Finsupp.module.{u_3, u_1, u_1} ι R R (Ring.toSemiring.{u_1} R _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Semiring.toModule.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Module.toDistribMulAction.{u_1, max u_1 u_2} R (TensorProduct.{u_4, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Ring.toSemiring.{u_1} R _inst_2) (TensorProduct.addCommMonoid.{u_4, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (TensorProduct.leftModule.{u_4, u_1, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R (Ring.toSemiring.{u_1} R _inst_2) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5 (Semiring.toModule.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (Algebra.to_smulCommClass.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3))) (SemilinearMapClass.distribMulActionHomClass.{u_1, max u_1 u_3, max u_1 u_2, max (max u_1 u_2) u_3} R (Finsupp.{u_3, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (TensorProduct.{u_4, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (LinearEquiv.{u_1, u_1, max u_1 u_3, max u_1 u_2} R R (Ring.toSemiring.{u_1} R _inst_2) (Ring.toSemiring.{u_1} R _inst_2) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (RingHomInvPair.ids.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (RingHomInvPair.ids.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (Finsupp.{u_3, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (TensorProduct.{u_4, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_3, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))))) (TensorProduct.addCommMonoid.{u_4, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_3, u_1, u_1} ι R R (Ring.toSemiring.{u_1} R _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Semiring.toModule.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (TensorProduct.leftModule.{u_4, u_1, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R (Ring.toSemiring.{u_1} R _inst_2) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5 (Semiring.toModule.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (Algebra.to_smulCommClass.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3))) (Ring.toSemiring.{u_1} R _inst_2) (Finsupp.addCommMonoid.{u_3, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))))) (TensorProduct.addCommMonoid.{u_4, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_3, u_1, u_1} ι R R (Ring.toSemiring.{u_1} R _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Semiring.toModule.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (TensorProduct.leftModule.{u_4, u_1, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R (Ring.toSemiring.{u_1} R _inst_2) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5 (Semiring.toModule.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (Algebra.to_smulCommClass.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3)) (SemilinearEquivClass.instSemilinearMapClass.{u_1, u_1, max u_1 u_3, max u_1 u_2, max (max u_1 u_2) u_3} R R (Finsupp.{u_3, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (TensorProduct.{u_4, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (LinearEquiv.{u_1, u_1, max u_1 u_3, max u_1 u_2} R R (Ring.toSemiring.{u_1} R _inst_2) (Ring.toSemiring.{u_1} R _inst_2) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (RingHomInvPair.ids.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (RingHomInvPair.ids.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (Finsupp.{u_3, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (TensorProduct.{u_4, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R M 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u_1, u_1} ι R R (Ring.toSemiring.{u_1} R _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Semiring.toModule.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (TensorProduct.leftModule.{u_4, u_1, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R (Ring.toSemiring.{u_1} R _inst_2) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5 (Semiring.toModule.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (Algebra.to_smulCommClass.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3))) (Ring.toSemiring.{u_1} R _inst_2) (Ring.toSemiring.{u_1} R _inst_2) (Finsupp.addCommMonoid.{u_3, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))))) (TensorProduct.addCommMonoid.{u_4, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_3, u_1, u_1} ι R R (Ring.toSemiring.{u_1} R _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Semiring.toModule.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (TensorProduct.leftModule.{u_4, 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(Ring.toSemiring.{u_1} R _inst_2))) i r)) (TensorProduct.tmul.{u_4, u_1, u_2} k (CommRing.toCommSemiring.{u_4} k _inst_1) R ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Finsupp.{u_3, u_4} ι k (MonoidWithZero.toZero.{u_4} k (Semiring.toMonoidWithZero.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))))) => M) (Finsupp.single.{u_3, u_4} ι k (MonoidWithZero.toZero.{u_4} k (Semiring.toMonoidWithZero.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)))) i (OfNat.ofNat.{u_4} k 1 (One.toOfNat1.{u_4} k (Semiring.toOne.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_4, u_1} k R (CommRing.toCommSemiring.{u_4} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5 r (FunLike.coe.{max (max (succ u_4) (succ u_2)) (succ u_3), max (succ u_4) (succ u_3), succ u_2} (LinearEquiv.{u_4, u_4, max u_4 u_3, u_2} k k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)) (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)) (RingHom.id.{u_4} k (Semiring.toNonAssocSemiring.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)))) (RingHom.id.{u_4} k (Semiring.toNonAssocSemiring.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)))) (RingHomInvPair.ids.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))) (RingHomInvPair.ids.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))) (Finsupp.{u_3, u_4} ι k (MonoidWithZero.toZero.{u_4} k (Semiring.toMonoidWithZero.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))))) M (Finsupp.addCommMonoid.{u_3, u_4} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_4} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_4} k (Semiring.toNonAssocSemiring.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)))))) _inst_4 (Finsupp.module.{u_3, u_4, u_4} ι k k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_4} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_4} k (Semiring.toNonAssocSemiring.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))))) (Semiring.toModule.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)))) _inst_5) (Finsupp.{u_3, u_4} ι k (MonoidWithZero.toZero.{u_4} k (Semiring.toMonoidWithZero.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))))) (fun (_x : Finsupp.{u_3, u_4} ι k (MonoidWithZero.toZero.{u_4} k (Semiring.toMonoidWithZero.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Finsupp.{u_3, u_4} ι k (MonoidWithZero.toZero.{u_4} k (Semiring.toMonoidWithZero.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))))) => M) _x) (SMulHomClass.toFunLike.{max (max u_4 u_2) u_3, u_4, max u_4 u_3, u_2} (LinearEquiv.{u_4, u_4, max u_4 u_3, u_2} k k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)) (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)) (RingHom.id.{u_4} k (Semiring.toNonAssocSemiring.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)))) (RingHom.id.{u_4} k (Semiring.toNonAssocSemiring.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)))) (RingHomInvPair.ids.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))) (RingHomInvPair.ids.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))) (Finsupp.{u_3, u_4} ι k (MonoidWithZero.toZero.{u_4} k (Semiring.toMonoidWithZero.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))))) M (Finsupp.addCommMonoid.{u_3, u_4} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_4} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_4} k (Semiring.toNonAssocSemiring.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)))))) _inst_4 (Finsupp.module.{u_3, u_4, u_4} ι k k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_4} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_4} k (Semiring.toNonAssocSemiring.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))))) (Semiring.toModule.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)))) _inst_5) k (Finsupp.{u_3, u_4} ι k (MonoidWithZero.toZero.{u_4} k (Semiring.toMonoidWithZero.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))))) M (SMulZeroClass.toSMul.{u_4, max u_4 u_3} k (Finsupp.{u_3, u_4} ι k (MonoidWithZero.toZero.{u_4} k (Semiring.toMonoidWithZero.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))))) (AddMonoid.toZero.{max u_4 u_3} (Finsupp.{u_3, u_4} ι k (MonoidWithZero.toZero.{u_4} k (Semiring.toMonoidWithZero.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))))) (AddCommMonoid.toAddMonoid.{max u_4 u_3} (Finsupp.{u_3, u_4} ι k (MonoidWithZero.toZero.{u_4} k (Semiring.toMonoidWithZero.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))))) (Finsupp.addCommMonoid.{u_3, u_4} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_4} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_4} k (Semiring.toNonAssocSemiring.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u_4, max u_4 u_3} k (Finsupp.{u_3, u_4} ι k (MonoidWithZero.toZero.{u_4} k (Semiring.toMonoidWithZero.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))))) (AddMonoid.toAddZeroClass.{max u_4 u_3} (Finsupp.{u_3, u_4} ι k (MonoidWithZero.toZero.{u_4} k (Semiring.toMonoidWithZero.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))))) (AddCommMonoid.toAddMonoid.{max u_4 u_3} (Finsupp.{u_3, u_4} ι k (MonoidWithZero.toZero.{u_4} k (Semiring.toMonoidWithZero.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))))) (Finsupp.addCommMonoid.{u_3, u_4} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_4} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_4} k (Semiring.toNonAssocSemiring.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)))))))) (DistribMulAction.toDistribSMul.{u_4, max u_4 u_3} k (Finsupp.{u_3, u_4} ι k (MonoidWithZero.toZero.{u_4} k (Semiring.toMonoidWithZero.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))))) (MonoidWithZero.toMonoid.{u_4} k (Semiring.toMonoidWithZero.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)))) (AddCommMonoid.toAddMonoid.{max u_4 u_3} (Finsupp.{u_3, u_4} ι k (MonoidWithZero.toZero.{u_4} k (Semiring.toMonoidWithZero.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))))) (Finsupp.addCommMonoid.{u_3, u_4} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_4} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_4} k (Semiring.toNonAssocSemiring.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))))))) (Module.toDistribMulAction.{u_4, max u_4 u_3} k (Finsupp.{u_3, u_4} ι k (MonoidWithZero.toZero.{u_4} k (Semiring.toMonoidWithZero.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))))) (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)) (Finsupp.addCommMonoid.{u_3, u_4} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_4} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_4} k (Semiring.toNonAssocSemiring.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)))))) (Finsupp.module.{u_3, u_4, u_4} ι k k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_4} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_4} k (Semiring.toNonAssocSemiring.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))))) (Semiring.toModule.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)))))))) (SMulZeroClass.toSMul.{u_4, u_2} k M (AddMonoid.toZero.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M _inst_4)) (DistribSMul.toSMulZeroClass.{u_4, u_2} k M (AddMonoid.toAddZeroClass.{u_2} M (AddCommMonoid.toAddMonoid.{u_2} M _inst_4)) (DistribMulAction.toDistribSMul.{u_4, u_2} k M (MonoidWithZero.toMonoid.{u_4} k (Semiring.toMonoidWithZero.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)))) (AddCommMonoid.toAddMonoid.{u_2} M _inst_4) (Module.toDistribMulAction.{u_4, u_2} k M (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)) _inst_4 _inst_5)))) (DistribMulActionHomClass.toSMulHomClass.{max (max u_4 u_2) u_3, u_4, max u_4 u_3, u_2} (LinearEquiv.{u_4, u_4, max u_4 u_3, u_2} k k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)) (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)) (RingHom.id.{u_4} k (Semiring.toNonAssocSemiring.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)))) (RingHom.id.{u_4} k (Semiring.toNonAssocSemiring.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)))) (RingHomInvPair.ids.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))) (RingHomInvPair.ids.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))) (Finsupp.{u_3, u_4} ι k (MonoidWithZero.toZero.{u_4} k (Semiring.toMonoidWithZero.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))))) M (Finsupp.addCommMonoid.{u_3, u_4} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_4} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_4} k (Semiring.toNonAssocSemiring.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)))))) _inst_4 (Finsupp.module.{u_3, u_4, u_4} ι k k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_4} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_4} k (Semiring.toNonAssocSemiring.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))))) (Semiring.toModule.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)))) _inst_5) k (Finsupp.{u_3, u_4} ι k (MonoidWithZero.toZero.{u_4} k (Semiring.toMonoidWithZero.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))))) M (MonoidWithZero.toMonoid.{u_4} k (Semiring.toMonoidWithZero.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)))) (AddCommMonoid.toAddMonoid.{max u_4 u_3} (Finsupp.{u_3, u_4} ι k (MonoidWithZero.toZero.{u_4} k (Semiring.toMonoidWithZero.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))))) (Finsupp.addCommMonoid.{u_3, u_4} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_4} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_4} k (Semiring.toNonAssocSemiring.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))))))) (AddCommMonoid.toAddMonoid.{u_2} M _inst_4) (Module.toDistribMulAction.{u_4, max u_4 u_3} k (Finsupp.{u_3, u_4} ι k (MonoidWithZero.toZero.{u_4} k (Semiring.toMonoidWithZero.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))))) (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)) (Finsupp.addCommMonoid.{u_3, u_4} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_4} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_4} k (Semiring.toNonAssocSemiring.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)))))) (Finsupp.module.{u_3, u_4, u_4} ι k k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_4} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_4} k (Semiring.toNonAssocSemiring.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))))) (Semiring.toModule.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))))) (Module.toDistribMulAction.{u_4, u_2} k M (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)) _inst_4 _inst_5) (SemilinearMapClass.distribMulActionHomClass.{u_4, max u_4 u_3, u_2, max (max u_4 u_2) u_3} k (Finsupp.{u_3, u_4} ι k (MonoidWithZero.toZero.{u_4} k (Semiring.toMonoidWithZero.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))))) M (LinearEquiv.{u_4, u_4, max u_4 u_3, u_2} k k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)) (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)) (RingHom.id.{u_4} k (Semiring.toNonAssocSemiring.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)))) (RingHom.id.{u_4} k (Semiring.toNonAssocSemiring.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)))) (RingHomInvPair.ids.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))) (RingHomInvPair.ids.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))) (Finsupp.{u_3, u_4} ι k (MonoidWithZero.toZero.{u_4} k (Semiring.toMonoidWithZero.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))))) M (Finsupp.addCommMonoid.{u_3, u_4} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_4} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_4} k (Semiring.toNonAssocSemiring.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)))))) _inst_4 (Finsupp.module.{u_3, u_4, u_4} ι k k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_4} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_4} k (Semiring.toNonAssocSemiring.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))))) (Semiring.toModule.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)))) _inst_5) (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)) (Finsupp.addCommMonoid.{u_3, u_4} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_4} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_4} k (Semiring.toNonAssocSemiring.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)))))) _inst_4 (Finsupp.module.{u_3, u_4, u_4} ι k k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_4} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_4} k (Semiring.toNonAssocSemiring.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))))) (Semiring.toModule.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)))) _inst_5 (SemilinearEquivClass.instSemilinearMapClass.{u_4, u_4, max u_4 u_3, u_2, max (max u_4 u_2) u_3} k k (Finsupp.{u_3, u_4} ι k (MonoidWithZero.toZero.{u_4} k (Semiring.toMonoidWithZero.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))))) M (LinearEquiv.{u_4, u_4, max u_4 u_3, u_2} k k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)) (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)) (RingHom.id.{u_4} k (Semiring.toNonAssocSemiring.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)))) (RingHom.id.{u_4} k (Semiring.toNonAssocSemiring.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)))) (RingHomInvPair.ids.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))) (RingHomInvPair.ids.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))) (Finsupp.{u_3, u_4} ι k (MonoidWithZero.toZero.{u_4} k (Semiring.toMonoidWithZero.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))))) M (Finsupp.addCommMonoid.{u_3, u_4} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_4} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_4} k (Semiring.toNonAssocSemiring.{u_4} k 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_inst_1)))) _inst_5 (RingHom.id.{u_4} k (Semiring.toNonAssocSemiring.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)))) (RingHom.id.{u_4} k (Semiring.toNonAssocSemiring.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)))) (RingHomInvPair.ids.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))) (RingHomInvPair.ids.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)))))))) (LinearEquiv.symm.{u_4, u_4, u_2, max u_4 u_3} k k M (Finsupp.{u_3, u_4} ι k (MonoidWithZero.toZero.{u_4} k (Semiring.toMonoidWithZero.{u_4} k (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1))))) (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)) (CommSemiring.toSemiring.{u_4} k (CommRing.toCommSemiring.{u_4} k _inst_1)) _inst_4 (Finsupp.addCommMonoid.{u_3, u_4} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_4} k 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+<too large>
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.basis_repr_symm_apply Algebra.TensorProduct.basis_repr_symm_applyₓ'. -/
@[simp]
theorem basis_repr_symm_apply (r : R) (i : ι) :
@@ -1564,10 +1387,7 @@ def endTensorEndAlgHom : End R M ⊗[R] End R N →ₐ[R] End R (M ⊗[R] N) :=
-/
/- warning: module.End_tensor_End_alg_hom_apply -> Module.endTensorEndAlgHom_apply is a dubious translation:
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_inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u1} R R R N N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_3 _inst_5 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 (smulCommClass_self.{u3, u1} R N (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_3)) (Module.toMulActionWithZero.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_5))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (TensorProduct.{u3, u2, u1} R _inst_1 (Module.End.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_4) (Module.End.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_5) 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(CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4 (smulCommClass_self.{u3, u2} R M (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Module.toMulActionWithZero.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u1} R R R N N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_3 _inst_5 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 (smulCommClass_self.{u3, u1} R N (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_3)) (Module.toMulActionWithZero.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_5))))) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 (Module.End.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_4) (Module.End.semiring.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u3, u2} R M _inst_1 _inst_2 _inst_4) (Module.End.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_5) (Module.End.semiring.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_5) (Module.instAlgebraEndToSemiringSemiring.{u3, u1} R N _inst_1 _inst_3 _inst_5))))))) (DistribSMul.toSMulZeroClass.{u3, max u1 u2} R (TensorProduct.{u3, u2, u1} R _inst_1 (Module.End.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_4) (Module.End.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_5) (LinearMap.addCommMonoid.{u3, u3, u2, u2} R R M M (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_2 _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, u1, u1} R R N N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_3 _inst_5 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u2} R R R M M (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_2 _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4 (smulCommClass_self.{u3, u2} R M (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Module.toMulActionWithZero.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u1} R R R N N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_3 _inst_5 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 (smulCommClass_self.{u3, u1} R N (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_3)) (Module.toMulActionWithZero.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_5))))) (AddMonoid.toAddZeroClass.{max u1 u2} (TensorProduct.{u3, u2, u1} R _inst_1 (Module.End.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_4) (Module.End.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_5) (LinearMap.addCommMonoid.{u3, u3, u2, u2} R R M M (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_2 _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, u1, u1} R R N N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_3 _inst_5 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u2} R R R M M (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_2 _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4 (smulCommClass_self.{u3, u2} R M (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Module.toMulActionWithZero.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u1} R R R N N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_3 _inst_5 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 (smulCommClass_self.{u3, u1} R N (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_3)) (Module.toMulActionWithZero.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_5))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (TensorProduct.{u3, u2, u1} R _inst_1 (Module.End.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_4) (Module.End.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_5) (LinearMap.addCommMonoid.{u3, u3, u2, u2} R R M M (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_2 _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, u1, u1} R R N N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_3 _inst_5 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u2} R R R M M (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_2 _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4 (smulCommClass_self.{u3, u2} R M (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Module.toMulActionWithZero.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u1} R R R N N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_3 _inst_5 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 (smulCommClass_self.{u3, u1} R N (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_3)) (Module.toMulActionWithZero.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_5))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (TensorProduct.{u3, u2, u1} R _inst_1 (Module.End.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_4) (Module.End.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_5) (LinearMap.addCommMonoid.{u3, u3, u2, u2} R R M M (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_2 _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, u1, u1} R R N N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_3 _inst_5 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u2} R R R M M (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_2 _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4 (smulCommClass_self.{u3, u2} R M (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Module.toMulActionWithZero.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u1} R R R N N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_3 _inst_5 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 (smulCommClass_self.{u3, u1} R N (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_3)) (Module.toMulActionWithZero.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_5))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (TensorProduct.{u3, u2, u1} R _inst_1 (Module.End.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_4) (Module.End.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_5) (LinearMap.addCommMonoid.{u3, u3, u2, u2} R R M M (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_2 _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, u1, u1} R R N N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_3 _inst_5 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u2} R R R M M (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_2 _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4 (smulCommClass_self.{u3, u2} R M (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Module.toMulActionWithZero.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u1} R R R N N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_3 _inst_5 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 (smulCommClass_self.{u3, u1} R N (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_3)) (Module.toMulActionWithZero.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_5))))) (Semiring.toNonAssocSemiring.{max u1 u2} (TensorProduct.{u3, u2, u1} R _inst_1 (Module.End.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_4) (Module.End.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_5) (LinearMap.addCommMonoid.{u3, u3, u2, u2} R R M M (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_2 _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, u1, u1} R R N N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_3 _inst_5 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u2} R R R M M (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_2 _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4 (smulCommClass_self.{u3, u2} R M (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Module.toMulActionWithZero.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u1} R R R N N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_3 _inst_5 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 (smulCommClass_self.{u3, u1} R N (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_3)) (Module.toMulActionWithZero.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_5))))) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 (Module.End.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_4) (Module.End.semiring.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u3, u2} R M _inst_1 _inst_2 _inst_4) (Module.End.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_5) (Module.End.semiring.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_5) (Module.instAlgebraEndToSemiringSemiring.{u3, u1} R N _inst_1 _inst_3 _inst_5))))))) (DistribMulAction.toDistribSMul.{u3, max u1 u2} R (TensorProduct.{u3, u2, u1} R _inst_1 (Module.End.{u3, 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(CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_3 _inst_5 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u2} R R R M M (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_2 _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4 (smulCommClass_self.{u3, u2} R M (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Module.toMulActionWithZero.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u1} R R R N N 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(CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_2 _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, u1, u1} R R N N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_3 _inst_5 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u2} R R R M M (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_2 _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4 (smulCommClass_self.{u3, u2} R M (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u2} M 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_inst_2 _inst_4) (Module.End.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_5) (LinearMap.addCommMonoid.{u3, u3, u2, u2} R R M M (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_2 _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, u1, u1} R R N N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_3 _inst_5 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u2} R R R M M (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_2 _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4 (smulCommClass_self.{u3, u2} R M (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Module.toMulActionWithZero.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u1} R R R N N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_3 _inst_5 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 (smulCommClass_self.{u3, u1} R N (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_3)) (Module.toMulActionWithZero.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_5))))) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 (Module.End.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_4) (Module.End.semiring.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u3, u2} R M _inst_1 _inst_2 _inst_4) (Module.End.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_5) (Module.End.semiring.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_5) (Module.instAlgebraEndToSemiringSemiring.{u3, u1} R N _inst_1 _inst_3 _inst_5)))))) (Module.toDistribMulAction.{u3, max u1 u2} R (TensorProduct.{u3, u2, u1} R _inst_1 (Module.End.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_4) (Module.End.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_5) (LinearMap.addCommMonoid.{u3, u3, u2, u2} R R M M (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_2 _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, u1, u1} R R N N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_3 _inst_5 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u2} R R R M M (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_2 _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4 (smulCommClass_self.{u3, u2} R M (CommSemiring.toCommMonoid.{u3} R _inst_1) 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_inst_3 _inst_3 _inst_5 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u2} R R R M M (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_2 _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4 (smulCommClass_self.{u3, u2} R M (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Module.toMulActionWithZero.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u1} R R R N N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 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(CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_3)) (Module.toMulActionWithZero.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_5))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (TensorProduct.{u3, u2, u1} R _inst_1 (Module.End.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_4) (Module.End.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_5) (LinearMap.addCommMonoid.{u3, u3, u2, u2} R R M M (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_2 _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, u1, u1} R R N N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_3 _inst_5 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u2} R R R M M (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_2 _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4 (smulCommClass_self.{u3, u2} R M (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Module.toMulActionWithZero.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u1} R R R N N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_3 _inst_5 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 (smulCommClass_self.{u3, u1} R N (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_3)) (Module.toMulActionWithZero.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_5))))) (Semiring.toNonAssocSemiring.{max u1 u2} (TensorProduct.{u3, u2, u1} R _inst_1 (Module.End.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_4) (Module.End.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_5) (LinearMap.addCommMonoid.{u3, u3, u2, u2} R R M M (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_2 _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.addCommMonoid.{u3, u3, u1, u1} R R N N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_3 _inst_5 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u2} R R R M M (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_2 _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4 (smulCommClass_self.{u3, u2} R M (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Module.toMulActionWithZero.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u1} R R R N N 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_inst_3 _inst_5 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u2} R R R M M (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_2 _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_4 (smulCommClass_self.{u3, u2} R M (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Module.toMulActionWithZero.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u1} R R R N N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_3 _inst_5 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 (smulCommClass_self.{u3, u1} R N (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_3)) (Module.toMulActionWithZero.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_5))))) _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 (Module.End.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_4) (Module.End.semiring.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u3, u2} R M _inst_1 _inst_2 _inst_4) 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(CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_5) (Module.instAlgebraEndToSemiringSemiring.{u3, u1} R N _inst_1 _inst_3 _inst_5)))) (Module.toDistribMulAction.{u3, max u1 u2} R (Module.End.{u3, max u1 u2} R (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_2 _inst_3 _inst_4 _inst_5) (CommSemiring.toSemiring.{u3} R _inst_1) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_2 _inst_3 _inst_4 _inst_5) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_2 _inst_3 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Module.End.{u3, max u1 u2} R (TensorProduct.{u3, u2, u1} R _inst_1 M N _inst_2 _inst_3 _inst_4 _inst_5) (CommSemiring.toSemiring.{u3} R _inst_1) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_2 _inst_3 _inst_4 _inst_5) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_1 M N _inst_2 _inst_3 _inst_4 _inst_5)) 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+<too large>
Case conversion may be inaccurate. Consider using '#align module.End_tensor_End_alg_hom_apply Module.endTensorEndAlgHom_applyₓ'. -/
theorem endTensorEndAlgHom_apply (f : End R M) (g : End R N) :
endTensorEndAlgHom (f ⊗ₜ[R] g) = TensorProduct.map f g := by
@@ -1578,10 +1398,7 @@ theorem endTensorEndAlgHom_apply (f : End R M) (g : End R N) :
end Module
/- warning: subalgebra.finite_dimensional_sup -> Subalgebra.finiteDimensional_sup is a dubious translation:
-lean 3 declaration is
- forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : CommRing.{u2} L] [_inst_3 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2))] (E1 : Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) (E2 : Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) [_inst_4 : FiniteDimensional.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) L (Subalgebra.setLike.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3)) E1) (Field.toDivisionRing.{u1} K _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) L (Subalgebra.setLike.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3)) E1) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) L (Subalgebra.setLike.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3)) E1) (Ring.toNonAssocRing.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) L (Subalgebra.setLike.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3)) E1) (Subalgebra.toRing.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (CommRing.toRing.{u2} L _inst_2) _inst_3 E1)))) (Subalgebra.module.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3 E1)] [_inst_5 : FiniteDimensional.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) L (Subalgebra.setLike.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3)) E2) (Field.toDivisionRing.{u1} K _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) L (Subalgebra.setLike.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3)) E2) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) L (Subalgebra.setLike.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3)) E2) (Ring.toNonAssocRing.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) L (Subalgebra.setLike.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3)) E2) (Subalgebra.toRing.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (CommRing.toRing.{u2} L _inst_2) _inst_3 E2)))) (Subalgebra.module.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3 E2)], FiniteDimensional.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) L (Subalgebra.setLike.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3)) (Sup.sup.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) (SemilatticeSup.toHasSup.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) (Lattice.toSemilatticeSup.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3))))) E1 E2)) (Field.toDivisionRing.{u1} K _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) L (Subalgebra.setLike.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3)) (Sup.sup.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) (SemilatticeSup.toHasSup.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) (Lattice.toSemilatticeSup.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3))))) E1 E2)) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) L (Subalgebra.setLike.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3)) (Sup.sup.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) (SemilatticeSup.toHasSup.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) (Lattice.toSemilatticeSup.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3))))) E1 E2)) (Ring.toNonAssocRing.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) L (Subalgebra.setLike.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3)) (Sup.sup.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) (SemilatticeSup.toHasSup.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) (Lattice.toSemilatticeSup.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3))))) E1 E2)) (Subalgebra.toRing.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (CommRing.toRing.{u2} L _inst_2) _inst_3 (Sup.sup.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) (SemilatticeSup.toHasSup.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) (Lattice.toSemilatticeSup.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3))))) E1 E2))))) (Subalgebra.module.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3 (Sup.sup.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) (SemilatticeSup.toHasSup.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) (Lattice.toSemilatticeSup.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_2)) _inst_3))))) E1 E2))
-but is expected to have type
- forall {K : Type.{u2}} {L : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : CommRing.{u1} L] [_inst_3 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2))] (E1 : Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) (E2 : Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) [_inst_4 : FiniteDimensional.{u2, u1} K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) L (Subalgebra.instSetLikeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3)) x E1)) (Field.toDivisionRing.{u2} K _inst_1) (Ring.toAddCommGroup.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) L (Subalgebra.instSetLikeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3)) x E1)) (CommRing.toRing.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) L (Subalgebra.instSetLikeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3)) x E1)) (SubringClass.toCommRing.{u1, u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) E1 L _inst_2 (Subalgebra.instSetLikeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) (Subalgebra.instSubringClassSubalgebraToCommSemiringToSemiringInstSetLikeSubalgebra.{u2, u1} K L (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)) (CommRing.toRing.{u1} L _inst_2) _inst_3)))) (Subalgebra.instModuleSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToNonAssocSemiringToSubsemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3 E1)] [_inst_5 : FiniteDimensional.{u2, u1} K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) L (Subalgebra.instSetLikeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3)) x E2)) (Field.toDivisionRing.{u2} K _inst_1) (Ring.toAddCommGroup.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) L (Subalgebra.instSetLikeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3)) x E2)) (CommRing.toRing.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) L (Subalgebra.instSetLikeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3)) x E2)) (SubringClass.toCommRing.{u1, u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) E2 L _inst_2 (Subalgebra.instSetLikeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) (Subalgebra.instSubringClassSubalgebraToCommSemiringToSemiringInstSetLikeSubalgebra.{u2, u1} K L (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)) (CommRing.toRing.{u1} L _inst_2) _inst_3)))) (Subalgebra.instModuleSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToNonAssocSemiringToSubsemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3 E2)], FiniteDimensional.{u2, u1} K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) L (Subalgebra.instSetLikeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3)) x (Sup.sup.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) (SemilatticeSup.toSup.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) (Lattice.toSemilatticeSup.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) (ConditionallyCompleteLattice.toLattice.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3))))) E1 E2))) (Field.toDivisionRing.{u2} K _inst_1) (Ring.toAddCommGroup.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) L (Subalgebra.instSetLikeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3)) x (Sup.sup.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) (SemilatticeSup.toSup.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) (Lattice.toSemilatticeSup.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) (ConditionallyCompleteLattice.toLattice.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3))))) E1 E2))) (CommRing.toRing.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) L (Subalgebra.instSetLikeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3)) x (Sup.sup.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) (SemilatticeSup.toSup.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) (Lattice.toSemilatticeSup.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) (ConditionallyCompleteLattice.toLattice.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3))))) E1 E2))) (SubringClass.toCommRing.{u1, u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) (Sup.sup.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) (SemilatticeSup.toSup.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) (Lattice.toSemilatticeSup.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) (ConditionallyCompleteLattice.toLattice.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3))))) E1 E2) L _inst_2 (Subalgebra.instSetLikeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) (Subalgebra.instSubringClassSubalgebraToCommSemiringToSemiringInstSetLikeSubalgebra.{u2, u1} K L (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)) (CommRing.toRing.{u1} L _inst_2) _inst_3)))) (Subalgebra.instModuleSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToNonAssocSemiringToSubsemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3 (Sup.sup.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) (SemilatticeSup.toSup.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) (Lattice.toSemilatticeSup.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) (ConditionallyCompleteLattice.toLattice.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_2)) _inst_3))))) E1 E2))
+<too large>
Case conversion may be inaccurate. Consider using '#align subalgebra.finite_dimensional_sup Subalgebra.finiteDimensional_supₓ'. -/
theorem Subalgebra.finiteDimensional_sup {K L : Type _} [Field K] [CommRing L] [Algebra K L]
(E1 E2 : Subalgebra K L) [FiniteDimensional K E1] [FiniteDimensional K E2] :
@@ -1604,10 +1421,7 @@ variable [Algebra R A] [Algebra R B]
variable [IsScalarTower R A M] [IsScalarTower R B M]
/- warning: tensor_product.algebra.module_aux -> TensorProduct.Algebra.moduleAux is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} {M : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u1, u4} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : Semiring.{u2} A] [_inst_5 : Semiring.{u3} B] [_inst_6 : Module.{u2, u4} A M _inst_4 _inst_2] [_inst_7 : Module.{u3, u4} B M _inst_5 _inst_2] [_inst_8 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_5] [_inst_10 : IsScalarTower.{u1, u2, u4} R A M (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_8))))) (SMulZeroClass.toHasSmul.{u2, u4} A M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (SMulWithZero.toSmulZeroClass.{u2, u4} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_4)))) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u4} A M (Semiring.toMonoidWithZero.{u2} A _inst_4) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (Module.toMulActionWithZero.{u2, u4} A M _inst_4 _inst_2 _inst_6)))) (SMulZeroClass.toHasSmul.{u1, u4} R M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (SMulWithZero.toSmulZeroClass.{u1, u4} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u4} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (Module.toMulActionWithZero.{u1, u4} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3))))] [_inst_11 : IsScalarTower.{u1, u3, u4} R B M (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_5)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_5)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_5)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_5))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_5 _inst_9))))) (SMulZeroClass.toHasSmul.{u3, u4} B M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (SMulWithZero.toSmulZeroClass.{u3, u4} B M (MulZeroClass.toHasZero.{u3} B (MulZeroOneClass.toMulZeroClass.{u3} B (MonoidWithZero.toMulZeroOneClass.{u3} B (Semiring.toMonoidWithZero.{u3} B _inst_5)))) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (MulActionWithZero.toSMulWithZero.{u3, u4} B M (Semiring.toMonoidWithZero.{u3} B _inst_5) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (Module.toMulActionWithZero.{u3, u4} B M _inst_5 _inst_2 _inst_7)))) (SMulZeroClass.toHasSmul.{u1, u4} R M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (SMulWithZero.toSmulZeroClass.{u1, u4} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u4} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (Module.toMulActionWithZero.{u1, u4} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3))))], LinearMap.{u1, u1, max u2 u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_5))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_8) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_5 _inst_9)) (LinearMap.{u1, u1, u4, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M _inst_2 _inst_2 _inst_3 _inst_3) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_5))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_8) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_5 _inst_9)) (LinearMap.addCommMonoid.{u1, u1, u4, u4} R R M M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_5))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_8) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_5 _inst_9)) (LinearMap.module.{u1, u1, u1, u4, u4} R R R M M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 (TensorProduct.Algebra.moduleAux._proof_1.{u1, u4} R M _inst_1 _inst_2 _inst_3))
-but is expected to have type
- forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} {M : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u1, u4} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : Semiring.{u2} A] [_inst_5 : Semiring.{u3} B] [_inst_6 : Module.{u2, u4} A M _inst_4 _inst_2] [_inst_7 : Module.{u3, u4} B M _inst_5 _inst_2] [_inst_8 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_5] [_inst_10 : IsScalarTower.{u1, u2, u4} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_4 _inst_8) (SMulZeroClass.toSMul.{u2, u4} A M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u2, u4} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_4)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u4} A M (Semiring.toMonoidWithZero.{u2} A _inst_4) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (Module.toMulActionWithZero.{u2, u4} A M _inst_4 _inst_2 _inst_6)))) (SMulZeroClass.toSMul.{u1, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u4} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u4} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (Module.toMulActionWithZero.{u1, u4} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3))))] [_inst_11 : IsScalarTower.{u1, u3, u4} R B M (Algebra.toSMul.{u1, u3} R B _inst_1 _inst_5 _inst_9) (SMulZeroClass.toSMul.{u3, u4} B M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u3, u4} B M (MonoidWithZero.toZero.{u3} B (Semiring.toMonoidWithZero.{u3} B _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u3, u4} B M (Semiring.toMonoidWithZero.{u3} B _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (Module.toMulActionWithZero.{u3, u4} B M _inst_5 _inst_2 _inst_7)))) (SMulZeroClass.toSMul.{u1, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u4} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u4} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (Module.toMulActionWithZero.{u1, u4} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3))))], LinearMap.{u1, u1, max u3 u2, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_5))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_8) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_5 _inst_9)) (LinearMap.{u1, u1, u4, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_4 _inst_8 B _inst_5 _inst_9) (LinearMap.addCommMonoid.{u1, u1, u4, u4} R R M M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_5))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_8) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_5 _inst_9)) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u4, u4} R R R M M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 (smulCommClass_self.{u1, u4} R M (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (Module.toMulActionWithZero.{u1, u4} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3))))
+<too large>
Case conversion may be inaccurate. Consider using '#align tensor_product.algebra.module_aux TensorProduct.Algebra.moduleAuxₓ'. -/
/-- An auxiliary definition, used for constructing the `module (A ⊗[R] B) M` in
`tensor_product.algebra.module` below. -/
@@ -1623,10 +1437,7 @@ def moduleAux : A ⊗[R] B →ₗ[R] M →ₗ[R] M :=
#align tensor_product.algebra.module_aux TensorProduct.Algebra.moduleAux
/- warning: tensor_product.algebra.module_aux_apply -> TensorProduct.Algebra.moduleAux_apply is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} {M : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u1, u4} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : Semiring.{u2} A] [_inst_5 : Semiring.{u3} B] [_inst_6 : Module.{u2, u4} A M _inst_4 _inst_2] [_inst_7 : Module.{u3, u4} B M _inst_5 _inst_2] [_inst_8 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_5] [_inst_10 : IsScalarTower.{u1, u2, u4} R A M (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_8))))) (SMulZeroClass.toHasSmul.{u2, u4} A M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (SMulWithZero.toSmulZeroClass.{u2, u4} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_4)))) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u4} A M (Semiring.toMonoidWithZero.{u2} A _inst_4) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (Module.toMulActionWithZero.{u2, u4} A M _inst_4 _inst_2 _inst_6)))) (SMulZeroClass.toHasSmul.{u1, u4} R M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (SMulWithZero.toSmulZeroClass.{u1, u4} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u4} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (Module.toMulActionWithZero.{u1, u4} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3))))] [_inst_11 : IsScalarTower.{u1, u3, u4} R B M (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_5)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_5)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_5)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_5))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_5 _inst_9))))) (SMulZeroClass.toHasSmul.{u3, u4} B M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (SMulWithZero.toSmulZeroClass.{u3, u4} B M (MulZeroClass.toHasZero.{u3} B (MulZeroOneClass.toMulZeroClass.{u3} B (MonoidWithZero.toMulZeroOneClass.{u3} B (Semiring.toMonoidWithZero.{u3} B _inst_5)))) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (MulActionWithZero.toSMulWithZero.{u3, u4} B M (Semiring.toMonoidWithZero.{u3} B _inst_5) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (Module.toMulActionWithZero.{u3, u4} B M _inst_5 _inst_2 _inst_7)))) (SMulZeroClass.toHasSmul.{u1, u4} R M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (SMulWithZero.toSmulZeroClass.{u1, u4} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u4} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (Module.toMulActionWithZero.{u1, u4} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3))))] (a : A) (b : B) (m : M), Eq.{succ u4} M (coeFn.{succ u4, succ u4} (LinearMap.{u1, u1, u4, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M _inst_2 _inst_2 _inst_3 _inst_3) (fun (_x : LinearMap.{u1, u1, u4, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M _inst_2 _inst_2 _inst_3 _inst_3) => M -> M) (LinearMap.hasCoeToFun.{u1, u1, u4, u4} R R M M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (coeFn.{max (succ (max u2 u3)) (succ u4), max (succ (max u2 u3)) (succ u4)} (LinearMap.{u1, u1, max u2 u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B 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(CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_5))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_8) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_5 _inst_9)) (LinearMap.module.{u1, u1, u1, u4, u4} R R R M M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 (TensorProduct.Algebra.moduleAux._proof_1.{u1, u4} R M _inst_1 _inst_2 _inst_3))) (fun (_x : LinearMap.{u1, u1, max u2 u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_5))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_8) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_5 _inst_9)) (LinearMap.{u1, u1, u4, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M _inst_2 _inst_2 _inst_3 _inst_3) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_5))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_8) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_5 _inst_9)) (LinearMap.addCommMonoid.{u1, u1, u4, u4} R R M M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_5))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_8) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_5 _inst_9)) (LinearMap.module.{u1, u1, u1, u4, u4} R R R M M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 (TensorProduct.Algebra.moduleAux._proof_1.{u1, u4} R M _inst_1 _inst_2 _inst_3))) => (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_5))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_8) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_5 _inst_9)) -> (LinearMap.{u1, u1, u4, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M _inst_2 _inst_2 _inst_3 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u2 u3, u4} R R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_5))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_8) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_5 _inst_9)) (LinearMap.{u1, u1, u4, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_5))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_8) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_5 _inst_9)) (LinearMap.module.{u1, u1, u1, u4, u4} R R R M M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 (TensorProduct.Algebra.moduleAux._proof_1.{u1, u4} R M _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (TensorProduct.Algebra.moduleAux.{u1, u2, u3, u4} R A B M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_5))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_8) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_5 _inst_9) a b)) m) (SMul.smul.{u2, u4} A M (SMulZeroClass.toHasSmul.{u2, u4} A M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (SMulWithZero.toSmulZeroClass.{u2, u4} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_4)))) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u4} A M (Semiring.toMonoidWithZero.{u2} A _inst_4) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (Module.toMulActionWithZero.{u2, u4} A M _inst_4 _inst_2 _inst_6)))) a (SMul.smul.{u3, u4} B M (SMulZeroClass.toHasSmul.{u3, u4} B M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (SMulWithZero.toSmulZeroClass.{u3, u4} B M (MulZeroClass.toHasZero.{u3} B (MulZeroOneClass.toMulZeroClass.{u3} B (MonoidWithZero.toMulZeroOneClass.{u3} B (Semiring.toMonoidWithZero.{u3} B _inst_5)))) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (MulActionWithZero.toSMulWithZero.{u3, u4} B M (Semiring.toMonoidWithZero.{u3} B _inst_5) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (Module.toMulActionWithZero.{u3, u4} B M _inst_5 _inst_2 _inst_7)))) b m))
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- forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} {M : Type.{u4}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u3, u4} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2] [_inst_4 : Semiring.{u2} A] [_inst_5 : Semiring.{u1} B] [_inst_6 : Module.{u2, u4} A M _inst_4 _inst_2] [_inst_7 : Module.{u1, u4} B M _inst_5 _inst_2] [_inst_8 : Algebra.{u3, u2} R A _inst_1 _inst_4] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_5] [_inst_10 : IsScalarTower.{u3, u2, u4} R A M (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_4 _inst_8) (SMulZeroClass.toSMul.{u2, u4} A M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u2, u4} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_4)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u4} A M (Semiring.toMonoidWithZero.{u2} A _inst_4) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (Module.toMulActionWithZero.{u2, u4} A M _inst_4 _inst_2 _inst_6)))) (SMulZeroClass.toSMul.{u3, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u3, u4} R M (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u3, u4} R M (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (Module.toMulActionWithZero.{u3, u4} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3))))] [_inst_11 : IsScalarTower.{u3, u1, u4} R B M (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_5 _inst_9) (SMulZeroClass.toSMul.{u1, u4} B M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u4} B M (MonoidWithZero.toZero.{u1} B 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B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_5))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_4 _inst_8) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_5 _inst_9)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_5))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_4 _inst_8) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_5 _inst_9)) => LinearMap.{u3, u3, u4, u4} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M M _inst_2 _inst_2 _inst_3 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u1 u2, u4} R R (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_5))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_4 _inst_8) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_5 _inst_9)) (LinearMap.{u3, u3, u4, u4} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M M _inst_2 _inst_2 _inst_3 _inst_3) (CommSemiring.toSemiring.{u3} R _inst_1) 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_inst_11) (TensorProduct.tmul.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_5))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_4 _inst_8) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_5 _inst_9) a b)) m) (HSMul.hSMul.{u2, u4, u4} A M M (instHSMul.{u2, u4} A M (SMulZeroClass.toSMul.{u2, u4} A M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u2, u4} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_4)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u4} A M (Semiring.toMonoidWithZero.{u2} A _inst_4) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (Module.toMulActionWithZero.{u2, u4} A M _inst_4 _inst_2 _inst_6))))) a (HSMul.hSMul.{u1, u4, u4} B M M (instHSMul.{u1, u4} B M (SMulZeroClass.toSMul.{u1, u4} B M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u4} B M (MonoidWithZero.toZero.{u1} B (Semiring.toMonoidWithZero.{u1} B _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u4} B M (Semiring.toMonoidWithZero.{u1} B _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (Module.toMulActionWithZero.{u1, u4} B M _inst_5 _inst_2 _inst_7))))) b m))
+<too large>
Case conversion may be inaccurate. Consider using '#align tensor_product.algebra.module_aux_apply TensorProduct.Algebra.moduleAux_applyₓ'. -/
theorem moduleAux_apply (a : A) (b : B) (m : M) : moduleAux (a ⊗ₜ[R] b) m = a • b • m :=
rfl
@@ -1635,10 +1446,7 @@ theorem moduleAux_apply (a : A) (b : B) (m : M) : moduleAux (a ⊗ₜ[R] b) m =
variable [SMulCommClass A B M]
/- warning: tensor_product.algebra.module -> TensorProduct.Algebra.module is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} {M : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u1, u4} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : Semiring.{u2} A] [_inst_5 : Semiring.{u3} B] [_inst_6 : Module.{u2, u4} A M _inst_4 _inst_2] [_inst_7 : Module.{u3, u4} B M _inst_5 _inst_2] [_inst_8 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_5] [_inst_10 : IsScalarTower.{u1, u2, u4} R A M (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_8))))) (SMulZeroClass.toHasSmul.{u2, u4} A M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (SMulWithZero.toSmulZeroClass.{u2, u4} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_4)))) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u4} A M (Semiring.toMonoidWithZero.{u2} A _inst_4) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (Module.toMulActionWithZero.{u2, u4} A M _inst_4 _inst_2 _inst_6)))) (SMulZeroClass.toHasSmul.{u1, u4} R M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (SMulWithZero.toSmulZeroClass.{u1, u4} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u4} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (Module.toMulActionWithZero.{u1, u4} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3))))] [_inst_11 : IsScalarTower.{u1, u3, u4} R B M (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_5)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_5)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_5)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_5))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_5 _inst_9))))) (SMulZeroClass.toHasSmul.{u3, u4} B M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (SMulWithZero.toSmulZeroClass.{u3, u4} B M (MulZeroClass.toHasZero.{u3} B (MulZeroOneClass.toMulZeroClass.{u3} B (MonoidWithZero.toMulZeroOneClass.{u3} B (Semiring.toMonoidWithZero.{u3} B _inst_5)))) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (MulActionWithZero.toSMulWithZero.{u3, u4} B M (Semiring.toMonoidWithZero.{u3} B _inst_5) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (Module.toMulActionWithZero.{u3, u4} B M _inst_5 _inst_2 _inst_7)))) (SMulZeroClass.toHasSmul.{u1, u4} R M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (SMulWithZero.toSmulZeroClass.{u1, u4} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u4} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (Module.toMulActionWithZero.{u1, u4} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3))))] [_inst_12 : SMulCommClass.{u2, u3, u4} A B M (SMulZeroClass.toHasSmul.{u2, u4} A M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (SMulWithZero.toSmulZeroClass.{u2, u4} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_4)))) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u4} A M (Semiring.toMonoidWithZero.{u2} A _inst_4) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (Module.toMulActionWithZero.{u2, u4} A M _inst_4 _inst_2 _inst_6)))) (SMulZeroClass.toHasSmul.{u3, u4} B M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (SMulWithZero.toSmulZeroClass.{u3, u4} B M (MulZeroClass.toHasZero.{u3} B (MulZeroOneClass.toMulZeroClass.{u3} B (MonoidWithZero.toMulZeroOneClass.{u3} B (Semiring.toMonoidWithZero.{u3} B _inst_5)))) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (MulActionWithZero.toSMulWithZero.{u3, u4} B M (Semiring.toMonoidWithZero.{u3} B _inst_5) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2))) (Module.toMulActionWithZero.{u3, u4} B M _inst_5 _inst_2 _inst_7))))], Module.{max u2 u3, u4} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_5))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_8) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_5 _inst_9)) M (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u3} R _inst_1 A _inst_4 _inst_8 B _inst_5 _inst_9) _inst_2
-but is expected to have type
- forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} {M : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u1, u4} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : Semiring.{u2} A] [_inst_5 : Semiring.{u3} B] [_inst_6 : Module.{u2, u4} A M _inst_4 _inst_2] [_inst_7 : Module.{u3, u4} B M _inst_5 _inst_2] [_inst_8 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_5] [_inst_10 : IsScalarTower.{u1, u2, u4} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_4 _inst_8) (SMulZeroClass.toSMul.{u2, u4} A M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u2, u4} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_4)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u4} A M (Semiring.toMonoidWithZero.{u2} A _inst_4) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (Module.toMulActionWithZero.{u2, u4} A M _inst_4 _inst_2 _inst_6)))) (SMulZeroClass.toSMul.{u1, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u4} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u4} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (Module.toMulActionWithZero.{u1, u4} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3))))] [_inst_11 : IsScalarTower.{u1, u3, u4} R B M (Algebra.toSMul.{u1, u3} R B _inst_1 _inst_5 _inst_9) (SMulZeroClass.toSMul.{u3, u4} B M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u3, u4} B M (MonoidWithZero.toZero.{u3} B (Semiring.toMonoidWithZero.{u3} B _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u3, u4} B M (Semiring.toMonoidWithZero.{u3} B _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (Module.toMulActionWithZero.{u3, u4} B M _inst_5 _inst_2 _inst_7)))) (SMulZeroClass.toSMul.{u1, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u4} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u4} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (Module.toMulActionWithZero.{u1, u4} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3))))] [_inst_12 : SMulCommClass.{u2, u3, u4} A B M (SMulZeroClass.toSMul.{u2, u4} A M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u2, u4} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_4)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u4} A M (Semiring.toMonoidWithZero.{u2} A _inst_4) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (Module.toMulActionWithZero.{u2, u4} A M _inst_4 _inst_2 _inst_6)))) (SMulZeroClass.toSMul.{u3, u4} B M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u3, u4} B M (MonoidWithZero.toZero.{u3} B (Semiring.toMonoidWithZero.{u3} B _inst_5)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u3, u4} B M (Semiring.toMonoidWithZero.{u3} B _inst_5) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_2)) (Module.toMulActionWithZero.{u3, u4} B M _inst_5 _inst_2 _inst_7))))], Module.{max u3 u2, u4} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_5))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_8) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_5 _inst_9)) M (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_4 _inst_8 B _inst_5 _inst_9) _inst_2
+<too large>
Case conversion may be inaccurate. Consider using '#align tensor_product.algebra.module TensorProduct.Algebra.moduleₓ'. -/
/-- If `M` is a representation of two different `R`-algebras `A` and `B` whose actions commute,
then it is a representation the `R`-algebra `A ⊗[R] B`.
mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b
@@ -86,7 +86,7 @@ variable [AddCommMonoid P] [Module R P] [Module A P] [IsScalarTower R A P]
lean 3 declaration is
forall {R : Type.{u1}} {A : Type.{u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} A M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u2, u3} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toHasSmul.{u1, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))] [_inst_8 : AddCommMonoid.{u4} N] [_inst_9 : Module.{u1, u4} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8] (a : A) (x : TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9), Eq.{succ (max u3 u4)} (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (SMul.smul.{u2, max u3 u4} A (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (TensorProduct.leftHasSMul.{u1, u2, u3, u4} R _inst_1 A (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) M N _inst_4 _inst_8 _inst_5 _inst_9 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but is expected to have type
- forall {R : Type.{u4}} {A : Type.{u1}} {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u4, u1} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] [_inst_6 : Module.{u1, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u4, u1, u3} R A M (Algebra.toSMul.{u4, u1} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u1, u3} A M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u1, u3} A M (MonoidWithZero.toZero.{u1} A (Semiring.toMonoidWithZero.{u1} A _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u1, u3} A M (Semiring.toMonoidWithZero.{u1} A _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u1, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toSMul.{u4, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u4, u3} R M (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u4, u3} R M (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5))))] [_inst_8 : AddCommMonoid.{u2} N] [_inst_9 : Module.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8] (a : A) (x : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9), Eq.{max (succ u3) (succ u2)} (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (HSMul.hSMul.{u1, max u3 u2, max u3 u2} A (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) 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R _inst_1) _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5)))))) (DistribMulAction.toDistribSMul.{u4, u3} R (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5))))) (Module.toDistribMulAction.{u4, u3} R (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5)))) (Algebra.toModule.{u4, u3} R (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_1 (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Module.instAlgebraEndToSemiringSemiring.{u4, u3} R M _inst_1 _inst_4 _inst_5)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u1, u4, u1, u3} (AlgHom.{u4, u1, u3} R A (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u4, u3} R M _inst_1 _inst_4 _inst_5)) R A (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5))))) (Module.toDistribMulAction.{u4, u1} R A (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u4, u1} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u4, u3} R (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5)))) (Algebra.toModule.{u4, u3} R (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_1 (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Module.instAlgebraEndToSemiringSemiring.{u4, u3} R M _inst_1 _inst_4 _inst_5))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u1, u4, u1, u3} (AlgHom.{u4, u1, u3} R A (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u4, u3} R M _inst_1 _inst_4 _inst_5)) R A (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5))) (Module.toDistribMulAction.{u4, u1} R A (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u4, u1} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u4, u3} R (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5)))) (Algebra.toModule.{u4, u3} R (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_1 (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Module.instAlgebraEndToSemiringSemiring.{u4, u3} R M _inst_1 _inst_4 _inst_5))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u4, u1, u3, max u3 u1} R A (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u4, u3} R M _inst_1 _inst_4 _inst_5) (AlgHom.{u4, u1, u3} R A (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u4, u3} R M _inst_1 _inst_4 _inst_5)) (AlgHom.algHomClass.{u4, u1, u3} R A (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u4, u3} R M _inst_1 _inst_4 _inst_5)))))) (Algebra.lsmul.{u4, u1, u3} R A M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) a)) x)
+ forall {R : Type.{u4}} {A : Type.{u1}} {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u4, u1} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] [_inst_6 : Module.{u1, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u4, u1, u3} R A M (Algebra.toSMul.{u4, u1} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u1, u3} A M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u1, u3} A M (MonoidWithZero.toZero.{u1} A (Semiring.toMonoidWithZero.{u1} A _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u1, u3} A M (Semiring.toMonoidWithZero.{u1} A _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u1, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toSMul.{u4, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u4, u3} R M (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u4, u3} R M (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5))))] [_inst_8 : AddCommMonoid.{u2} N] [_inst_9 : Module.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8] (a : A) (x : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9), Eq.{max (succ u3) (succ u2)} (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (HSMul.hSMul.{u1, max u3 u2, max u3 u2} A (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (instHSMul.{u1, max u3 u2} A (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (TensorProduct.leftHasSMul.{u4, u1, u3, u2} R _inst_1 A (MonoidWithZero.toMonoid.{u1} A (Semiring.toMonoidWithZero.{u1} A _inst_2)) M N _inst_4 _inst_8 _inst_5 _inst_9 (Module.toDistribMulAction.{u1, u3} A M _inst_2 _inst_4 _inst_6) (IsScalarTower.to_smulCommClass.{u4, u1, u3} R _inst_1 A _inst_2 _inst_3 M _inst_4 _inst_6 _inst_5 _inst_7))) a x) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (LinearMap.{u4, u4, max u2 u3, max u2 u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (TensorProduct.addCommMonoid.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (TensorProduct.addCommMonoid.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9)) (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (fun (_x : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) => TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u2, max u3 u2} R R (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (TensorProduct.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (TensorProduct.addCommMonoid.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (TensorProduct.addCommMonoid.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u2} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.rTensor.{u4, u2, u3, u3} R _inst_1 N M M _inst_8 _inst_4 _inst_4 _inst_9 _inst_5 _inst_5 (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (AlgHom.{u4, u1, u3} R A (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u4, u3} R M _inst_1 _inst_4 _inst_5)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _x) (SMulHomClass.toFunLike.{max u3 u1, u4, u1, u3} (AlgHom.{u4, u1, u3} R A (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u4, u3} R M _inst_1 _inst_4 _inst_5)) R A (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (SMulZeroClass.toSMul.{u4, u1} R A (AddMonoid.toZero.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u4, u1} R A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (DistribMulAction.toDistribSMul.{u4, u1} R A (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Module.toDistribMulAction.{u4, u1} R A (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u4, u1} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u4, u3} R (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (AddMonoid.toZero.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5)))))) (DistribSMul.toSMulZeroClass.{u4, u3} R (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (AddMonoid.toAddZeroClass.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5)))))) (DistribMulAction.toDistribSMul.{u4, u3} R (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5))))) (Module.toDistribMulAction.{u4, u3} R (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5)))) (Algebra.toModule.{u4, u3} R (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_1 (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Module.instAlgebraEndToSemiringSemiring.{u4, u3} R M _inst_1 _inst_4 _inst_5)))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u1, u4, u1, u3} (AlgHom.{u4, u1, u3} R A (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u4, u3} R M _inst_1 _inst_4 _inst_5)) R A (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5))))) (Module.toDistribMulAction.{u4, u1} R A (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u4, u1} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u4, u3} R (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5)))) (Algebra.toModule.{u4, u3} R (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_1 (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Module.instAlgebraEndToSemiringSemiring.{u4, u3} R M _inst_1 _inst_4 _inst_5))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u1, u4, u1, u3} (AlgHom.{u4, u1, u3} R A (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u4, u3} R M _inst_1 _inst_4 _inst_5)) R A (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5))) (Module.toDistribMulAction.{u4, u1} R A (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u4, u1} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u4, u3} R (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u3} (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5)))) (Algebra.toModule.{u4, u3} R (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_1 (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) (Module.instAlgebraEndToSemiringSemiring.{u4, u3} R M _inst_1 _inst_4 _inst_5))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u4, u1, u3, max u3 u1} R A (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u4, u3} R M _inst_1 _inst_4 _inst_5) (AlgHom.{u4, u1, u3} R A (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u4, u3} R M _inst_1 _inst_4 _inst_5)) (AlgHom.algHomClass.{u4, u1, u3} R A (Module.End.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_1 _inst_2 (Module.End.semiring.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_5) _inst_3 (Module.instAlgebraEndToSemiringSemiring.{u4, u3} R M _inst_1 _inst_4 _inst_5)))))) (Algebra.lsmul.{u4, u1, u3} R A M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) a)) x)
Case conversion may be inaccurate. Consider using '#align tensor_product.algebra_tensor_module.smul_eq_lsmul_rtensor TensorProduct.AlgebraTensorModule.smul_eq_lsmul_rTensorₓ'. -/
theorem smul_eq_lsmul_rTensor (a : A) (x : M ⊗[R] N) : a • x = (lsmul R M a).rTensor N x :=
rfl
@@ -139,7 +139,7 @@ theorem curry_injective : Function.Injective (curry : (M ⊗ N →ₗ[A] P) →
lean 3 declaration is
forall {R : Type.{u1}} {A : Type.{u2}} {M : Type.{u3}} {N : Type.{u4}} {P : Type.{u5}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} A M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u2, u3} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u2, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toHasSmul.{u1, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))] [_inst_8 : AddCommMonoid.{u4} N] [_inst_9 : Module.{u1, u4} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8] [_inst_10 : AddCommMonoid.{u5} P] [_inst_11 : Module.{u1, u5} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_10] [_inst_12 : Module.{u2, u5} A P _inst_2 _inst_10] [_inst_13 : IsScalarTower.{u1, u2, u5} R A P (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u5} A P (AddZeroClass.toHasZero.{u5} P (AddMonoid.toAddZeroClass.{u5} P (AddCommMonoid.toAddMonoid.{u5} P _inst_10))) (SMulWithZero.toSmulZeroClass.{u2, u5} A P (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u5} P (AddMonoid.toAddZeroClass.{u5} P (AddCommMonoid.toAddMonoid.{u5} P _inst_10))) (MulActionWithZero.toSMulWithZero.{u2, u5} A P (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u5} P (AddMonoid.toAddZeroClass.{u5} P (AddCommMonoid.toAddMonoid.{u5} P _inst_10))) (Module.toMulActionWithZero.{u2, u5} A P _inst_2 _inst_10 _inst_12)))) (SMulZeroClass.toHasSmul.{u1, u5} R P 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but is expected to have type
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(SMulZeroClass.toSMul.{u1, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))] [_inst_8 : AddCommMonoid.{u4} N] [_inst_9 : Module.{u1, u4} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8] [_inst_10 : AddCommMonoid.{u2} P] [_inst_11 : Module.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_10] [_inst_12 : Module.{u5, u2} A P _inst_2 _inst_10] [_inst_13 : IsScalarTower.{u1, u5, u2} R A P (Algebra.toSMul.{u1, u5} R A _inst_1 _inst_2 _inst_3) 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u5, max u3 u4, u2} A A (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) P _inst_2 _inst_2 (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) _inst_10 (TensorProduct.leftModule.{u1, u5, u3, u4} R _inst_1 A _inst_2 M N _inst_4 _inst_8 _inst_5 _inst_9 _inst_6 (IsScalarTower.to_smulCommClass.{u1, u5, u3} R _inst_1 A _inst_2 _inst_3 M _inst_4 _inst_6 _inst_5 _inst_7)) _inst_12 (RingHom.id.{u5} A (Semiring.toNonAssocSemiring.{u5} A _inst_2))) h (TensorProduct.tmul.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9 x y))) -> (Eq.{max (max (succ u3) (succ u4)) (succ u2)} (LinearMap.{u5, u5, max u4 u3, u2} A A _inst_2 _inst_2 (RingHom.id.{u5} A (Semiring.toNonAssocSemiring.{u5} A _inst_2)) (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) P (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) _inst_10 (TensorProduct.leftModule.{u1, u5, u3, u4} R _inst_1 A _inst_2 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+ forall {R : Type.{u1}} {A : Type.{u5}} {M : Type.{u3}} {N : Type.{u4}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u5} A] [_inst_3 : Algebra.{u1, u5} R A _inst_1 _inst_2] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u5, u3} A M _inst_2 _inst_4] [_inst_7 : IsScalarTower.{u1, u5, u3} R A M (Algebra.toSMul.{u1, u5} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u5, u3} A M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u5, u3} A M (MonoidWithZero.toZero.{u5} A (Semiring.toMonoidWithZero.{u5} A _inst_2)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u5, u3} A M (Semiring.toMonoidWithZero.{u5} A _inst_2) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u5, u3} A M _inst_2 _inst_4 _inst_6)))) (SMulZeroClass.toSMul.{u1, u3} R M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))] [_inst_8 : AddCommMonoid.{u4} N] [_inst_9 : Module.{u1, u4} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8] [_inst_10 : AddCommMonoid.{u2} P] [_inst_11 : Module.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_10] [_inst_12 : Module.{u5, u2} A P _inst_2 _inst_10] [_inst_13 : IsScalarTower.{u1, u5, u2} R A P (Algebra.toSMul.{u1, u5} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u5, u2} A P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_10)) (SMulWithZero.toSMulZeroClass.{u5, u2} A P (MonoidWithZero.toZero.{u5} A (Semiring.toMonoidWithZero.{u5} A _inst_2)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_10)) (MulActionWithZero.toSMulWithZero.{u5, u2} A P (Semiring.toMonoidWithZero.{u5} A _inst_2) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_10)) (Module.toMulActionWithZero.{u5, u2} A P _inst_2 _inst_10 _inst_12)))) (SMulZeroClass.toSMul.{u1, u2} R P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_10)) (SMulWithZero.toSMulZeroClass.{u1, u2} R P (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_10)) (MulActionWithZero.toSMulWithZero.{u1, u2} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_10)) (Module.toMulActionWithZero.{u1, u2} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_10 _inst_11))))] {g : LinearMap.{u5, u5, max u4 u3, u2} A A _inst_2 _inst_2 (RingHom.id.{u5} A (Semiring.toNonAssocSemiring.{u5} A _inst_2)) (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) P (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) _inst_10 (TensorProduct.leftModule.{u1, u5, u3, u4} R _inst_1 A _inst_2 M N _inst_4 _inst_8 _inst_5 _inst_9 _inst_6 (IsScalarTower.to_smulCommClass.{u1, u5, u3} R _inst_1 A _inst_2 _inst_3 M _inst_4 _inst_6 _inst_5 _inst_7)) _inst_12} {h : LinearMap.{u5, u5, max u4 u3, u2} A A _inst_2 _inst_2 (RingHom.id.{u5} A (Semiring.toNonAssocSemiring.{u5} A _inst_2)) (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) P (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) _inst_10 (TensorProduct.leftModule.{u1, u5, u3, u4} R _inst_1 A _inst_2 M N _inst_4 _inst_8 _inst_5 _inst_9 _inst_6 (IsScalarTower.to_smulCommClass.{u1, u5, u3} R _inst_1 A _inst_2 _inst_3 M _inst_4 _inst_6 _inst_5 _inst_7)) _inst_12}, (forall (x : M) (y : N), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) => P) (TensorProduct.tmul.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9 x y)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u4), succ u2} (LinearMap.{u5, u5, max u4 u3, u2} A A _inst_2 _inst_2 (RingHom.id.{u5} A (Semiring.toNonAssocSemiring.{u5} A _inst_2)) (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) P (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) _inst_10 (TensorProduct.leftModule.{u1, u5, u3, u4} R _inst_1 A _inst_2 M N _inst_4 _inst_8 _inst_5 _inst_9 _inst_6 (IsScalarTower.to_smulCommClass.{u1, u5, u3} R _inst_1 A _inst_2 _inst_3 M _inst_4 _inst_6 _inst_5 _inst_7)) _inst_12) (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (fun (_x : TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) => P) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, max u3 u4, u2} A A (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) P _inst_2 _inst_2 (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) _inst_10 (TensorProduct.leftModule.{u1, u5, u3, u4} R _inst_1 A _inst_2 M N _inst_4 _inst_8 _inst_5 _inst_9 _inst_6 (IsScalarTower.to_smulCommClass.{u1, u5, u3} R _inst_1 A _inst_2 _inst_3 M _inst_4 _inst_6 _inst_5 _inst_7)) _inst_12 (RingHom.id.{u5} A (Semiring.toNonAssocSemiring.{u5} A _inst_2))) g (TensorProduct.tmul.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9 x y)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u3) (succ u4), succ u2} (LinearMap.{u5, u5, max u4 u3, u2} A A _inst_2 _inst_2 (RingHom.id.{u5} A (Semiring.toNonAssocSemiring.{u5} A _inst_2)) (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) P (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) _inst_10 (TensorProduct.leftModule.{u1, u5, u3, u4} R _inst_1 A _inst_2 M N _inst_4 _inst_8 _inst_5 _inst_9 _inst_6 (IsScalarTower.to_smulCommClass.{u1, u5, u3} R _inst_1 A _inst_2 _inst_3 M _inst_4 _inst_6 _inst_5 _inst_7)) _inst_12) (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) (fun (_x : TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) => P) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, max u3 u4, u2} A A (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) P _inst_2 _inst_2 (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) _inst_10 (TensorProduct.leftModule.{u1, u5, u3, u4} R _inst_1 A _inst_2 M N _inst_4 _inst_8 _inst_5 _inst_9 _inst_6 (IsScalarTower.to_smulCommClass.{u1, u5, u3} R _inst_1 A _inst_2 _inst_3 M _inst_4 _inst_6 _inst_5 _inst_7)) _inst_12 (RingHom.id.{u5} A (Semiring.toNonAssocSemiring.{u5} A _inst_2))) h (TensorProduct.tmul.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9 x y))) -> (Eq.{max (max (succ u3) (succ u4)) (succ u2)} (LinearMap.{u5, u5, max u4 u3, u2} A A _inst_2 _inst_2 (RingHom.id.{u5} A (Semiring.toNonAssocSemiring.{u5} A _inst_2)) (TensorProduct.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) P (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 M N _inst_4 _inst_8 _inst_5 _inst_9) _inst_10 (TensorProduct.leftModule.{u1, u5, u3, u4} R _inst_1 A _inst_2 M N _inst_4 _inst_8 _inst_5 _inst_9 _inst_6 (IsScalarTower.to_smulCommClass.{u1, u5, u3} R _inst_1 A _inst_2 _inst_3 M _inst_4 _inst_6 _inst_5 _inst_7)) _inst_12) g h)
Case conversion may be inaccurate. Consider using '#align tensor_product.algebra_tensor_module.ext TensorProduct.AlgebraTensorModule.extₓ'. -/
theorem ext {g h : M ⊗[R] N →ₗ[A] P} (H : ∀ x y, g (x ⊗ₜ y) = h (x ⊗ₜ y)) : g = h :=
curry_injective <| LinearMap.ext₂ H
@@ -183,7 +183,7 @@ def lift (f : M →ₗ[A] N →ₗ[R] P) : M ⊗[R] N →ₗ[A] P :=
lean 3 declaration is
forall {R : Type.{u1}} {A : Type.{u2}} {M : Type.{u3}} {N : Type.{u4}} {P : Type.{u5}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u2, u3} A M (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R A M (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} A M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u2, u3} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u2, u3} A M (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u2, u3} A M (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4 _inst_6)))) (SMulZeroClass.toHasSmul.{u1, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))] [_inst_8 : AddCommMonoid.{u4} N] [_inst_9 : Module.{u1, u4} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8] [_inst_10 : AddCommMonoid.{u5} P] [_inst_11 : Module.{u1, u5} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_10] [_inst_12 : Module.{u2, u5} A P (CommSemiring.toSemiring.{u2} A _inst_2) _inst_10] [_inst_13 : IsScalarTower.{u1, u2, u5} R A P (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u5} A P (AddZeroClass.toHasZero.{u5} P (AddMonoid.toAddZeroClass.{u5} P (AddCommMonoid.toAddMonoid.{u5} P _inst_10))) (SMulWithZero.toSmulZeroClass.{u2, u5} A P (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) (AddZeroClass.toHasZero.{u5} P (AddMonoid.toAddZeroClass.{u5} P (AddCommMonoid.toAddMonoid.{u5} P _inst_10))) (MulActionWithZero.toSMulWithZero.{u2, u5} A P (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (AddZeroClass.toHasZero.{u5} P (AddMonoid.toAddZeroClass.{u5} P (AddCommMonoid.toAddMonoid.{u5} P _inst_10))) (Module.toMulActionWithZero.{u2, u5} A P (CommSemiring.toSemiring.{u2} A _inst_2) _inst_10 _inst_12)))) (SMulZeroClass.toHasSmul.{u1, u5} R P (AddZeroClass.toHasZero.{u5} P (AddMonoid.toAddZeroClass.{u5} P (AddCommMonoid.toAddMonoid.{u5} P _inst_10))) (SMulWithZero.toSmulZeroClass.{u1, u5} R P (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u5} P 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(Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) f x) y)
but is expected to have type
- forall {R : Type.{u1}} {A : Type.{u5}} {M : Type.{u4}} {N : Type.{u2}} {P : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u5} A] [_inst_3 : Algebra.{u1, u5} R A _inst_1 (CommSemiring.toSemiring.{u5} A _inst_2)] [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : Module.{u1, u4} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u5, u4} A M (CommSemiring.toSemiring.{u5} A _inst_2) _inst_4] [_inst_7 : IsScalarTower.{u1, u5, u4} R A M (Algebra.toSMul.{u1, u5} R A _inst_1 (CommSemiring.toSemiring.{u5} A _inst_2) _inst_3) (SMulZeroClass.toSMul.{u5, u4} A M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u5, u4} A M (CommMonoidWithZero.toZero.{u5} A (CommSemiring.toCommMonoidWithZero.{u5} A _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u5, u4} A M (Semiring.toMonoidWithZero.{u5} A (CommSemiring.toSemiring.{u5} A _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_4)) (Module.toMulActionWithZero.{u5, u4} A M (CommSemiring.toSemiring.{u5} A _inst_2) _inst_4 _inst_6)))) (SMulZeroClass.toSMul.{u1, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u1, u4} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u1, u4} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_4)) (Module.toMulActionWithZero.{u1, u4} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))] [_inst_8 : AddCommMonoid.{u2} N] [_inst_9 : Module.{u1, u2} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8] [_inst_10 : AddCommMonoid.{u3} P] [_inst_11 : Module.{u1, u3} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_10] [_inst_12 : Module.{u5, u3} A P (CommSemiring.toSemiring.{u5} A _inst_2) _inst_10] [_inst_13 : IsScalarTower.{u1, u5, u3} R A P (Algebra.toSMul.{u1, u5} R A _inst_1 (CommSemiring.toSemiring.{u5} A _inst_2) _inst_3) (SMulZeroClass.toSMul.{u5, u3} A P (AddMonoid.toZero.{u3} P (AddCommMonoid.toAddMonoid.{u3} P _inst_10)) (SMulWithZero.toSMulZeroClass.{u5, u3} A P (CommMonoidWithZero.toZero.{u5} A (CommSemiring.toCommMonoidWithZero.{u5} A _inst_2)) (AddMonoid.toZero.{u3} P (AddCommMonoid.toAddMonoid.{u3} P _inst_10)) (MulActionWithZero.toSMulWithZero.{u5, u3} A P (Semiring.toMonoidWithZero.{u5} A (CommSemiring.toSemiring.{u5} A _inst_2)) (AddMonoid.toZero.{u3} P (AddCommMonoid.toAddMonoid.{u3} P _inst_10)) (Module.toMulActionWithZero.{u5, u3} A P (CommSemiring.toSemiring.{u5} A _inst_2) _inst_10 _inst_12)))) (SMulZeroClass.toSMul.{u1, u3} R P (AddMonoid.toZero.{u3} P (AddCommMonoid.toAddMonoid.{u3} P _inst_10)) (SMulWithZero.toSMulZeroClass.{u1, u3} R P (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} P (AddCommMonoid.toAddMonoid.{u3} P _inst_10)) (MulActionWithZero.toSMulWithZero.{u1, u3} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} P (AddCommMonoid.toAddMonoid.{u3} P _inst_10)) (Module.toMulActionWithZero.{u1, u3} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_10 _inst_11))))] (f : LinearMap.{u5, u5, u4, max u3 u2} A A (CommSemiring.toSemiring.{u5} A _inst_2) (CommSemiring.toSemiring.{u5} A _inst_2) (RingHom.id.{u5} A (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_2))) M (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_8 _inst_10 _inst_9 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) 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+ forall {R : Type.{u1}} {A : Type.{u5}} {M : Type.{u4}} {N : Type.{u2}} {P : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u5} A] [_inst_3 : Algebra.{u1, u5} R A _inst_1 (CommSemiring.toSemiring.{u5} A _inst_2)] [_inst_4 : AddCommMonoid.{u4} M] [_inst_5 : Module.{u1, u4} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] [_inst_6 : Module.{u5, u4} A M (CommSemiring.toSemiring.{u5} A _inst_2) _inst_4] [_inst_7 : IsScalarTower.{u1, u5, u4} R A M (Algebra.toSMul.{u1, u5} R A _inst_1 (CommSemiring.toSemiring.{u5} A _inst_2) _inst_3) (SMulZeroClass.toSMul.{u5, u4} A M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u5, u4} A M (CommMonoidWithZero.toZero.{u5} A (CommSemiring.toCommMonoidWithZero.{u5} A _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u5, u4} A M (Semiring.toMonoidWithZero.{u5} A (CommSemiring.toSemiring.{u5} A _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_4)) (Module.toMulActionWithZero.{u5, u4} A M (CommSemiring.toSemiring.{u5} A _inst_2) _inst_4 _inst_6)))) (SMulZeroClass.toSMul.{u1, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u1, u4} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u1, u4} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_4)) (Module.toMulActionWithZero.{u1, u4} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5))))] [_inst_8 : AddCommMonoid.{u2} N] [_inst_9 : Module.{u1, u2} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8] [_inst_10 : AddCommMonoid.{u3} P] [_inst_11 : Module.{u1, u3} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_10] [_inst_12 : Module.{u5, u3} A P (CommSemiring.toSemiring.{u5} A _inst_2) _inst_10] [_inst_13 : IsScalarTower.{u1, u5, u3} R A P (Algebra.toSMul.{u1, u5} R A _inst_1 (CommSemiring.toSemiring.{u5} A _inst_2) _inst_3) (SMulZeroClass.toSMul.{u5, u3} A P (AddMonoid.toZero.{u3} P (AddCommMonoid.toAddMonoid.{u3} P _inst_10)) (SMulWithZero.toSMulZeroClass.{u5, u3} A P (CommMonoidWithZero.toZero.{u5} A (CommSemiring.toCommMonoidWithZero.{u5} A _inst_2)) (AddMonoid.toZero.{u3} P (AddCommMonoid.toAddMonoid.{u3} P _inst_10)) (MulActionWithZero.toSMulWithZero.{u5, u3} A P (Semiring.toMonoidWithZero.{u5} A (CommSemiring.toSemiring.{u5} A _inst_2)) (AddMonoid.toZero.{u3} P (AddCommMonoid.toAddMonoid.{u3} P _inst_10)) (Module.toMulActionWithZero.{u5, u3} A P (CommSemiring.toSemiring.{u5} A _inst_2) _inst_10 _inst_12)))) (SMulZeroClass.toSMul.{u1, u3} R P (AddMonoid.toZero.{u3} P (AddCommMonoid.toAddMonoid.{u3} P _inst_10)) (SMulWithZero.toSMulZeroClass.{u1, u3} R P (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} P (AddCommMonoid.toAddMonoid.{u3} P _inst_10)) (MulActionWithZero.toSMulWithZero.{u1, u3} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} P (AddCommMonoid.toAddMonoid.{u3} P _inst_10)) (Module.toMulActionWithZero.{u1, u3} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_10 _inst_11))))] (f : LinearMap.{u5, u5, u4, max u3 u2} A A (CommSemiring.toSemiring.{u5} A _inst_2) (CommSemiring.toSemiring.{u5} A _inst_2) (RingHom.id.{u5} A (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_2))) M (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_8 _inst_10 _inst_9 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) 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(CommSemiring.toSemiring.{u5} A _inst_2))) M (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_8 _inst_10 _inst_9 _inst_11) _inst_4 (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8 _inst_10 _inst_9 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_6 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u5, u2, u3} R R A N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8 _inst_10 _inst_9 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u5} A _inst_2) _inst_12 (IsScalarTower.to_smulCommClass.{u1, u5, u3} R _inst_1 A 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(RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_6 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u5, u2, u3} R R A N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8 _inst_10 _inst_9 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u5} A _inst_2) _inst_12 (IsScalarTower.to_smulCommClass.{u1, u5, u3} R _inst_1 A (CommSemiring.toSemiring.{u5} A _inst_2) _inst_3 P _inst_10 _inst_12 _inst_11 _inst_13)) (RingHom.id.{u5} A (Semiring.toNonAssocSemiring.{u5} A (CommSemiring.toSemiring.{u5} A _inst_2)))) f x) y)
Case conversion may be inaccurate. Consider using '#align tensor_product.algebra_tensor_module.lift_tmul TensorProduct.AlgebraTensorModule.lift_tmulₓ'. -/
@[simp]
theorem lift_tmul (f : M →ₗ[A] N →ₗ[R] P) (x : M) (y : N) : lift f (x ⊗ₜ y) = f x y :=
@@ -325,7 +325,7 @@ variable {A}
lean 3 declaration is
forall {R : Type.{u1}} {A : Type.{u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_6 : AddCommMonoid.{u3} M] [_inst_7 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] [_inst_8 : AddCommMonoid.{u4} N] [_inst_9 : Module.{u1, u4} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8] (f : LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M N _inst_6 _inst_8 _inst_7 _inst_9) (a : A) (x : M), Eq.{succ (max u2 u4)} (TensorProduct.{u1, u2, u4} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_9) (coeFn.{max (succ (max u2 u3)) (succ (max u2 u4)), max (succ (max u2 u3)) (succ (max u2 u4))} (LinearMap.{u2, u2, max u2 u3, max u2 u4} A A _inst_2 _inst_2 (RingHom.id.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (TensorProduct.{u1, u2, u3} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_6 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_7) (TensorProduct.{u1, u2, u4} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_9) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_6 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_7) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_9) (TensorProduct.leftModule.{u1, u2, u2, u3} R _inst_1 A _inst_2 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_6 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_7 (Semiring.toModule.{u2} A _inst_2) (Algebra.to_smulCommClass.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (TensorProduct.leftModule.{u1, u2, u2, u4} R _inst_1 A _inst_2 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_9 (Semiring.toModule.{u2} A _inst_2) (Algebra.to_smulCommClass.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (fun (_x : LinearMap.{u2, u2, max u2 u3, max u2 u4} A A _inst_2 _inst_2 (RingHom.id.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (TensorProduct.{u1, u2, u3} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_6 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_7) (TensorProduct.{u1, u2, u4} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_9) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_6 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_7) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_9) (TensorProduct.leftModule.{u1, u2, u2, u3} R _inst_1 A _inst_2 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_6 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_7 (Semiring.toModule.{u2} A _inst_2) (Algebra.to_smulCommClass.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (TensorProduct.leftModule.{u1, u2, u2, u4} R _inst_1 A _inst_2 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_9 (Semiring.toModule.{u2} A _inst_2) (Algebra.to_smulCommClass.{u1, u2} R A _inst_1 _inst_2 _inst_3))) => (TensorProduct.{u1, u2, u3} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_6 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_7) -> (TensorProduct.{u1, u2, u4} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_9)) (LinearMap.hasCoeToFun.{u2, u2, max u2 u3, max u2 u4} A A (TensorProduct.{u1, u2, u3} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_6 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_7) (TensorProduct.{u1, u2, u4} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_9) _inst_2 _inst_2 (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_6 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_7) (TensorProduct.addCommMonoid.{u1, u2, u4} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_9) (TensorProduct.leftModule.{u1, u2, u2, u3} R _inst_1 A _inst_2 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_6 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_7 (Semiring.toModule.{u2} A _inst_2) (Algebra.to_smulCommClass.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (TensorProduct.leftModule.{u1, u2, u2, u4} R _inst_1 A _inst_2 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_9 (Semiring.toModule.{u2} A _inst_2) (Algebra.to_smulCommClass.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (LinearMap.baseChange.{u1, u2, u3, u4} R A M N _inst_1 _inst_2 _inst_3 _inst_6 _inst_7 _inst_8 _inst_9 f) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_6 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_7 a x)) (TensorProduct.tmul.{u1, u2, u4} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_8 (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) _inst_9 a (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M N _inst_6 _inst_8 _inst_7 _inst_9) (fun (_x : LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M N _inst_6 _inst_8 _inst_7 _inst_9) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, u3, u4} R R M N (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_8 _inst_7 _inst_9 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f x))
but is expected to have type
- forall {R : Type.{u2}} {A : Type.{u4}} {M : Type.{u1}} {N : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u4} A] [_inst_3 : Algebra.{u2, u4} R A _inst_1 _inst_2] [_inst_6 : AddCommMonoid.{u1} M] [_inst_7 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_6] [_inst_8 : AddCommMonoid.{u3} N] [_inst_9 : Module.{u2, u3} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_8] (f : LinearMap.{u2, u2, u1, u3} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) M N _inst_6 _inst_8 _inst_7 _inst_9) (a : A) (x : M), Eq.{max (succ u4) (succ u3)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u2, u4, u1} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_6 (Algebra.toModule.{u2, u4} R A 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_6 (Algebra.toModule.{u2, u4} R A _inst_1 _inst_2 _inst_3) _inst_7 (Semiring.toModule.{u4} A _inst_2) (Algebra.to_smulCommClass.{u2, u4} R A _inst_1 _inst_2 _inst_3)) (TensorProduct.leftModule.{u2, u4, u4, u3} R _inst_1 A _inst_2 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_8 (Algebra.toModule.{u2, u4} R A _inst_1 _inst_2 _inst_3) _inst_9 (Semiring.toModule.{u4} A _inst_2) (Algebra.to_smulCommClass.{u2, u4} R A _inst_1 _inst_2 _inst_3))) (TensorProduct.{u2, u4, u1} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_6 (Algebra.toModule.{u2, u4} R A _inst_1 _inst_2 _inst_3) _inst_7) (fun (_x : TensorProduct.{u2, u4, u1} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_6 (Algebra.toModule.{u2, u4} R A _inst_1 _inst_2 _inst_3) _inst_7) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u2, u4, u1} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_6 (Algebra.toModule.{u2, u4} R A _inst_1 _inst_2 _inst_3) _inst_7) => TensorProduct.{u2, u4, u3} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_8 (Algebra.toModule.{u2, u4} R A _inst_1 _inst_2 _inst_3) _inst_9) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u4 u1, max u4 u3} A A (TensorProduct.{u2, u4, u1} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_6 (Algebra.toModule.{u2, u4} R A _inst_1 _inst_2 _inst_3) _inst_7) (TensorProduct.{u2, u4, u3} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_8 (Algebra.toModule.{u2, u4} R A _inst_1 _inst_2 _inst_3) _inst_9) _inst_2 _inst_2 (TensorProduct.addCommMonoid.{u2, u4, u1} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_6 (Algebra.toModule.{u2, u4} R A _inst_1 _inst_2 _inst_3) _inst_7) (TensorProduct.addCommMonoid.{u2, u4, u3} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_8 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_inst_8 _inst_9 f) (TensorProduct.tmul.{u2, u4, u1} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_6 (Algebra.toModule.{u2, u4} R A _inst_1 _inst_2 _inst_3) _inst_7 a x)) (TensorProduct.tmul.{u2, u4, u3} R _inst_1 A ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_8 (Algebra.toModule.{u2, u4} R A _inst_1 _inst_2 _inst_3) _inst_9 a (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (LinearMap.{u2, u2, u1, u3} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) M N _inst_6 _inst_8 _inst_7 _inst_9) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u3} R R M N (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_6 _inst_8 _inst_7 _inst_9 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) f x))
+ forall {R : Type.{u2}} {A : Type.{u4}} {M : Type.{u1}} {N : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u4} A] [_inst_3 : Algebra.{u2, u4} R A _inst_1 _inst_2] [_inst_6 : AddCommMonoid.{u1} M] [_inst_7 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_6] [_inst_8 : AddCommMonoid.{u3} N] [_inst_9 : Module.{u2, u3} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_8] (f : LinearMap.{u2, u2, u1, u3} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) M N _inst_6 _inst_8 _inst_7 _inst_9) (a : A) (x : M), Eq.{max (succ u4) (succ u3)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u2, u4, u1} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_6 (Algebra.toModule.{u2, u4} R A _inst_1 _inst_2 _inst_3) _inst_7) => TensorProduct.{u2, u4, u3} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_8 (Algebra.toModule.{u2, u4} R A _inst_1 _inst_2 _inst_3) _inst_9) (TensorProduct.tmul.{u2, u4, u1} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_6 (Algebra.toModule.{u2, u4} R A _inst_1 _inst_2 _inst_3) _inst_7 a x)) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u3), max (succ u4) (succ u1), max (succ u4) (succ u3)} (LinearMap.{u4, u4, max u1 u4, max u3 u4} A A _inst_2 _inst_2 (RingHom.id.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2)) (TensorProduct.{u2, u4, u1} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_6 (Algebra.toModule.{u2, u4} R A _inst_1 _inst_2 _inst_3) _inst_7) (TensorProduct.{u2, u4, u3} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_8 (Algebra.toModule.{u2, u4} R A _inst_1 _inst_2 _inst_3) _inst_9) (TensorProduct.addCommMonoid.{u2, u4, u1} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_6 (Algebra.toModule.{u2, u4} R A _inst_1 _inst_2 _inst_3) _inst_7) (TensorProduct.addCommMonoid.{u2, u4, u3} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_8 (Algebra.toModule.{u2, u4} R A _inst_1 _inst_2 _inst_3) _inst_9) (TensorProduct.leftModule.{u2, u4, u4, u1} R _inst_1 A _inst_2 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_6 (Algebra.toModule.{u2, u4} R A _inst_1 _inst_2 _inst_3) _inst_7 (Semiring.toModule.{u4} A _inst_2) (Algebra.to_smulCommClass.{u2, u4} R A _inst_1 _inst_2 _inst_3)) (TensorProduct.leftModule.{u2, u4, u4, u3} R _inst_1 A _inst_2 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_8 (Algebra.toModule.{u2, u4} R A _inst_1 _inst_2 _inst_3) _inst_9 (Semiring.toModule.{u4} A _inst_2) (Algebra.to_smulCommClass.{u2, u4} R A _inst_1 _inst_2 _inst_3))) (TensorProduct.{u2, u4, u1} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_6 (Algebra.toModule.{u2, u4} R A _inst_1 _inst_2 _inst_3) _inst_7) (fun (_x : TensorProduct.{u2, u4, u1} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_6 (Algebra.toModule.{u2, u4} R A _inst_1 _inst_2 _inst_3) _inst_7) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u2, u4, u1} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_6 (Algebra.toModule.{u2, u4} R A _inst_1 _inst_2 _inst_3) _inst_7) => TensorProduct.{u2, u4, u3} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_8 (Algebra.toModule.{u2, u4} R A _inst_1 _inst_2 _inst_3) _inst_9) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u4 u1, max u4 u3} A A (TensorProduct.{u2, u4, u1} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_6 (Algebra.toModule.{u2, u4} R A _inst_1 _inst_2 _inst_3) _inst_7) (TensorProduct.{u2, u4, u3} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_8 (Algebra.toModule.{u2, u4} R A _inst_1 _inst_2 _inst_3) _inst_9) _inst_2 _inst_2 (TensorProduct.addCommMonoid.{u2, u4, u1} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_6 (Algebra.toModule.{u2, u4} R A _inst_1 _inst_2 _inst_3) _inst_7) (TensorProduct.addCommMonoid.{u2, u4, u3} R _inst_1 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_8 (Algebra.toModule.{u2, u4} R A _inst_1 _inst_2 _inst_3) _inst_9) (TensorProduct.leftModule.{u2, u4, u4, u1} R _inst_1 A _inst_2 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_6 (Algebra.toModule.{u2, u4} R A _inst_1 _inst_2 _inst_3) _inst_7 (Semiring.toModule.{u4} A _inst_2) (Algebra.to_smulCommClass.{u2, u4} R A _inst_1 _inst_2 _inst_3)) (TensorProduct.leftModule.{u2, u4, u4, u3} R _inst_1 A _inst_2 A N (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_8 (Algebra.toModule.{u2, u4} R A _inst_1 _inst_2 _inst_3) _inst_9 (Semiring.toModule.{u4} A _inst_2) (Algebra.to_smulCommClass.{u2, u4} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) (LinearMap.baseChange.{u2, u4, u1, u3} R A M N _inst_1 _inst_2 _inst_3 _inst_6 _inst_7 _inst_8 _inst_9 f) (TensorProduct.tmul.{u2, u4, u1} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_6 (Algebra.toModule.{u2, u4} R A _inst_1 _inst_2 _inst_3) _inst_7 a x)) (TensorProduct.tmul.{u2, u4, u3} R _inst_1 A ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => N) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) _inst_8 (Algebra.toModule.{u2, u4} R A _inst_1 _inst_2 _inst_3) _inst_9 a (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (LinearMap.{u2, u2, u1, u3} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) M N _inst_6 _inst_8 _inst_7 _inst_9) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u3} R R M N (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_6 _inst_8 _inst_7 _inst_9 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) f x))
Case conversion may be inaccurate. Consider using '#align linear_map.base_change_tmul LinearMap.baseChange_tmulₓ'. -/
@[simp]
theorem baseChange_tmul (a : A) (x : M) : f.base_change A (a ⊗ₜ x) = a ⊗ₜ f x :=
@@ -336,7 +336,7 @@ theorem baseChange_tmul (a : A) (x : M) : f.base_change A (a ⊗ₜ x) = a ⊗
lean 3 declaration is
forall {R : Type.{u1}} {A : Type.{u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_6 : AddCommMonoid.{u3} M] [_inst_7 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] [_inst_8 : AddCommMonoid.{u4} N] [_inst_9 : Module.{u1, u4} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_8] (f : LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M N _inst_6 _inst_8 _inst_7 _inst_9), Eq.{max (succ (max u2 u3)) (succ (max u2 u4))} ((fun (_x : LinearMap.{u2, u2, max u2 u3, max u2 u4} A A _inst_2 _inst_2 (RingHom.id.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (TensorProduct.{u1, u2, u3} R _inst_1 A M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A 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but is expected to have type
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Case conversion may be inaccurate. Consider using '#align linear_map.base_change_eq_ltensor LinearMap.baseChange_eq_ltensorₓ'. -/
theorem baseChange_eq_ltensor : (f.base_change A : A ⊗ M → A ⊗ N) = f.lTensor A :=
rfl
@@ -472,7 +472,7 @@ def mulAux (a₁ : A) (b₁ : B) : A ⊗[R] B →ₗ[R] A ⊗[R] B :=
lean 3 declaration is
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but is expected to have type
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_inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.TensorProduct.mulAux.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5 a₁ b₁) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a₂ b₂)) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) a₁ a₂) (HMul.hMul.{u3, u3, u3} B B B (instHMul.{u3} B (NonUnitalNonAssocSemiring.toMul.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) b₁ b₂))
+ forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (a₁ : A) (a₂ : A) (b₁ : B) (b₂ : B), Eq.{max (succ u2) (succ u3)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a₂ b₂)) (FunLike.coe.{max (succ u2) (succ u3), max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, max u3 u2, max u3 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (fun (_x : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u3, max u2 u3} R R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.TensorProduct.mulAux.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5 a₁ b₁) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a₂ b₂)) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) a₁ a₂) (HMul.hMul.{u3, u3, u3} B B B (instHMul.{u3} B (NonUnitalNonAssocSemiring.toMul.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) b₁ b₂))
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.mul_aux_apply Algebra.TensorProduct.mulAux_applyₓ'. -/
@[simp]
theorem mulAux_apply (a₁ a₂ : A) (b₁ b₂ : B) :
@@ -511,7 +511,7 @@ def mul : A ⊗[R] B →ₗ[R] A ⊗[R] B →ₗ[R] A ⊗[R] B :=
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (a₁ : A) (a₂ : A) (b₁ : B) (b₂ : B), Eq.{succ (max u2 u3)} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (coeFn.{succ (max u2 u3), succ (max u2 u3)} (LinearMap.{u1, u1, max u2 u3, max u2 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R 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(Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u3, max u2 u3} R R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (LinearMap.{u1, u1, max u2 u3, max u2 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, max u2 u3} R R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (LinearMap.module.{u1, u1, u1, max u2 u3, max u2 u3} R R R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.TensorProduct.mul._proof_1.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.TensorProduct.mul.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a₁ b₁)) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a₂ b₂)) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) a₁ a₂) (HMul.hMul.{u3, u3, u3} B B B (instHMul.{u3} B (Distrib.toHasMul.{u3} B (NonUnitalNonAssocSemiring.toDistrib.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) b₁ b₂))
but is expected to have type
- forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (a₁ : A) (a₂ : A) (b₁ : B) (b₂ : B), Eq.{max (succ u2) (succ u3)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.TensorProduct.mul.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a₁ b₁)) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a₂ b₂)) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) a₁ a₂) (HMul.hMul.{u3, u3, u3} B B B (instHMul.{u3} B (NonUnitalNonAssocSemiring.toMul.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) b₁ b₂))
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.mul_apply Algebra.TensorProduct.mul_applyₓ'. -/
@[simp]
theorem mul_apply (a₁ a₂ : A) (b₁ b₂ : B) :
@@ -523,7 +523,7 @@ theorem mul_apply (a₁ a₂ : A) (b₁ b₂ : B) :
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (mul : LinearMap.{u1, u1, max u2 u3, max u2 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (LinearMap.{u1, u1, max u2 u3, max u2 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, max u2 u3} R R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (LinearMap.module.{u1, u1, u1, max u2 u3, max u2 u3} R R R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (smulCommClass_self.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) 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u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (LinearMap.module.{u1, u1, u1, max u2 u3, max u2 u3} R R R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 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(Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (Module.toMulActionWithZero.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))))) => (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (Module.toMulActionWithZero.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) mul y) z)))
but is expected to have type
- forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (mul : LinearMap.{u1, u1, max u3 u2, max u3 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (LinearMap.{u1, u1, max u3 u2, max u3 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, max u2 u3} R R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, max u2 u3} R R R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A 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_inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} 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R B _inst_1 _inst_4 _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (smulCommClass_self.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))) (Module.toMulActionWithZero.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) mul y) z)))
+ forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (mul : LinearMap.{u1, u1, max u3 u2, max u3 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (LinearMap.{u1, u1, max u3 u2, max u3 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, max u2 u3} R R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, max u2 u3} R R R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A 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R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => LinearMap.{u1, u1, max u3 u2, max u3 u2} R R 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u3} R B _inst_1 _inst_4 _inst_5))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u3, max u2 u3} R R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (LinearMap.{u1, u1, max u3 u2, max u3 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))) (Module.toMulActionWithZero.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) mul y) z)))
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.mul_assoc' Algebra.TensorProduct.mul_assoc'ₓ'. -/
theorem mul_assoc' (mul : A ⊗[R] B →ₗ[R] A ⊗[R] B →ₗ[R] A ⊗[R] B)
(h :
@@ -553,7 +553,7 @@ theorem mul_assoc' (mul : A ⊗[R] B →ₗ[R] A ⊗[R] B →ₗ[R] A ⊗[R] B)
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (x : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (y : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (z : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)), Eq.{succ (max u2 u3)} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (coeFn.{succ (max u2 u3), succ (max u2 u3)} (LinearMap.{u1, u1, max u2 u3, max u2 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))) => (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) -> (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u3, max u2 u3} R R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) 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but is expected to have type
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, max u2 u3} R R R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (smulCommClass_self.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))) (Module.toMulActionWithZero.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.TensorProduct.mul.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) y) z))
+ forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (x : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (y : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (z : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)), Eq.{max (succ u2) (succ u3)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B 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R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => LinearMap.{u1, u1, max u3 u2, max u3 u2} R R 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u3} R B _inst_1 _inst_4 _inst_5))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u2, max u3 u2} R R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (LinearMap.{u1, u1, max u3 u2, max u3 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.TensorProduct.mul.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) y) z))
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.mul_assoc Algebra.TensorProduct.mul_assocₓ'. -/
theorem mul_assoc (x y z : A ⊗[R] B) : mul (mul x y) z = mul x (mul y z) :=
mul_assoc' mul
@@ -567,7 +567,7 @@ theorem mul_assoc (x y z : A ⊗[R] B) : mul (mul x y) z = mul x (mul y z) :=
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (x : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)), Eq.{succ (max u2 u3)} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B 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_inst_5) (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) (OfNat.ofNat.{u3} B 1 (OfNat.mk.{u3} B 1 (One.one.{u3} B (AddMonoidWithOne.toOne.{u3} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} B (NonAssocSemiring.toAddCommMonoidWithOne.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))))))) x) x
but is expected to have type
- forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (x : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)), Eq.{max (succ u2) (succ u3)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))) (Module.toMulActionWithZero.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.TensorProduct.mul.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (OfNat.ofNat.{u2} A 1 (One.toOfNat1.{u2} A (Semiring.toOne.{u2} A _inst_2))) (OfNat.ofNat.{u3} B 1 (One.toOfNat1.{u3} B (Semiring.toOne.{u3} B _inst_4))))) x) x
+ forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (x : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)), Eq.{max (succ u2) (succ u3)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (OfNat.ofNat.{u2} A 1 (One.toOfNat1.{u2} A (Semiring.toOne.{u2} A _inst_2))) (OfNat.ofNat.{u3} B 1 (One.toOfNat1.{u3} B (Semiring.toOne.{u3} B _inst_4))))) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (fun (_x : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u2, max u3 u2} R R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.TensorProduct.mul.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (OfNat.ofNat.{u2} A 1 (One.toOfNat1.{u2} A (Semiring.toOne.{u2} A _inst_2))) (OfNat.ofNat.{u3} B 1 (One.toOfNat1.{u3} B (Semiring.toOne.{u3} B _inst_4))))) x) x
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.one_mul Algebra.TensorProduct.one_mulₓ'. -/
theorem one_mul (x : A ⊗[R] B) : mul (1 ⊗ₜ 1) x = x := by
apply TensorProduct.induction_on x <;> simp (config := { contextual := true })
@@ -577,7 +577,7 @@ theorem one_mul (x : A ⊗[R] B) : mul (1 ⊗ₜ 1) x = x := by
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (x : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)), Eq.{succ (max u2 u3)} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B 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_inst_5) (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) (OfNat.ofNat.{u3} B 1 (OfNat.mk.{u3} B 1 (One.one.{u3} B (AddMonoidWithOne.toOne.{u3} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} B (NonAssocSemiring.toAddCommMonoidWithOne.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))))))) x
but is expected to have type
- forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (x : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)), Eq.{max (succ u2) (succ u3)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, max u2 u3} R R R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (smulCommClass_self.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))) (Module.toMulActionWithZero.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.TensorProduct.mul.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) x) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (OfNat.ofNat.{u2} A 1 (One.toOfNat1.{u2} A (Semiring.toOne.{u2} A _inst_2))) (OfNat.ofNat.{u3} B 1 (One.toOfNat1.{u3} B (Semiring.toOne.{u3} B _inst_4))))) x
+ forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (x : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)), Eq.{max (succ u2) (succ u3)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (OfNat.ofNat.{u2} A 1 (One.toOfNat1.{u2} A (Semiring.toOne.{u2} A _inst_2))) (OfNat.ofNat.{u3} B 1 (One.toOfNat1.{u3} B (Semiring.toOne.{u3} B _inst_4))))) (FunLike.coe.{max (succ u2) (succ u3), max (succ u2) (succ u3), max (succ u2) (succ u3)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => LinearMap.{u1, u1, max u3 u2, max u3 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, max u2 u3} R R R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (smulCommClass_self.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))) (Module.toMulActionWithZero.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.TensorProduct.mul.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) x) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (OfNat.ofNat.{u2} A 1 (One.toOfNat1.{u2} A (Semiring.toOne.{u2} A _inst_2))) (OfNat.ofNat.{u3} B 1 (One.toOfNat1.{u3} B (Semiring.toOne.{u3} B _inst_4))))) x
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.mul_one Algebra.TensorProduct.mul_oneₓ'. -/
theorem mul_one (x : A ⊗[R] B) : mul x (1 ⊗ₜ 1) = x := by
apply TensorProduct.induction_on x <;> simp (config := { contextual := true })
@@ -712,7 +712,7 @@ variable {C : Type v₃} [Semiring C] [Algebra R C]
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {C : Type.{u4}} [_inst_10 : Semiring.{u4} C] [_inst_11 : Algebra.{u1, u4} R C _inst_1 _inst_10] {g : AlgHom.{u1, max u2 u3, u4} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C _inst_1 (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_10 (Algebra.TensorProduct.TensorProduct.algebra.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_11} {h : AlgHom.{u1, max u2 u3, u4} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C _inst_1 (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_10 (Algebra.TensorProduct.TensorProduct.algebra.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_11}, (forall (a : A) (b : B), Eq.{succ u4} C (coeFn.{max (succ (max u2 u3)) (succ u4), max (succ (max u2 u3)) (succ u4)} (AlgHom.{u1, max u2 u3, u4} R (TensorProduct.{u1, u2, u3} R _inst_1 A B 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(Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C _inst_1 (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_10 (Algebra.TensorProduct.TensorProduct.algebra.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_11) => (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) -> C) ([anonymous].{u1, max u2 u3, u4} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a b))) -> (Eq.{max (max (succ u2) (succ u3)) (succ u4)} (AlgHom.{u1, max u3 u2, u4} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C _inst_1 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+ forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {C : Type.{u4}} [_inst_10 : Semiring.{u4} C] [_inst_11 : Algebra.{u1, u4} R C _inst_1 _inst_10] {g : AlgHom.{u1, max u3 u2, u4} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_10 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_11} {h : AlgHom.{u1, max u3 u2, u4} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B 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_inst_2 _inst_3 B _inst_4 _inst_5) _inst_10 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_11) R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R 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_inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5))))) (AddCommMonoid.toAddMonoid.{u4} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_10)))) (Module.toDistribMulAction.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Semiring.toNonAssocSemiring.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5)))) (Algebra.toModule.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5))) (Module.toDistribMulAction.{u1, u4} R C (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_10))) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_10 _inst_11)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u2 u3) u4, u1, max u2 u3, u4} (AlgHom.{u1, max u3 u2, u4} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_10 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_11) R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Semiring.toNonAssocSemiring.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_10)) (Module.toDistribMulAction.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Semiring.toNonAssocSemiring.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5)))) (Algebra.toModule.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5))) (Module.toDistribMulAction.{u1, u4} R C (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_10))) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_10 _inst_11)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, max u2 u3, u4, max (max u2 u3) u4} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_10 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_11 (AlgHom.{u1, max u3 u2, u4} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_10 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_11) (AlgHom.algHomClass.{u1, max u2 u3, u4} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_10 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_11))))) h (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a b))) -> (Eq.{max (max (succ u2) (succ u3)) (succ u4)} (AlgHom.{u1, max u3 u2, u4} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_10 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_11) g h)
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.ext Algebra.TensorProduct.extₓ'. -/
@[ext]
theorem ext {g h : A ⊗[R] B →ₐ[R] C} (H : ∀ a b, g (a ⊗ₜ b) = h (a ⊗ₜ b)) : g = h :=
@@ -886,7 +886,7 @@ variable {D : Type v₄} [Semiring D] [Algebra R D]
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {C : Type.{u4}} [_inst_6 : Semiring.{u4} C] [_inst_7 : Algebra.{u1, u4} R C _inst_1 _inst_6] (f : LinearMap.{u1, u1, max u2 u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)), (forall (a₁ : A) (a₂ : A) (b₁ : B) (b₂ : B), Eq.{succ u4} C (coeFn.{max (succ (max u2 u3)) (succ u4), max (succ (max u2 u3)) (succ u4)} (LinearMap.{u1, u1, max u2 u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C 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but is expected to have type
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(Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (OfNat.ofNat.{u3} B 1 (One.toOfNat1.{u3} B (Semiring.toOne.{u3} B _inst_4))))) (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (RingHom.{u1, u4} R C (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} C _inst_6)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => C) _x) (MulHomClass.toFunLike.{max u1 u4, u1, u4} (RingHom.{u1, u4} R C (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} C _inst_6)) R C (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R C (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} C _inst_6)) R C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R C (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} C _inst_6)) R C (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} C _inst_6) (RingHom.instRingHomClassRingHom.{u1, u4} R C (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} C _inst_6))))) (algebraMap.{u1, u4} R C _inst_1 _inst_6 _inst_7) r)) -> (AlgHom.{u1, max u3 u2, u4} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_6 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_7)
+ forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {C : Type.{u4}} [_inst_6 : Semiring.{u4} C] [_inst_7 : Algebra.{u1, u4} R C _inst_1 _inst_6] (f : LinearMap.{u1, u1, max u3 u2, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)), (forall (a₁ : A) (a₂ : A) (b₁ : B) (b₂ : B), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => C) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) a₁ a₂) (HMul.hMul.{u3, u3, u3} B B B (instHMul.{u3} B (NonUnitalNonAssocSemiring.toMul.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) b₁ b₂))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u2) (succ u3), succ u4} (LinearMap.{u1, u1, max u3 u2, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B 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_inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (fun (_x : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => C) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u3, u4} R R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B 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_inst_4 _inst_5) _inst_6 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_7)
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.alg_hom_of_linear_map_tensor_product Algebra.TensorProduct.algHomOfLinearMapTensorProductₓ'. -/
/-- Build an algebra morphism from a linear map out of a tensor product,
and evidence of multiplicativity on pure tensors.
@@ -918,7 +918,7 @@ def algHomOfLinearMapTensorProduct (f : A ⊗[R] B →ₗ[R] C)
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {C : Type.{u4}} [_inst_6 : Semiring.{u4} C] [_inst_7 : Algebra.{u1, u4} R C _inst_1 _inst_6] (f : LinearMap.{u1, u1, max u2 u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (w₁ : forall (a₁ : A) (a₂ : A) (b₁ : B) (b₂ : B), Eq.{succ u4} C (coeFn.{max (succ (max u2 u3)) (succ u4), max (succ (max u2 u3)) (succ u4)} (LinearMap.{u1, u1, max u2 u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C 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_inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (fun (_x : LinearMap.{u1, u1, max u2 u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A 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but is expected to have type
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(TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) 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u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_6 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(Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_6 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_7) (AlgHom.algHomClass.{u1, max u2 u3, u4} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B 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_inst_4 _inst_5 C _inst_6 _inst_7 f w₁ w₂) x) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u2) (succ u3), succ u4} (LinearMap.{u1, u1, max u3 u2, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => C) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u3, u4} R R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f x)
+ forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {C : Type.{u4}} [_inst_6 : Semiring.{u4} C] [_inst_7 : Algebra.{u1, u4} R C _inst_1 _inst_6] (f : LinearMap.{u1, u1, max u3 u2, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (w₁ : forall (a₁ : A) (a₂ : A) (b₁ : B) (b₂ : B), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => C) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) a₁ a₂) (HMul.hMul.{u3, u3, u3} B B B (instHMul.{u3} B (NonUnitalNonAssocSemiring.toMul.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) b₁ b₂))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u2) (succ u3), succ u4} (LinearMap.{u1, u1, max u3 u2, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B 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_inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Semiring.toNonAssocSemiring.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6)) (Module.toDistribMulAction.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Semiring.toNonAssocSemiring.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5)))) (Algebra.toModule.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5))) (Module.toDistribMulAction.{u1, u4} R C (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, max u2 u3, u4, max (max u2 u3) u4} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_6 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_7 (AlgHom.{u1, max u3 u2, u4} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_6 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_7) (AlgHom.algHomClass.{u1, max u2 u3, u4} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_6 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_7))))) (Algebra.TensorProduct.algHomOfLinearMapTensorProduct.{u1, u2, u3, u4} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5 C _inst_6 _inst_7 f w₁ w₂) x) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u2) (succ u3), succ u4} (LinearMap.{u1, u1, max u3 u2, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (fun (_x : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => C) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u3, u4} R R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f x)
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.alg_hom_of_linear_map_tensor_product_apply Algebra.TensorProduct.algHomOfLinearMapTensorProduct_applyₓ'. -/
@[simp]
theorem algHomOfLinearMapTensorProduct_apply (f w₁ w₂ x) :
@@ -930,7 +930,7 @@ theorem algHomOfLinearMapTensorProduct_apply (f w₁ w₂ x) :
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {C : Type.{u4}} [_inst_6 : Semiring.{u4} C] [_inst_7 : Algebra.{u1, u4} R C _inst_1 _inst_6] (f : LinearEquiv.{u1, u1, max u2 u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Algebra.TensorProduct.algEquivOfLinearEquivTensorProduct._proof_1.{u1} R _inst_1) (Algebra.TensorProduct.algEquivOfLinearEquivTensorProduct._proof_2.{u1} R _inst_1) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B 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but is expected to have type
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B 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(RingHomClass.toNonUnitalRingHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R C (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} C _inst_6)) R C (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} C _inst_6) (RingHom.instRingHomClassRingHom.{u1, u4} R C (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} C _inst_6))))) (algebraMap.{u1, u4} R C _inst_1 _inst_6 _inst_7) r)) -> (AlgEquiv.{u1, max u3 u2, u4} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_6 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_7)
+ forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {C : Type.{u4}} [_inst_6 : Semiring.{u4} C] [_inst_7 : Algebra.{u1, u4} R C _inst_1 _inst_6] (f : LinearEquiv.{u1, u1, max u3 u2, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)), (forall (a₁ : A) (a₂ : A) (b₁ : B) (b₂ : B), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => C) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) a₁ a₂) (HMul.hMul.{u3, u3, u3} B B B (instHMul.{u3} B (NonUnitalNonAssocSemiring.toMul.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) b₁ b₂))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u2) (succ u3), succ u4} (LinearEquiv.{u1, u1, max u3 u2, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (fun (_x : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => C) _x) (SMulHomClass.toFunLike.{max (max u2 u3) u4, u1, max u2 u3, u4} (LinearEquiv.{u1, u1, max u3 u2, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (SMulZeroClass.toSMul.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AddMonoid.toZero.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5))) (DistribSMul.toSMulZeroClass.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B 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(Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) f (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (OfNat.ofNat.{u3} B 1 (One.toOfNat1.{u3} B (Semiring.toOne.{u3} B _inst_4))))) (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (RingHom.{u1, u4} R C (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} C _inst_6)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => C) _x) (MulHomClass.toFunLike.{max u1 u4, u1, u4} (RingHom.{u1, u4} R C (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} C _inst_6)) R C (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u4, u1, u4} (RingHom.{u1, u4} R C (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} C _inst_6)) R C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6)) 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(Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_6 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_7)
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.alg_equiv_of_linear_equiv_tensor_product Algebra.TensorProduct.algEquivOfLinearEquivTensorProductₓ'. -/
/-- Build an algebra equivalence from a linear equivalence out of a tensor product,
and evidence of multiplicativity on pure tensors.
@@ -945,7 +945,7 @@ def algEquivOfLinearEquivTensorProduct (f : A ⊗[R] B ≃ₗ[R] C)
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {C : Type.{u4}} [_inst_6 : Semiring.{u4} C] [_inst_7 : Algebra.{u1, u4} R C _inst_1 _inst_6] (f : LinearEquiv.{u1, u1, max u2 u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Algebra.TensorProduct.algEquivOfLinearEquivTensorProduct._proof_1.{u1} R _inst_1) (Algebra.TensorProduct.algEquivOfLinearEquivTensorProduct._proof_2.{u1} R _inst_1) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (w₁ : forall (a₁ : A) (a₂ : A) (b₁ : B) (b₂ : B), Eq.{succ u4} C (coeFn.{max (succ (max u2 u3)) (succ u4), max (succ (max u2 u3)) (succ u4)} (LinearEquiv.{u1, u1, max u2 u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Algebra.TensorProduct.algEquivOfLinearEquivTensorProduct._proof_3.{u1} R _inst_1) (Algebra.TensorProduct.algEquivOfLinearEquivTensorProduct._proof_4.{u1} R _inst_1) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (fun (_x : LinearEquiv.{u1, u1, max u2 u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Algebra.TensorProduct.algEquivOfLinearEquivTensorProduct._proof_3.{u1} R _inst_1) (Algebra.TensorProduct.algEquivOfLinearEquivTensorProduct._proof_4.{u1} R _inst_1) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) => (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) -> C) (LinearEquiv.hasCoeToFun.{u1, u1, max u2 u3, u4} R R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, 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u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Algebra.TensorProduct.algEquivOfLinearEquivTensorProduct._proof_1.{u1} R _inst_1) (Algebra.TensorProduct.algEquivOfLinearEquivTensorProduct._proof_2.{u1} R _inst_1)) f x)
but is expected to have type
- forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {C : Type.{u4}} [_inst_6 : Semiring.{u4} C] [_inst_7 : Algebra.{u1, u4} R C _inst_1 _inst_6] (f : LinearEquiv.{u1, u1, max u3 u2, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B 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(Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) a₁ a₂) (HMul.hMul.{u3, u3, u3} B B B (instHMul.{u3} B (NonUnitalNonAssocSemiring.toMul.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) b₁ b₂))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u2) (succ u3), succ u4} (LinearEquiv.{u1, u1, max u3 u2, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B 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(CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max u2 u3, u4, max (max u2 u3) u4} R R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (LinearEquiv.{u1, u1, max u3 u2, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) 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_inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) f x)
+ forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {C : Type.{u4}} [_inst_6 : Semiring.{u4} C] [_inst_7 : Algebra.{u1, u4} R C _inst_1 _inst_6] (f : LinearEquiv.{u1, u1, max u3 u2, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (w₁ : forall (a₁ : A) (a₂ : A) (b₁ : B) (b₂ : B), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => C) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) a₁ a₂) (HMul.hMul.{u3, u3, u3} B B B (instHMul.{u3} B (NonUnitalNonAssocSemiring.toMul.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) b₁ b₂))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u2) (succ u3), succ u4} (LinearEquiv.{u1, u1, max u3 u2, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) 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(Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5))) (DistribMulAction.toDistribSMul.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_6 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) _inst_7) R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B 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A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Semiring.toNonAssocSemiring.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5)))))) (DistribMulAction.toDistribSMul.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Semiring.toNonAssocSemiring.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Semiring.toNonAssocSemiring.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5)))) (Algebra.toModule.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5)))))) (SMulZeroClass.toSMul.{u1, u4} R C (AddMonoid.toZero.{u4} C (AddCommMonoid.toAddMonoid.{u4} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u4} R C (AddMonoid.toAddZeroClass.{u4} C (AddCommMonoid.toAddMonoid.{u4} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u4} R C (MonoidWithZero.toMonoid.{u1} R 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_inst_6)))) (Module.toDistribMulAction.{u1, u4} R C (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u3) u4, u1, max u2 u3, u4} (LinearEquiv.{u1, u1, max u3 u2, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u3} (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5)) (AddCommMonoid.toAddMonoid.{u4} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6)))) (Module.toDistribMulAction.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))) (Module.toDistribMulAction.{u1, u4} R C (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, max u2 u3, u4, max (max u2 u3) u4} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (LinearEquiv.{u1, u1, max u3 u2, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max u2 u3, u4, max (max u2 u3) u4} R R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (LinearEquiv.{u1, u1, max u3 u2, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max u2 u3, u4} R R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) f x)
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.alg_equiv_of_linear_equiv_tensor_product_apply Algebra.TensorProduct.algEquivOfLinearEquivTensorProduct_applyₓ'. -/
@[simp]
theorem algEquivOfLinearEquivTensorProduct_apply (f w₁ w₂ x) :
@@ -957,7 +957,7 @@ theorem algEquivOfLinearEquivTensorProduct_apply (f w₁ w₂ x) :
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {C : Type.{u4}} [_inst_6 : Semiring.{u4} C] [_inst_7 : Algebra.{u1, u4} R C _inst_1 _inst_6] {D : Type.{u5}} [_inst_8 : Semiring.{u5} D] [_inst_9 : Algebra.{u1, u5} R D _inst_1 _inst_8] (f : LinearEquiv.{u1, u1, max (max u2 u3) u4, u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Algebra.TensorProduct.algEquivOfLinearEquivTripleTensorProduct._proof_1.{u1} R _inst_1) (Algebra.TensorProduct.algEquivOfLinearEquivTripleTensorProduct._proof_2.{u1} R _inst_1) (TensorProduct.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) D (TensorProduct.addCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} D (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} D (Semiring.toNonAssocSemiring.{u5} D _inst_8))) (TensorProduct.module.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u5} R D _inst_1 _inst_8 _inst_9)), (forall (a₁ : A) (a₂ : A) (b₁ : B) (b₂ : B) (c₁ : C) (c₂ : C), Eq.{succ u5} D (coeFn.{max (succ (max (max u2 u3) u4)) (succ u5), max (succ (max (max u2 u3) u4)) (succ u5)} (LinearEquiv.{u1, u1, max (max u2 u3) u4, u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Algebra.TensorProduct.algEquivOfLinearEquivTripleTensorProduct._proof_3.{u1} R _inst_1) (Algebra.TensorProduct.algEquivOfLinearEquivTripleTensorProduct._proof_4.{u1} R _inst_1) (TensorProduct.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) D (TensorProduct.addCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u5} R D _inst_1 _inst_8 _inst_9)) (fun (_x : LinearEquiv.{u1, u1, max (max u2 u3) u4, u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Algebra.TensorProduct.algEquivOfLinearEquivTripleTensorProduct._proof_3.{u1} R _inst_1) (Algebra.TensorProduct.algEquivOfLinearEquivTripleTensorProduct._proof_4.{u1} R _inst_1) (TensorProduct.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) D (TensorProduct.addCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) 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_inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u5} R D _inst_1 _inst_8 _inst_9)) => (TensorProduct.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B 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(TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) D (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} D (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} D (Semiring.toNonAssocSemiring.{u5} D _inst_8))) (TensorProduct.module.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B 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(Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u5} D _inst_8)) (fun (_x : RingHom.{u1, u5} R D (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u5} D _inst_8)) => R -> D) (RingHom.hasCoeToFun.{u1, u5} R D (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u5} D _inst_8)) (algebraMap.{u1, u5} R D _inst_1 _inst_8 _inst_9) r)) -> (AlgEquiv.{u1, max (max u2 u3) u4, u5} R (TensorProduct.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) D _inst_1 (Algebra.TensorProduct.TensorProduct.semiring.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (Algebra.TensorProduct.TensorProduct.algebra.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) C _inst_6 _inst_7) _inst_8 (Algebra.TensorProduct.TensorProduct.algebra.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (Algebra.TensorProduct.TensorProduct.algebra.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) C _inst_6 _inst_7) _inst_9)
but is expected to have type
- forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {C : Type.{u4}} [_inst_6 : Semiring.{u4} C] [_inst_7 : Algebra.{u1, u4} R C _inst_1 _inst_6] {D : Type.{u5}} [_inst_8 : Semiring.{u5} D] [_inst_9 : Algebra.{u1, u5} R D _inst_1 _inst_8] (f : LinearEquiv.{u1, u1, max u4 u3 u2, u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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_inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) a₁ a₂) (HMul.hMul.{u3, u3, u3} B B B (instHMul.{u3} B (NonUnitalNonAssocSemiring.toMul.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) b₁ b₂)) (HMul.hMul.{u4, u4, u4} C C C (instHMul.{u4} C (NonUnitalNonAssocSemiring.toMul.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6)))) c₁ c₂))) (HMul.hMul.{u5, u5, u5} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) => D) (TensorProduct.tmul.{u1, max u2 u3, 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) => D) (TensorProduct.tmul.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a₂ b₂) c₂)) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) => D) (TensorProduct.tmul.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) D (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) C _inst_6 _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} D (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} D (Semiring.toNonAssocSemiring.{u5} D _inst_8))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u5} R D _inst_1 _inst_8 _inst_9) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) f (TensorProduct.tmul.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (OfNat.ofNat.{u3} B 1 (One.toOfNat1.{u3} B (Semiring.toOne.{u3} B _inst_4)))) (OfNat.ofNat.{u4} C 1 (One.toOfNat1.{u4} C (Semiring.toOne.{u4} C _inst_6))))) (FunLike.coe.{max (succ u1) (succ u5), succ u1, succ u5} (RingHom.{u1, u5} R D (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u5} D _inst_8)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => D) _x) (MulHomClass.toFunLike.{max u1 u5, u1, u5} (RingHom.{u1, u5} R D (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u5} D _inst_8)) R D (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u5} D (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} D (Semiring.toNonAssocSemiring.{u5} D _inst_8))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u5, u1, u5} (RingHom.{u1, u5} R D (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u5} D _inst_8)) R D (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} D (Semiring.toNonAssocSemiring.{u5} D _inst_8)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u5, u1, u5} (RingHom.{u1, u5} R D (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u5} D _inst_8)) R D (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u5} D _inst_8) (RingHom.instRingHomClassRingHom.{u1, u5} R D (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u5} D _inst_8))))) (algebraMap.{u1, u5} R D _inst_1 _inst_8 _inst_9) r)) -> (AlgEquiv.{u1, max u4 u3 u2, u5} R (TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) D _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) C _inst_6 _inst_7) _inst_8 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) C _inst_6 _inst_7) _inst_9)
+ forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {C : Type.{u4}} [_inst_6 : Semiring.{u4} C] [_inst_7 : Algebra.{u1, u4} R C _inst_1 _inst_6] {D : Type.{u5}} [_inst_8 : Semiring.{u5} D] [_inst_9 : Algebra.{u1, u5} R D _inst_1 _inst_8] (f : LinearEquiv.{u1, u1, max u4 u3 u2, u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) D (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) 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_inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) a₁ a₂) (HMul.hMul.{u3, u3, u3} B B B (instHMul.{u3} B (NonUnitalNonAssocSemiring.toMul.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) b₁ b₂)) (HMul.hMul.{u4, u4, u4} C C C (instHMul.{u4} C (NonUnitalNonAssocSemiring.toMul.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6)))) c₁ c₂))) (HMul.hMul.{u5, u5, u5} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) => D) (TensorProduct.tmul.{u1, max u2 u3, 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) => D) (TensorProduct.tmul.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a₂ b₂) c₂)) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) => D) (TensorProduct.tmul.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a₁ b₁) c₁)) (instHMul.{u5} ((fun 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B _inst_1 _inst_4 _inst_5)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) C _inst_6 _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} D (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} D (Semiring.toNonAssocSemiring.{u5} D _inst_8))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u5} R D _inst_1 _inst_8 _inst_9) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) f (TensorProduct.tmul.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => D) _x) (MulHomClass.toFunLike.{max u1 u5, u1, u5} (RingHom.{u1, u5} R D (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u5} D _inst_8)) R D (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u5} D (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} D (Semiring.toNonAssocSemiring.{u5} D _inst_8))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u5, u1, u5} (RingHom.{u1, u5} R D (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u5} D _inst_8)) R D (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} D (Semiring.toNonAssocSemiring.{u5} D _inst_8)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u5, u1, u5} (RingHom.{u1, u5} R D (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u5} D _inst_8)) R D (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u5} D _inst_8) (RingHom.instRingHomClassRingHom.{u1, u5} R D (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u5} D _inst_8))))) (algebraMap.{u1, u5} R D _inst_1 _inst_8 _inst_9) r)) -> (AlgEquiv.{u1, max u4 u3 u2, u5} R (TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) D _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) C _inst_6 _inst_7) _inst_8 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) C _inst_6 _inst_7) _inst_9)
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.alg_equiv_of_linear_equiv_triple_tensor_product Algebra.TensorProduct.algEquivOfLinearEquivTripleTensorProductₓ'. -/
/-- Build an algebra equivalence from a linear equivalence out of a triple tensor product,
and evidence of multiplicativity on pure tensors.
@@ -1001,7 +1001,7 @@ def algEquivOfLinearEquivTripleTensorProduct (f : (A ⊗[R] B) ⊗[R] C ≃ₗ[R
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {C : Type.{u4}} [_inst_6 : Semiring.{u4} C] [_inst_7 : Algebra.{u1, u4} R C _inst_1 _inst_6] {D : Type.{u5}} [_inst_8 : Semiring.{u5} D] [_inst_9 : Algebra.{u1, u5} R D _inst_1 _inst_8] (f : LinearEquiv.{u1, u1, max (max u2 u3) u4, u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Algebra.TensorProduct.algEquivOfLinearEquivTripleTensorProduct._proof_1.{u1} R _inst_1) (Algebra.TensorProduct.algEquivOfLinearEquivTripleTensorProduct._proof_2.{u1} R _inst_1) (TensorProduct.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) D (TensorProduct.addCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B 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(Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B 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(Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Algebra.TensorProduct.algEquivOfLinearEquivTripleTensorProduct._proof_1.{u1} R _inst_1) (Algebra.TensorProduct.algEquivOfLinearEquivTripleTensorProduct._proof_2.{u1} R _inst_1) (TensorProduct.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) D (TensorProduct.addCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} D (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} D (Semiring.toNonAssocSemiring.{u5} D _inst_8))) (TensorProduct.module.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u5} R D _inst_1 _inst_8 _inst_9)) => (TensorProduct.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) -> D) (LinearEquiv.hasCoeToFun.{u1, u1, max (max u2 u3) u4, u5} R R (TensorProduct.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) D (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} D (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} D (Semiring.toNonAssocSemiring.{u5} D _inst_8))) (TensorProduct.module.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u5} R D _inst_1 _inst_8 _inst_9) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Algebra.TensorProduct.algEquivOfLinearEquivTripleTensorProduct._proof_1.{u1} R _inst_1) (Algebra.TensorProduct.algEquivOfLinearEquivTripleTensorProduct._proof_2.{u1} R _inst_1)) f x)
but is expected to have type
- forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {C : Type.{u4}} [_inst_6 : Semiring.{u4} C] [_inst_7 : Algebra.{u1, u4} R C _inst_1 _inst_6] {D : Type.{u5}} [_inst_8 : Semiring.{u5} D] [_inst_9 : Algebra.{u1, u5} R D _inst_1 _inst_8] (f : LinearEquiv.{u1, u1, max u4 u3 u2, u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) D (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) 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_inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) a₁ a₂) (HMul.hMul.{u3, u3, u3} B B B (instHMul.{u3} B (NonUnitalNonAssocSemiring.toMul.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) b₁ b₂)) (HMul.hMul.{u4, u4, u4} C C C (instHMul.{u4} C (NonUnitalNonAssocSemiring.toMul.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6)))) c₁ c₂))) (HMul.hMul.{u5, u5, u5} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) => D) (TensorProduct.tmul.{u1, max u2 u3, 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TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) => D) (TensorProduct.tmul.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a₂ b₂) c₂)) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) => D) (TensorProduct.tmul.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a₁ b₁) c₁)) (instHMul.{u5} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) => D) (TensorProduct.tmul.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 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A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) D (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) C _inst_6 _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} D (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} D (Semiring.toNonAssocSemiring.{u5} D _inst_8))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u5} R D _inst_1 _inst_8 _inst_9)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) C _inst_6 _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} D (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} D (Semiring.toNonAssocSemiring.{u5} D _inst_8))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u5} R D _inst_1 _inst_8 _inst_9) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u2 u3) u4, u5} R R (TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) D (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) C _inst_6 _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} D (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} D (Semiring.toNonAssocSemiring.{u5} D _inst_8))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u5} R D _inst_1 _inst_8 _inst_9) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) f x)
+ forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {C : Type.{u4}} [_inst_6 : Semiring.{u4} C] [_inst_7 : Algebra.{u1, u4} R C _inst_1 _inst_6] {D : Type.{u5}} [_inst_8 : Semiring.{u5} D] [_inst_9 : Algebra.{u1, u5} R D _inst_1 _inst_8] (f : LinearEquiv.{u1, u1, max u4 u3 u2, u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) D (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) C _inst_6 _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} D (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} D (Semiring.toNonAssocSemiring.{u5} D _inst_8))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, 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_inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) a₁ a₂) (HMul.hMul.{u3, u3, u3} B B B (instHMul.{u3} B (NonUnitalNonAssocSemiring.toMul.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) b₁ b₂)) (HMul.hMul.{u4, u4, u4} C C C (instHMul.{u4} C (NonUnitalNonAssocSemiring.toMul.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6)))) c₁ c₂))) (HMul.hMul.{u5, u5, u5} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) => D) (TensorProduct.tmul.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a₁ b₁) c₁)) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) => D) (TensorProduct.tmul.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a₂ b₂) c₂)) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) => D) (TensorProduct.tmul.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a₁ b₁) c₁)) (instHMul.{u5} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) => D) (TensorProduct.tmul.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, 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_inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) D (LinearEquiv.{u1, u1, max u4 u3 u2, u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) D (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) C _inst_6 _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} D (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} D (Semiring.toNonAssocSemiring.{u5} D _inst_8))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u5} R D _inst_1 _inst_8 _inst_9)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) C _inst_6 _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} D (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} D (Semiring.toNonAssocSemiring.{u5} D _inst_8))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u5} R D _inst_1 _inst_8 _inst_9) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u2 u3) u4, u5} R R (TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) D (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) C _inst_6 _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} D (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} D (Semiring.toNonAssocSemiring.{u5} D _inst_8))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u5} R D _inst_1 _inst_8 _inst_9) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) f x)
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.alg_equiv_of_linear_equiv_triple_tensor_product_apply Algebra.TensorProduct.algEquivOfLinearEquivTripleTensorProduct_applyₓ'. -/
@[simp]
theorem algEquivOfLinearEquivTripleTensorProduct_apply (f w₁ w₂ x) :
@@ -1042,7 +1042,7 @@ protected def lid : R ⊗[R] A ≃ₐ[R] A :=
lean 3 declaration is
forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (A : Type.{u2}) [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R) (a : A), Eq.{succ u2} A (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (AlgEquiv.{u1, max u1 u2, u2} R (TensorProduct.{u1, u1, u2} R _inst_1 R A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A _inst_1 (Algebra.TensorProduct.TensorProduct.semiring.{u1, u1, u2} R _inst_1 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) A _inst_2 _inst_3) _inst_2 (Algebra.TensorProduct.TensorProduct.algebra.{u1, u1, u2} R _inst_1 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) A _inst_2 _inst_3) _inst_3) (fun (_x : AlgEquiv.{u1, max u1 u2, u2} R (TensorProduct.{u1, u1, u2} R _inst_1 R A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A _inst_1 (Algebra.TensorProduct.TensorProduct.semiring.{u1, u1, u2} R _inst_1 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) A _inst_2 _inst_3) _inst_2 (Algebra.TensorProduct.TensorProduct.algebra.{u1, u1, u2} R _inst_1 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) A _inst_2 _inst_3) _inst_3) => (TensorProduct.{u1, u1, u2} R _inst_1 R A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) -> A) (AlgEquiv.hasCoeToFun.{u1, max u1 u2, u2} R (TensorProduct.{u1, u1, u2} R _inst_1 R A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) 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(AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) r a)
but is expected to have type
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) r a)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (AlgEquiv.{u1, max u2 u1, u2} R (TensorProduct.{u1, u1, u2} R _inst_1 R A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A _inst_1 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_inst_2 _inst_3)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u1, u2} R _inst_1 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) A _inst_2 _inst_3)))) (Algebra.toModule.{u1, max u1 u2} R (TensorProduct.{u1, u1, u2} R _inst_1 R A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _inst_1 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(Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u1, max u1 u2, u2} (AlgEquiv.{u1, max u2 u1, u2} R (TensorProduct.{u1, u1, u2} R _inst_1 R A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u1, u2} R _inst_1 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) A _inst_2 _inst_3) _inst_2 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u1, u2} R _inst_1 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) A _inst_2 _inst_3) _inst_3) R (TensorProduct.{u1, u1, u2} R _inst_1 R A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (MonoidWithZero.toMonoid.{u1} 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u1, u2} R _inst_1 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) A _inst_2 _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (Module.toDistribMulAction.{u1, max u1 u2} R (TensorProduct.{u1, u1, u2} R _inst_1 R A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (TensorProduct.{u1, u1, u2} R _inst_1 R A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (TensorProduct.{u1, u1, u2} R _inst_1 R A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toNonAssocSemiring.{max u1 u2} (TensorProduct.{u1, u1, u2} R _inst_1 R A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u1, u2} R _inst_1 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) A _inst_2 _inst_3)))) (Algebra.toModule.{u1, max u1 u2} R (TensorProduct.{u1, u1, u2} R _inst_1 R A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u1, u2} R _inst_1 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) A _inst_2 _inst_3) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u1, u2} R _inst_1 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) A _inst_2 _inst_3))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, max u1 u2, u2, max u1 u2} R (TensorProduct.{u1, u1, u2} R _inst_1 R A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A _inst_1 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_inst_1 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) A _inst_2 _inst_3) _inst_3) (AlgEquivClass.toAlgHomClass.{max u1 u2, u1, max u1 u2, u2} (AlgEquiv.{u1, max u2 u1, u2} R (TensorProduct.{u1, u1, u2} R _inst_1 R A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u1, u2} R _inst_1 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) A _inst_2 _inst_3) _inst_2 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u1, u2} R _inst_1 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) A _inst_2 _inst_3) _inst_3) R (TensorProduct.{u1, u1, u2} R _inst_1 R A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u1, u2} R _inst_1 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) A _inst_2 _inst_3) _inst_2 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u1, u2} R _inst_1 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) A _inst_2 _inst_3) _inst_3 (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, max u1 u2, u2} R (TensorProduct.{u1, u1, u2} R _inst_1 R A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R 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(Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u1, u2} R _inst_1 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) A _inst_2 _inst_3) _inst_3)))))) (Algebra.TensorProduct.lid.{u1, u2} R _inst_1 A _inst_2 _inst_3) (TensorProduct.tmul.{u1, u1, u2} R _inst_1 R A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) r a)) (HSMul.hSMul.{u1, u2, u2} R A A (instHSMul.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) r a)
+ forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (A : Type.{u2}) [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R) (a : A), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : TensorProduct.{u1, u1, u2} R _inst_1 R A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => A) (TensorProduct.tmul.{u1, u1, u2} R _inst_1 R A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) r a)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (AlgEquiv.{u1, max u2 u1, u2} R (TensorProduct.{u1, u1, u2} R _inst_1 R A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u1, u2} R _inst_1 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) A _inst_2 _inst_3) _inst_2 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u1, u2} R _inst_1 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1) A _inst_2 _inst_3) _inst_3) (TensorProduct.{u1, u1, u2} R _inst_1 R A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (_x : TensorProduct.{u1, u1, u2} R _inst_1 R A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : TensorProduct.{u1, u1, u2} R _inst_1 R A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R 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Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.lid_tmul Algebra.TensorProduct.lid_tmulₓ'. -/
@[simp]
theorem lid_tmul (r : R) (a : A) : (TensorProduct.lid R A : R ⊗ A → A) (r ⊗ₜ a) = r • a := by
@@ -1066,7 +1066,7 @@ protected def rid : A ⊗[R] R ≃ₐ[R] A :=
lean 3 declaration is
forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (A : Type.{u2}) [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R) (a : A), Eq.{succ u2} A (coeFn.{max (succ (max u2 u1)) (succ u2), max (succ (max u2 u1)) (succ u2)} (AlgEquiv.{u1, max u2 u1, u2} R (TensorProduct.{u1, u2, u1} R _inst_1 A R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A _inst_1 (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_2 (Algebra.TensorProduct.TensorProduct.algebra.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_3) (fun (_x : AlgEquiv.{u1, max u2 u1, u2} R (TensorProduct.{u1, u2, u1} R _inst_1 A R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A _inst_1 (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_2 (Algebra.TensorProduct.TensorProduct.algebra.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 R 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(AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) r a)
but is expected to have type
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(CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (TensorProduct.{u1, u2, u1} R _inst_1 A R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (TensorProduct.{u1, u2, u1} R _inst_1 A R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (TensorProduct.{u1, u2, u1} R _inst_1 A R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (TensorProduct.{u1, u2, u1} R _inst_1 A R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 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(Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, max u1 u2, u2, max u1 u2} R (TensorProduct.{u1, u2, u1} R _inst_1 A R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A _inst_1 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_inst_2 _inst_3 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_3) (AlgEquivClass.toAlgHomClass.{max u1 u2, u1, max u1 u2, u2} (AlgEquiv.{u1, max u1 u2, u2} R (TensorProduct.{u1, u2, u1} R _inst_1 A R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_2 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_3) R (TensorProduct.{u1, u2, u1} R _inst_1 A R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_2 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_3 (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, max u1 u2, u2} R (TensorProduct.{u1, u2, u1} R _inst_1 A R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_2 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_3)))))) (Algebra.TensorProduct.rid.{u1, u2} R _inst_1 A _inst_2 _inst_3) (TensorProduct.tmul.{u1, u2, u1} R _inst_1 A R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) a r)) (HSMul.hSMul.{u1, u2, u2} R A A (instHSMul.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) r a)
+ forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (A : Type.{u2}) [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R) (a : A), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : TensorProduct.{u1, u2, u1} R _inst_1 A R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => A) (TensorProduct.tmul.{u1, u2, u1} R _inst_1 A R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) a r)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (AlgEquiv.{u1, max u1 u2, u2} R (TensorProduct.{u1, u2, u1} R _inst_1 A R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A _inst_1 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(Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (TensorProduct.{u1, u2, u1} R _inst_1 A R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (TensorProduct.{u1, u2, u1} R _inst_1 A R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, max u1 u2, u2, max u1 u2} R (TensorProduct.{u1, u2, u1} R _inst_1 A R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_2 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_3 (AlgEquiv.{u1, max u1 u2, u2} R (TensorProduct.{u1, u2, u1} R _inst_1 A R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_2 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_3) (AlgEquivClass.toAlgHomClass.{max u1 u2, u1, max u1 u2, u2} (AlgEquiv.{u1, max u1 u2, u2} R (TensorProduct.{u1, u2, u1} R _inst_1 A R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_2 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_3) R (TensorProduct.{u1, u2, u1} R _inst_1 A R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_2 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_3 (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, max u1 u2, u2} R (TensorProduct.{u1, u2, u1} R _inst_1 A R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_2 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_3)))))) (Algebra.TensorProduct.rid.{u1, u2} R _inst_1 A _inst_2 _inst_3) (TensorProduct.tmul.{u1, u2, u1} R _inst_1 A R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) a r)) (HSMul.hSMul.{u1, u2, u2} R A A (instHSMul.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) r a)
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.rid_tmul Algebra.TensorProduct.rid_tmulₓ'. -/
@[simp]
theorem rid_tmul (r : R) (a : A) : (TensorProduct.rid R A : A ⊗ R → A) (a ⊗ₜ r) = r • a := by
@@ -1098,7 +1098,7 @@ protected def comm : A ⊗[R] B ≃ₐ[R] B ⊗[R] A :=
lean 3 declaration is
forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (A : Type.{u2}) [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (B : Type.{u3}) [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (a : A) (b : B), Eq.{succ (max u3 u2)} (TensorProduct.{u1, u3, u2} R _inst_1 B A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeFn.{max (succ (max u2 u3)) (succ (max u3 u2)), max (succ (max u2 u3)) (succ (max u3 u2))} (AlgEquiv.{u1, max u2 u3, max u3 u2} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.{u1, u3, u2} R _inst_1 B A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _inst_1 (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (Algebra.TensorProduct.TensorProduct.semiring.{u1, u3, u2} R _inst_1 B _inst_4 _inst_5 A _inst_2 _inst_3) (Algebra.TensorProduct.TensorProduct.algebra.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (Algebra.TensorProduct.TensorProduct.algebra.{u1, u3, u2} R _inst_1 B _inst_4 _inst_5 A _inst_2 _inst_3)) (fun (_x : AlgEquiv.{u1, max u2 u3, max u3 u2} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.{u1, u3, u2} R _inst_1 B A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _inst_1 (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (Algebra.TensorProduct.TensorProduct.semiring.{u1, u3, u2} R _inst_1 B _inst_4 _inst_5 A _inst_2 _inst_3) (Algebra.TensorProduct.TensorProduct.algebra.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (Algebra.TensorProduct.TensorProduct.algebra.{u1, u3, u2} R _inst_1 B _inst_4 _inst_5 A _inst_2 _inst_3)) => (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) -> (TensorProduct.{u1, u3, u2} R _inst_1 B A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (AlgEquiv.hasCoeToFun.{u1, max u2 u3, max u3 u2} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (TensorProduct.{u1, u3, u2} R _inst_1 B A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _inst_1 (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (Algebra.TensorProduct.TensorProduct.semiring.{u1, u3, u2} R _inst_1 B _inst_4 _inst_5 A _inst_2 _inst_3) (Algebra.TensorProduct.TensorProduct.algebra.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (Algebra.TensorProduct.TensorProduct.algebra.{u1, u3, u2} R _inst_1 B _inst_4 _inst_5 A _inst_2 _inst_3)) (Algebra.TensorProduct.comm.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a b)) (TensorProduct.tmul.{u1, u3, u2} R _inst_1 B A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) b a)
but is expected to have type
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(Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u3, u2} R _inst_1 B _inst_4 _inst_5 A _inst_2 _inst_3) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u3, u2} R _inst_1 B _inst_4 _inst_5 A _inst_2 _inst_3))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, max u2 u3, max u2 u3, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 A B 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Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.comm_tmul Algebra.TensorProduct.comm_tmulₓ'. -/
@[simp]
theorem comm_tmul (a : A) (b : B) :
@@ -1126,7 +1126,7 @@ variable {R A B C}
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {C : Type.{u4}} [_inst_6 : Semiring.{u4} C] [_inst_7 : Algebra.{u1, u4} R C _inst_1 _inst_6] (a₁ : A) (a₂ : A) (b₁ : B) (b₂ : B) (c₁ : C) (c₂ : C), Eq.{succ (max u2 u3 u4)} (TensorProduct.{u1, u2, max u3 u4} R _inst_1 A (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (TensorProduct.module.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (coeFn.{max (succ (max (max u2 u3) u4)) (succ (max u2 u3 u4)), max (succ (max (max u2 u3) u4)) (succ (max u2 u3 u4))} (LinearEquiv.{u1, u1, max (max u2 u3) u4, max u2 u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.assoc._proof_1.{u1} R _inst_1) (TensorProduct.assoc._proof_2.{u1} R _inst_1) (TensorProduct.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (TensorProduct.{u1, u2, max u3 u4} R _inst_1 A (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (TensorProduct.module.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (TensorProduct.addCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (TensorProduct.addCommMonoid.{u1, u2, max u3 u4} R _inst_1 A (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (TensorProduct.module.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (TensorProduct.module.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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u4} R C _inst_1 _inst_6 _inst_7)) (TensorProduct.module.{u1, u2, max u3 u4} R _inst_1 A (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (TensorProduct.module.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)))) (fun (_x : LinearEquiv.{u1, u1, max (max u2 u3) u4, max u2 u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.assoc._proof_1.{u1} R _inst_1) (TensorProduct.assoc._proof_2.{u1} R _inst_1) (TensorProduct.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (TensorProduct.{u1, u2, max u3 u4} R _inst_1 A (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (TensorProduct.module.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (TensorProduct.addCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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u4} R C _inst_1 _inst_6 _inst_7)) (TensorProduct.addCommMonoid.{u1, u2, max u3 u4} R _inst_1 A (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a₂ b₂) c₂)))
but is expected to have type
- forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {C : Type.{u4}} [_inst_6 : Semiring.{u4} C] [_inst_7 : Algebra.{u1, u4} R C _inst_1 _inst_6] (a₁ : A) (a₂ : A) (b₁ : B) (b₂ : B) (c₁ : C) (c₂ : C), Eq.{max (max (succ u2) (succ u3)) (succ u4)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B 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_inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (Module.toDistribMulAction.{u1, max (max u2 u3) u4} R (TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B 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(Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) => TensorProduct.{u1, u2, max u4 u3} R _inst_1 A (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (TensorProduct.tmul.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a₁ b₁) c₁)) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (TensorProduct.tmul.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a₂ b₂) c₂)) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (TensorProduct.tmul.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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_inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (AddMonoid.toAddZeroClass.{max (max u2 u3) u4} (TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A 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(DistribMulAction.toDistribSMul.{u1, max (max u2 u3) u4} R (TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u4} (TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (Module.toDistribMulAction.{u1, max (max u2 u3) u4} R (TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (TensorProduct.addCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A 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u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)))) (DistribSMul.toSMulZeroClass.{u1, max (max u2 u3) u4} R (TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a₂ b₂) c₂)))
+ forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {C : Type.{u4}} [_inst_6 : Semiring.{u4} C] [_inst_7 : Algebra.{u1, u4} R C _inst_1 _inst_6] (a₁ : A) (a₂ : A) (b₁ : B) (b₂ : B) (c₁ : C) (c₂ : C), Eq.{max (max (succ u2) (succ u3)) (succ u4)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) => TensorProduct.{u1, u2, max u4 u3} R _inst_1 A (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (TensorProduct.tmul.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C 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_inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) a₁ a₂) (HMul.hMul.{u3, u3, u3} B B B (instHMul.{u3} B (NonUnitalNonAssocSemiring.toMul.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) b₁ b₂)) (HMul.hMul.{u4, u4, u4} C C C (instHMul.{u4} C (NonUnitalNonAssocSemiring.toMul.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6)))) c₁ c₂))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (max (succ u2) (succ u3)) (succ u4), max (max (succ u2) (succ u3)) (succ u4)} (LinearEquiv.{u1, u1, max u4 u3 u2, max (max u4 u3) u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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_inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (Module.toDistribMulAction.{u1, max (max u2 u3) u4} R (TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B 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(Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) => TensorProduct.{u1, u2, max u4 u3} R _inst_1 A (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (TensorProduct.tmul.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a₁ b₁) c₁)) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (TensorProduct.tmul.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a₂ b₂) c₂)) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (TensorProduct.tmul.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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_inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (AddMonoid.toAddZeroClass.{max (max u2 u3) u4} (TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A 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(DistribMulAction.toDistribSMul.{u1, max (max u2 u3) u4} R (TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u4} (TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (Module.toDistribMulAction.{u1, max (max u2 u3) u4} R (TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (TensorProduct.addCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A 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u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)))) (DistribSMul.toSMulZeroClass.{u1, max (max u2 u3) u4} R (TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) 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_inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a₂ b₂) c₂)))
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.assoc_aux_1 Algebra.TensorProduct.assoc_aux_1ₓ'. -/
theorem assoc_aux_1 (a₁ a₂ : A) (b₁ b₂ : B) (c₁ c₂ : C) :
(TensorProduct.assoc R A B C) (((a₁ * a₂) ⊗ₜ[R] (b₁ * b₂)) ⊗ₜ[R] (c₁ * c₂)) =
@@ -1139,7 +1139,7 @@ theorem assoc_aux_1 (a₁ a₂ : A) (b₁ b₂ : B) (c₁ c₂ : C) :
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {C : Type.{u4}} [_inst_6 : Semiring.{u4} C] [_inst_7 : Algebra.{u1, u4} R C _inst_1 _inst_6] (r : R), Eq.{succ (max u2 u3 u4)} (TensorProduct.{u1, u2, max u3 u4} R _inst_1 A (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (TensorProduct.module.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (coeFn.{max (succ (max (max u2 u3) u4)) (succ (max u2 u3 u4)), max (succ (max (max u2 u3) u4)) (succ (max u2 u3 u4))} (LinearEquiv.{u1, u1, max (max u2 u3) u4, max u2 u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (TensorProduct.assoc._proof_1.{u1} R _inst_1) (TensorProduct.assoc._proof_2.{u1} R _inst_1) (TensorProduct.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (TensorProduct.{u1, u2, max u3 u4} R _inst_1 A (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (TensorProduct.module.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (TensorProduct.addCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (TensorProduct.addCommMonoid.{u1, u2, max u3 u4} R _inst_1 A (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (TensorProduct.module.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (TensorProduct.module.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A 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(Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (TensorProduct.module.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)))) (fun (_x : LinearEquiv.{u1, u1, max (max u2 u3) u4, max u2 u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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(TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A 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_inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3 u4} (TensorProduct.{u1, u2, max u3 u4} R _inst_1 A (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (TensorProduct.module.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, max u3 u4} R _inst_1 A _inst_2 _inst_3 (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.TensorProduct.TensorProduct.semiring.{u1, u3, u4} R _inst_1 B _inst_4 _inst_5 C _inst_6 _inst_7) (Algebra.TensorProduct.TensorProduct.algebra.{u1, u3, u4} R _inst_1 B _inst_4 _inst_5 C _inst_6 _inst_7)))) => R -> (TensorProduct.{u1, u2, max u3 u4} R _inst_1 A (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (TensorProduct.module.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)))) (RingHom.hasCoeToFun.{u1, max u2 u3 u4} R (TensorProduct.{u1, u2, max u3 u4} R _inst_1 A (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (TensorProduct.module.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3 u4} (TensorProduct.{u1, u2, max u3 u4} R _inst_1 A (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (TensorProduct.module.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, max u3 u4} R _inst_1 A _inst_2 _inst_3 (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.TensorProduct.TensorProduct.semiring.{u1, u3, u4} R _inst_1 B _inst_4 _inst_5 C _inst_6 _inst_7) (Algebra.TensorProduct.TensorProduct.algebra.{u1, u3, u4} R _inst_1 B _inst_4 _inst_5 C _inst_6 _inst_7)))) (algebraMap.{u1, max u2 u3 u4} R (TensorProduct.{u1, u2, max u3 u4} R _inst_1 A (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (TensorProduct.module.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) _inst_1 (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, max u3 u4} R _inst_1 A _inst_2 _inst_3 (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.TensorProduct.TensorProduct.semiring.{u1, u3, u4} R _inst_1 B _inst_4 _inst_5 C _inst_6 _inst_7) (Algebra.TensorProduct.TensorProduct.algebra.{u1, u3, u4} R _inst_1 B _inst_4 _inst_5 C _inst_6 _inst_7)) (Algebra.TensorProduct.TensorProduct.algebra.{u1, u2, max u3 u4} R _inst_1 A _inst_2 _inst_3 (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.TensorProduct.TensorProduct.semiring.{u1, u3, u4} R _inst_1 B _inst_4 _inst_5 C _inst_6 _inst_7) (Algebra.TensorProduct.TensorProduct.algebra.{u1, u3, u4} R _inst_1 B _inst_4 _inst_5 C _inst_6 _inst_7))) r)
but is expected to have type
- forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {C : Type.{u4}} [_inst_6 : Semiring.{u4} C] [_inst_7 : Algebra.{u1, u4} R C _inst_1 _inst_6] (r : R), Eq.{max (max (succ u2) (succ u3)) (succ u4)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 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_inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u4} (TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A 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u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, max u3 u4} R _inst_1 A _inst_2 _inst_3 (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u3, u4} R _inst_1 B _inst_4 _inst_5 C _inst_6 _inst_7) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u3, u4} R _inst_1 B _inst_4 _inst_5 C _inst_6 _inst_7)) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, max u3 u4} R _inst_1 A _inst_2 _inst_3 (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u3, u4} R _inst_1 B _inst_4 _inst_5 C _inst_6 _inst_7) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u3, u4} R _inst_1 B _inst_4 _inst_5 C _inst_6 _inst_7))) r)
+ forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {C : Type.{u4}} [_inst_6 : Semiring.{u4} C] [_inst_7 : Algebra.{u1, u4} R C _inst_1 _inst_6] (r : R), Eq.{max (max (succ u2) (succ u3)) (succ u4)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) => TensorProduct.{u1, u2, max u4 u3} R _inst_1 A (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (TensorProduct.tmul.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) 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_inst_4 _inst_5) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (OfNat.ofNat.{u3} B 1 (One.toOfNat1.{u3} B (Semiring.toOne.{u3} B _inst_4)))) (OfNat.ofNat.{u4} C 1 (One.toOfNat1.{u4} C (Semiring.toOne.{u4} C _inst_6))))) (FunLike.coe.{max (max (succ u2) (succ 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_inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B 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_inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u4} (TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (TensorProduct.addCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C 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_inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (TensorProduct.addCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A 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R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max (max u4 u3) u2} (TensorProduct.{u1, u2, max u4 u3} R _inst_1 A (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, max u3 u4} R _inst_1 A _inst_2 _inst_3 (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u3, u4} R _inst_1 B _inst_4 _inst_5 C _inst_6 _inst_7) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u3, u4} R _inst_1 B _inst_4 _inst_5 C _inst_6 _inst_7))))))) (algebraMap.{u1, max (max u4 u3) u2} R (TensorProduct.{u1, u2, max u4 u3} R _inst_1 A (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, max u3 u4} R _inst_1 A _inst_2 _inst_3 (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u3, u4} R _inst_1 B _inst_4 _inst_5 C _inst_6 _inst_7) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u3, u4} R _inst_1 B _inst_4 _inst_5 C _inst_6 _inst_7)) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, max u3 u4} R _inst_1 A _inst_2 _inst_3 (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u3, u4} R _inst_1 B _inst_4 _inst_5 C _inst_6 _inst_7) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u3, u4} R _inst_1 B _inst_4 _inst_5 C _inst_6 _inst_7))) r)
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.assoc_aux_2 Algebra.TensorProduct.assoc_aux_2ₓ'. -/
theorem assoc_aux_2 (r : R) :
(TensorProduct.assoc R A B C) (((algebraMap R A) r ⊗ₜ[R] 1) ⊗ₜ[R] 1) =
@@ -1169,7 +1169,7 @@ variable {R A B C}
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {C : Type.{u4}} [_inst_6 : Semiring.{u4} C] [_inst_7 : Algebra.{u1, u4} R C _inst_1 _inst_6] (a : A) (b : B) (c : C), Eq.{succ (max u2 u3 u4)} (TensorProduct.{u1, u2, max u3 u4} R _inst_1 A (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (TensorProduct.module.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (coeFn.{max (succ (max (max u2 u3) u4)) (succ (max u2 u3 u4)), max (succ (max (max u2 u3) u4)) (succ (max u2 u3 u4))} (AlgEquiv.{u1, max (max u2 u3) u4, max u2 u3 u4} R (TensorProduct.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.module.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (TensorProduct.{u1, u2, max u3 u4} R _inst_1 A (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, 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_inst_5) (Algebra.TensorProduct.TensorProduct.algebra.{u1, u2, u3} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5) C _inst_6 _inst_7) (Algebra.TensorProduct.TensorProduct.algebra.{u1, u2, max u3 u4} R _inst_1 A _inst_2 _inst_3 (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.TensorProduct.TensorProduct.semiring.{u1, u3, u4} R _inst_1 B _inst_4 _inst_5 C _inst_6 _inst_7) (Algebra.TensorProduct.TensorProduct.algebra.{u1, u3, u4} R _inst_1 B _inst_4 _inst_5 C _inst_6 _inst_7))) (Algebra.TensorProduct.assoc.{u1, u2, u3, u4} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5 C _inst_6 _inst_7) (TensorProduct.tmul.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) 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(Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) b c))
but is expected to have type
- forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {C : Type.{u4}} [_inst_6 : Semiring.{u4} C] [_inst_7 : Algebra.{u1, u4} R C _inst_1 _inst_6] (a : A) (b : B) (c : C), Eq.{max (max (succ u2) (succ u3)) (succ u4)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) => TensorProduct.{u1, u2, max u4 u3} R _inst_1 A (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (TensorProduct.tmul.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a b) c)) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (max (succ u2) (succ u3)) (succ u4), max (max (succ u2) (succ u3)) (succ u4)} (LinearEquiv.{u1, u1, max u4 u3 u2, max (max u4 u3) u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (TensorProduct.addCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C 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_inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (TensorProduct.addCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, max u3 u4} R _inst_1 A (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (TensorProduct.assoc.{u1, u2, u3, u4} R _inst_1 A B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (TensorProduct.tmul.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a b) c)) (TensorProduct.tmul.{u1, u2, max u4 u3} R _inst_1 A (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) a (TensorProduct.tmul.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) b c))
+ forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {C : Type.{u4}} [_inst_6 : Semiring.{u4} C] [_inst_7 : Algebra.{u1, u4} R C _inst_1 _inst_6] (a : A) (b : B) (c : C), Eq.{max (max (succ u2) (succ u3)) (succ u4)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : TensorProduct.{u1, max u3 u2, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) => TensorProduct.{u1, u2, max u4 u3} R _inst_1 A (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (TensorProduct.tmul.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (TensorProduct.addCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (Module.toDistribMulAction.{u1, max (max u2 u3) u4} R (TensorProduct.{u1, u2, max u4 u3} R _inst_1 A (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (TensorProduct.addCommMonoid.{u1, u2, max u3 u4} R _inst_1 A (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, max u3 u4} R _inst_1 A (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (TensorProduct.assoc.{u1, u2, u3, u4} R _inst_1 A B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (TensorProduct.tmul.{u1, max u2 u3, u4} R _inst_1 (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) C (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) (TensorProduct.tmul.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) a b) c)) (TensorProduct.tmul.{u1, u2, max u4 u3} R _inst_1 A (TensorProduct.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (TensorProduct.addCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) a (TensorProduct.tmul.{u1, u3, u4} R _inst_1 B C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7) b c))
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.assoc_tmul Algebra.TensorProduct.assoc_tmulₓ'. -/
@[simp]
theorem assoc_tmul (a : A) (b : B) (c : C) :
@@ -1260,7 +1260,7 @@ def congr (f : A ≃ₐ[R] B) (g : C ≃ₐ[R] D) : A ⊗[R] C ≃ₐ[R] B ⊗[R
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {C : Type.{u4}} [_inst_6 : Semiring.{u4} C] [_inst_7 : Algebra.{u1, u4} R C _inst_1 _inst_6] {D : Type.{u5}} [_inst_8 : Semiring.{u5} D] [_inst_9 : Algebra.{u1, u5} R D _inst_1 _inst_8] (f : AlgEquiv.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (g : AlgEquiv.{u1, u4, u5} R C D _inst_1 _inst_6 _inst_8 _inst_7 _inst_9) (x : TensorProduct.{u1, u2, u4} R _inst_1 A C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, 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_inst_7)))))) (DistribMulAction.toDistribSMul.{u1, max u2 u4} R (TensorProduct.{u1, u2, u4} R _inst_1 A C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u4} (TensorProduct.{u1, u2, u4} R _inst_1 A C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C 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_inst_6 _inst_7) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u3, u5} R _inst_1 B _inst_4 _inst_5 D _inst_8 _inst_9) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u4} R _inst_1 A _inst_2 _inst_3 C _inst_6 _inst_7) 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B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} D (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} D (Semiring.toNonAssocSemiring.{u5} D _inst_8))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u5} R D _inst_1 _inst_8 _inst_9)) _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u4} R _inst_1 A _inst_2 _inst_3 C _inst_6 _inst_7) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u3, u5} R _inst_1 B _inst_4 _inst_5 D _inst_8 _inst_9) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u4} R _inst_1 A _inst_2 _inst_3 C _inst_6 _inst_7) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u3, u5} R _inst_1 B _inst_4 _inst_5 D _inst_8 _inst_9)))))) (Algebra.TensorProduct.map.{u1, u2, u3, u4, u5} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5 C _inst_6 _inst_7 D _inst_8 _inst_9 (AlgHomClass.toAlgHom.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgEquiv.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgEquivClass.toAlgHomClass.{max u2 u3, u1, u2, u3} (AlgEquiv.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5)) f) (AlgHomClass.toAlgHom.{u1, u4, u5, max u4 u5} R C D _inst_1 _inst_6 _inst_8 _inst_7 _inst_9 (AlgEquiv.{u1, u4, u5} R C D _inst_1 _inst_6 _inst_8 _inst_7 _inst_9) (AlgEquivClass.toAlgHomClass.{max u4 u5, u1, u4, u5} (AlgEquiv.{u1, u4, u5} R C D _inst_1 _inst_6 _inst_8 _inst_7 _inst_9) R C D _inst_1 _inst_6 _inst_8 _inst_7 _inst_9 (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u4, u5} R C D _inst_1 _inst_6 _inst_8 _inst_7 _inst_9)) g)) x)
+ forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {C : Type.{u4}} [_inst_6 : Semiring.{u4} C] [_inst_7 : Algebra.{u1, u4} R C _inst_1 _inst_6] {D : Type.{u5}} [_inst_8 : Semiring.{u5} D] [_inst_9 : Algebra.{u1, u5} R D _inst_1 _inst_8] (f : AlgEquiv.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (g : AlgEquiv.{u1, u4, u5} R C D _inst_1 _inst_6 _inst_8 _inst_7 _inst_9) (x : TensorProduct.{u1, u2, u4} R _inst_1 A C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) => TensorProduct.{u1, u3, u5} R _inst_1 B D (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} D (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} D (Semiring.toNonAssocSemiring.{u5} D _inst_8))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u5} R D _inst_1 _inst_8 _inst_9)) _x) (SMulHomClass.toFunLike.{max (max (max u2 u3) u4) u5, u1, max u2 u4, max u3 u5} (AlgEquiv.{u1, max u4 u2, max u5 u3} R (TensorProduct.{u1, u2, u4} R _inst_1 A C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A 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B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} D (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} D (Semiring.toNonAssocSemiring.{u5} D _inst_8))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u5} R D _inst_1 _inst_8 _inst_9)) _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u4} R _inst_1 A _inst_2 _inst_3 C _inst_6 _inst_7) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u3, u5} R _inst_1 B _inst_4 _inst_5 D _inst_8 _inst_9) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u4} R _inst_1 A _inst_2 _inst_3 C _inst_6 _inst_7) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u3, u5} R _inst_1 B _inst_4 _inst_5 D _inst_8 _inst_9)))))) (Algebra.TensorProduct.map.{u1, u2, u3, u4, u5} R _inst_1 A _inst_2 _inst_3 B _inst_4 _inst_5 C _inst_6 _inst_7 D _inst_8 _inst_9 (AlgHomClass.toAlgHom.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgEquiv.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgEquivClass.toAlgHomClass.{max u2 u3, u1, u2, u3} (AlgEquiv.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5)) f) (AlgHomClass.toAlgHom.{u1, u4, u5, max u4 u5} R C D _inst_1 _inst_6 _inst_8 _inst_7 _inst_9 (AlgEquiv.{u1, u4, u5} R C D _inst_1 _inst_6 _inst_8 _inst_7 _inst_9) (AlgEquivClass.toAlgHomClass.{max u4 u5, u1, u4, u5} (AlgEquiv.{u1, u4, u5} R C D _inst_1 _inst_6 _inst_8 _inst_7 _inst_9) R C D _inst_1 _inst_6 _inst_8 _inst_7 _inst_9 (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u4, u5} R C D _inst_1 _inst_6 _inst_8 _inst_7 _inst_9)) g)) x)
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.congr_apply Algebra.TensorProduct.congr_applyₓ'. -/
@[simp]
theorem congr_apply (f : A ≃ₐ[R] B) (g : C ≃ₐ[R] D) (x) :
@@ -1272,7 +1272,7 @@ theorem congr_apply (f : A ≃ₐ[R] B) (g : C ≃ₐ[R] D) (x) :
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {C : Type.{u4}} [_inst_6 : Semiring.{u4} C] [_inst_7 : Algebra.{u1, u4} R C _inst_1 _inst_6] {D : Type.{u5}} [_inst_8 : Semiring.{u5} D] [_inst_9 : Algebra.{u1, u5} R D _inst_1 _inst_8] (f : AlgEquiv.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (g : AlgEquiv.{u1, u4, u5} R C D _inst_1 _inst_6 _inst_8 _inst_7 _inst_9) (x : TensorProduct.{u1, u3, u5} R _inst_1 B D (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} D (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} D (Semiring.toNonAssocSemiring.{u5} D _inst_8))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u5} R D _inst_1 _inst_8 _inst_9)), Eq.{succ (max u2 u4)} (TensorProduct.{u1, u2, u4} R _inst_1 A C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (coeFn.{max (succ (max u3 u5)) (succ (max u2 u4)), max (succ (max u3 u5)) (succ (max u2 u4))} (AlgEquiv.{u1, max u3 u5, max u2 u4} R (TensorProduct.{u1, u3, u5} R _inst_1 B D (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} D (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} D (Semiring.toNonAssocSemiring.{u5} D _inst_8))) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7))) (AlgEquiv.hasCoeToFun.{u1, max u3 u5, max u2 u4} R (TensorProduct.{u1, u3, u5} R _inst_1 B D (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} D (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} D (Semiring.toNonAssocSemiring.{u5} D _inst_8))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u5} R D _inst_1 _inst_8 _inst_9)) (TensorProduct.{u1, u2, u4} R _inst_1 A C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) _inst_1 (Algebra.TensorProduct.TensorProduct.semiring.{u1, u3, u5} R _inst_1 B _inst_4 _inst_5 D _inst_8 _inst_9) (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u4} R _inst_1 A _inst_2 _inst_3 C _inst_6 _inst_7) (Algebra.TensorProduct.TensorProduct.algebra.{u1, u3, u5} R _inst_1 B _inst_4 _inst_5 D _inst_8 _inst_9) (Algebra.TensorProduct.TensorProduct.algebra.{u1, u2, u4} R _inst_1 A _inst_2 _inst_3 C _inst_6 _inst_7)) (fun (_x : AlgHom.{u1, max u3 u5, max u2 u4} R (TensorProduct.{u1, u3, u5} R _inst_1 B D (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B 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_inst_9)))))) (DistribMulAction.toDistribSMul.{u1, max u3 u5} R (TensorProduct.{u1, u3, u5} R _inst_1 B D (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} D (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} D (Semiring.toNonAssocSemiring.{u5} D _inst_8))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u5} R D _inst_1 _inst_8 _inst_9)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u5} (TensorProduct.{u1, u3, u5} R _inst_1 B D (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} D (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} D (Semiring.toNonAssocSemiring.{u5} D 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B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f)) (AlgHomClass.toAlgHom.{u1, u5, u4, max u4 u5} R D C _inst_1 _inst_8 _inst_6 _inst_9 _inst_7 (AlgEquiv.{u1, u5, u4} R D C _inst_1 _inst_8 _inst_6 _inst_9 _inst_7) (AlgEquivClass.toAlgHomClass.{max u4 u5, u1, u5, u4} (AlgEquiv.{u1, u5, u4} R D C _inst_1 _inst_8 _inst_6 _inst_9 _inst_7) R D C _inst_1 _inst_8 _inst_6 _inst_9 _inst_7 (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u5, u4} R D C _inst_1 _inst_8 _inst_6 _inst_9 _inst_7)) (AlgEquiv.symm.{u1, u4, u5} R C D _inst_1 _inst_6 _inst_8 _inst_7 _inst_9 g))) x)
+ forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {B : Type.{u3}} [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {C : Type.{u4}} [_inst_6 : Semiring.{u4} C] [_inst_7 : Algebra.{u1, u4} R C _inst_1 _inst_6] {D : Type.{u5}} [_inst_8 : Semiring.{u5} D] [_inst_9 : Algebra.{u1, u5} R D _inst_1 _inst_8] (f : AlgEquiv.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (g : AlgEquiv.{u1, u4, u5} R C D _inst_1 _inst_6 _inst_8 _inst_7 _inst_9) (x : TensorProduct.{u1, u3, u5} R _inst_1 B D (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} D (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} D (Semiring.toNonAssocSemiring.{u5} D _inst_8))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u5} R D _inst_1 _inst_8 _inst_9)), Eq.{max (succ u2) (succ u4)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : TensorProduct.{u1, u3, u5} R _inst_1 B D (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} D (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} D (Semiring.toNonAssocSemiring.{u5} D _inst_8))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u5} R D _inst_1 _inst_8 _inst_9)) => TensorProduct.{u1, u2, u4} R _inst_1 A C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} D (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} D (Semiring.toNonAssocSemiring.{u5} D _inst_8))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u5} R D _inst_1 _inst_8 _inst_9)) => TensorProduct.{u1, u2, u4} R _inst_1 A C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) _x) (SMulHomClass.toFunLike.{max (max (max u2 u3) u4) u5, u1, max u3 u5, max u2 u4} (AlgEquiv.{u1, max u3 u5, max u2 u4} R (TensorProduct.{u1, u3, u5} R _inst_1 B D (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B 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_inst_9)))))) (DistribMulAction.toDistribSMul.{u1, max u3 u5} R (TensorProduct.{u1, u3, u5} R _inst_1 B D (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} D (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} D (Semiring.toNonAssocSemiring.{u5} D _inst_8))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u5} R D _inst_1 _inst_8 _inst_9)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u5} (TensorProduct.{u1, u3, u5} R _inst_1 B D (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} D (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} D (Semiring.toNonAssocSemiring.{u5} D 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_inst_9)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u5} (TensorProduct.{u1, u3, u5} R _inst_1 B D (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} D (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} D (Semiring.toNonAssocSemiring.{u5} D _inst_8))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u5} R D _inst_1 _inst_8 _inst_9)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u5} (TensorProduct.{u1, u3, u5} R _inst_1 B D (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} D (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} D (Semiring.toNonAssocSemiring.{u5} D _inst_8))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u5} R D _inst_1 _inst_8 _inst_9)) (Semiring.toNonAssocSemiring.{max u3 u5} (TensorProduct.{u1, u3, u5} R _inst_1 B D (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} D (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} D (Semiring.toNonAssocSemiring.{u5} D _inst_8))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u5} R D _inst_1 _inst_8 _inst_9)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u3, u5} R _inst_1 B _inst_4 _inst_5 D _inst_8 _inst_9)))) (Algebra.toModule.{u1, max u3 u5} R (TensorProduct.{u1, u3, u5} R _inst_1 B D (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} D (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} D (Semiring.toNonAssocSemiring.{u5} D _inst_8))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u5} R D _inst_1 _inst_8 _inst_9)) _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u3, u5} R _inst_1 B _inst_4 _inst_5 D _inst_8 _inst_9) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u3, u5} R _inst_1 B _inst_4 _inst_5 D _inst_8 _inst_9))) (Module.toDistribMulAction.{u1, max u2 u4} R (TensorProduct.{u1, u2, u4} R _inst_1 A C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u4} (TensorProduct.{u1, u2, u4} R _inst_1 A C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u4} (TensorProduct.{u1, u2, u4} R _inst_1 A C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Semiring.toNonAssocSemiring.{max u2 u4} (TensorProduct.{u1, u2, u4} R _inst_1 A C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u4} R _inst_1 A _inst_2 _inst_3 C _inst_6 _inst_7)))) (Algebra.toModule.{u1, max u2 u4} R (TensorProduct.{u1, u2, u4} R _inst_1 A C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u4} R _inst_1 A _inst_2 _inst_3 C _inst_6 _inst_7) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u4} R _inst_1 A _inst_2 _inst_3 C _inst_6 _inst_7))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, max u3 u5, max u2 u4, max (max (max u2 u3) u4) u5} R (TensorProduct.{u1, u3, u5} R _inst_1 B D (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} D (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} D (Semiring.toNonAssocSemiring.{u5} D _inst_8))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u5} R D _inst_1 _inst_8 _inst_9)) (TensorProduct.{u1, u2, u4} R _inst_1 A C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u3, u5} R _inst_1 B _inst_4 _inst_5 D _inst_8 _inst_9) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u4} R _inst_1 A _inst_2 _inst_3 C _inst_6 _inst_7) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u3, u5} R _inst_1 B _inst_4 _inst_5 D _inst_8 _inst_9) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u4} R _inst_1 A _inst_2 _inst_3 C _inst_6 _inst_7) (AlgHom.{u1, max u5 u3, max u4 u2} R (TensorProduct.{u1, u3, u5} R _inst_1 B D (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} D (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} D (Semiring.toNonAssocSemiring.{u5} D _inst_8))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u5} R D _inst_1 _inst_8 _inst_9)) (TensorProduct.{u1, u2, u4} R _inst_1 A C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u3, u5} R _inst_1 B _inst_4 _inst_5 D _inst_8 _inst_9) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u4} R _inst_1 A _inst_2 _inst_3 C _inst_6 _inst_7) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u3, u5} R _inst_1 B _inst_4 _inst_5 D _inst_8 _inst_9) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u4} R _inst_1 A _inst_2 _inst_3 C _inst_6 _inst_7)) (AlgHom.algHomClass.{u1, max u3 u5, max u2 u4} R (TensorProduct.{u1, u3, u5} R _inst_1 B D (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} D (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} D (Semiring.toNonAssocSemiring.{u5} D _inst_8))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.toModule.{u1, u5} R D _inst_1 _inst_8 _inst_9)) (TensorProduct.{u1, u2, u4} R _inst_1 A C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_6))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_6 _inst_7)) _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u3, u5} R _inst_1 B _inst_4 _inst_5 D _inst_8 _inst_9) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u4} R _inst_1 A _inst_2 _inst_3 C _inst_6 _inst_7) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u3, u5} R _inst_1 B _inst_4 _inst_5 D _inst_8 _inst_9) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u4} R _inst_1 A _inst_2 _inst_3 C _inst_6 _inst_7)))))) (Algebra.TensorProduct.map.{u1, u3, u2, u5, u4} R _inst_1 B _inst_4 _inst_5 A _inst_2 _inst_3 D _inst_8 _inst_9 C _inst_6 _inst_7 (AlgHomClass.toAlgHom.{u1, u3, u2, max u2 u3} R B A _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 (AlgEquiv.{u1, u3, u2} R B A _inst_1 _inst_4 _inst_2 _inst_5 _inst_3) (AlgEquivClass.toAlgHomClass.{max u2 u3, u1, u3, u2} (AlgEquiv.{u1, u3, u2} R B A _inst_1 _inst_4 _inst_2 _inst_5 _inst_3) R B A _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u3, u2} R B A _inst_1 _inst_4 _inst_2 _inst_5 _inst_3)) (AlgEquiv.symm.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f)) (AlgHomClass.toAlgHom.{u1, u5, u4, max u4 u5} R D C _inst_1 _inst_8 _inst_6 _inst_9 _inst_7 (AlgEquiv.{u1, u5, u4} R D C _inst_1 _inst_8 _inst_6 _inst_9 _inst_7) (AlgEquivClass.toAlgHomClass.{max u4 u5, u1, u5, u4} (AlgEquiv.{u1, u5, u4} R D C _inst_1 _inst_8 _inst_6 _inst_9 _inst_7) R D C _inst_1 _inst_8 _inst_6 _inst_9 _inst_7 (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u5, u4} R D C _inst_1 _inst_8 _inst_6 _inst_9 _inst_7)) (AlgEquiv.symm.{u1, u4, u5} R C D _inst_1 _inst_6 _inst_8 _inst_7 _inst_9 g))) x)
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.congr_symm_apply Algebra.TensorProduct.congr_symm_applyₓ'. -/
@[simp]
theorem congr_symm_apply (f : A ≃ₐ[R] B) (g : C ≃ₐ[R] D) (x) :
@@ -1357,7 +1357,7 @@ def productMap : A ⊗[R] B →ₐ[R] S :=
lean 3 declaration is
forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} {S : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Semiring.{u3} B] [_inst_4 : CommSemiring.{u4} S] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_6 : Algebra.{u1, u3} R B _inst_1 _inst_3] [_inst_7 : Algebra.{u1, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_4)] (f : AlgHom.{u1, u2, u4} R A S _inst_1 _inst_2 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_5 _inst_7) (g : AlgHom.{u1, u3, u4} R B S _inst_1 _inst_3 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_6 _inst_7) (a : A) (b : B), Eq.{succ u4} S (coeFn.{max (succ (max u2 u3)) (succ u4), max (succ (max u2 u3)) (succ u4)} (AlgHom.{u1, max u2 u3, u4} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_3 _inst_6)) S _inst_1 (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u3} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) (CommSemiring.toSemiring.{u4} S _inst_4) (Algebra.TensorProduct.TensorProduct.algebra.{u1, u2, u3} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) _inst_7) (fun (_x : AlgHom.{u1, max u2 u3, u4} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_3 _inst_6)) S _inst_1 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but is expected to have type
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(Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4)))) (Algebra.toModule.{u3, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_7)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u2, u4, max u2 u4} R A S _inst_1 _inst_2 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_5 _inst_7 (AlgHom.{u3, u2, u4} R A S _inst_1 _inst_2 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_5 _inst_7) (AlgHom.algHomClass.{u3, u2, u4} R A S _inst_1 _inst_2 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_5 _inst_7))))) f a) (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (AlgHom.{u3, u1, u4} R B S _inst_1 _inst_3 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_6 _inst_7) B (fun (_x : B) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : B) => S) _x) (SMulHomClass.toFunLike.{max u1 u4, u3, u1, u4} (AlgHom.{u3, u1, u4} R B S _inst_1 _inst_3 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_6 _inst_7) R B S (SMulZeroClass.toSMul.{u3, u1} R B (AddMonoid.toZero.{u1} B (AddCommMonoid.toAddMonoid.{u1} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))))) (DistribSMul.toSMulZeroClass.{u3, u1} R B (AddMonoid.toAddZeroClass.{u1} B (AddCommMonoid.toAddMonoid.{u1} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))))) (DistribMulAction.toDistribSMul.{u3, u1} R B (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3)))) (Module.toDistribMulAction.{u3, u1} R B (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6))))) (SMulZeroClass.toSMul.{u3, u4} R S (AddMonoid.toZero.{u4} S (AddCommMonoid.toAddMonoid.{u4} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4)))))) (DistribSMul.toSMulZeroClass.{u3, u4} R S (AddMonoid.toAddZeroClass.{u4} S (AddCommMonoid.toAddMonoid.{u4} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4)))))) (DistribMulAction.toDistribSMul.{u3, u4} R S (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u4} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4))))) (Module.toDistribMulAction.{u3, u4} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4)))) (Algebra.toModule.{u3, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u4, u3, u1, u4} (AlgHom.{u3, u1, u4} R B S _inst_1 _inst_3 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_6 _inst_7) R B S (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3)))) (AddCommMonoid.toAddMonoid.{u4} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4))))) (Module.toDistribMulAction.{u3, u1} R B (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (Module.toDistribMulAction.{u3, u4} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4)))) (Algebra.toModule.{u3, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_7)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u4, u3, u1, u4} (AlgHom.{u3, u1, u4} R B S _inst_1 _inst_3 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_6 _inst_7) R B S (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4))) (Module.toDistribMulAction.{u3, u1} R B (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (Module.toDistribMulAction.{u3, u4} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4)))) (Algebra.toModule.{u3, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_7)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u1, u4, max u1 u4} R B S _inst_1 _inst_3 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_6 _inst_7 (AlgHom.{u3, u1, u4} R B S _inst_1 _inst_3 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_6 _inst_7) (AlgHom.algHomClass.{u3, u1, u4} R B S _inst_1 _inst_3 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_6 _inst_7))))) g b))
+ forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} {S : Type.{u4}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Semiring.{u1} B] [_inst_4 : CommSemiring.{u4} S] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_2] [_inst_6 : Algebra.{u3, u1} R B _inst_1 _inst_3] [_inst_7 : Algebra.{u3, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_4)] (f : AlgHom.{u3, u2, u4} R A S _inst_1 _inst_2 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_5 _inst_7) (g : AlgHom.{u3, u1, u4} R B S _inst_1 _inst_3 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_6 _inst_7) (a : A) (b : B), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) => S) (TensorProduct.tmul.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6) a b)) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u4), max (succ u2) (succ u1), succ u4} (AlgHom.{u3, max u1 u2, u4} R (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) S _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) (CommSemiring.toSemiring.{u4} S _inst_4) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) _inst_7) (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (fun (_x : TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) => S) _x) (SMulHomClass.toFunLike.{max (max u2 u1) u4, u3, max u2 u1, u4} (AlgHom.{u3, max u1 u2, u4} R (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) S _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) (CommSemiring.toSemiring.{u4} S _inst_4) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) _inst_7) R (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) S (SMulZeroClass.toSMul.{u3, max u2 u1} R (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (AddMonoid.toZero.{max u2 u1} (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (AddCommMonoid.toAddMonoid.{max u2 u1} (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B 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_inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (Semiring.toNonAssocSemiring.{max u2 u1} (TensorProduct.{u3, 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_inst_3 _inst_6)))) (Algebra.toModule.{u3, max u2 u1} R (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6)))))) (SMulZeroClass.toSMul.{u3, u4} R S (AddMonoid.toZero.{u4} S (AddCommMonoid.toAddMonoid.{u4} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4)))))) (DistribSMul.toSMulZeroClass.{u3, u4} R S (AddMonoid.toAddZeroClass.{u4} S (AddCommMonoid.toAddMonoid.{u4} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4)))))) 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(Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) S _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) (CommSemiring.toSemiring.{u4} S _inst_4) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) _inst_7) R (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) S (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u1} (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3)))) (AddCommMonoid.toAddMonoid.{u4} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4))))) (Module.toDistribMulAction.{u3, u1} R B (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (Module.toDistribMulAction.{u3, u4} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4)))) (Algebra.toModule.{u3, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_7)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u4, u3, u1, u4} (AlgHom.{u3, u1, u4} R B S _inst_1 _inst_3 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_6 _inst_7) R B S (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4))) (Module.toDistribMulAction.{u3, u1} R B (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (Module.toDistribMulAction.{u3, u4} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4)))) (Algebra.toModule.{u3, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_7)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u1, u4, max u1 u4} R B S _inst_1 _inst_3 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_6 _inst_7 (AlgHom.{u3, u1, u4} R B S _inst_1 _inst_3 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_6 _inst_7) (AlgHom.algHomClass.{u3, u1, u4} R B S _inst_1 _inst_3 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_6 _inst_7))))) g b))
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.product_map_apply_tmul Algebra.TensorProduct.productMap_apply_tmulₓ'. -/
@[simp]
theorem productMap_apply_tmul (a : A) (b : B) : productMap f g (a ⊗ₜ b) = f a * g b :=
@@ -1370,7 +1370,7 @@ theorem productMap_apply_tmul (a : A) (b : B) : productMap f g (a ⊗ₜ b) = f
lean 3 declaration is
forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} {S : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Semiring.{u3} B] [_inst_4 : CommSemiring.{u4} S] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_6 : Algebra.{u1, u3} R B _inst_1 _inst_3] [_inst_7 : Algebra.{u1, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_4)] (f : AlgHom.{u1, u2, u4} R A S _inst_1 _inst_2 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_5 _inst_7) (g : AlgHom.{u1, u3, u4} R B S _inst_1 _inst_3 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_6 _inst_7) (a : A), Eq.{succ u4} S (coeFn.{max (succ (max u2 u3)) (succ u4), max (succ (max u2 u3)) (succ u4)} (AlgHom.{u1, max u2 u3, u4} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_3 _inst_6)) S _inst_1 (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u3} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) (CommSemiring.toSemiring.{u4} S _inst_4) (Algebra.TensorProduct.TensorProduct.algebra.{u1, u2, u3} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) _inst_7) (fun (_x : AlgHom.{u1, max u2 u3, u4} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_3 _inst_6)) S _inst_1 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B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_3 _inst_6)) S _inst_1 (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u3} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) (CommSemiring.toSemiring.{u4} S _inst_4) (Algebra.TensorProduct.TensorProduct.algebra.{u1, u2, u3} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) _inst_7) (Algebra.TensorProduct.productMap.{u1, u2, u3, u4} R A B S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f g) (coeFn.{max (succ u2) (succ (max u2 u3)), max (succ u2) (succ (max u2 u3))} (AlgHom.{u1, u2, max u2 u3} R A (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B 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but is expected to have type
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_inst_5 B _inst_3 _inst_6)))))) (SMulZeroClass.toSMul.{u3, u4} R S (AddMonoid.toZero.{u4} S (AddCommMonoid.toAddMonoid.{u4} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4)))))) (DistribSMul.toSMulZeroClass.{u3, u4} R S (AddMonoid.toAddZeroClass.{u4} S (AddCommMonoid.toAddMonoid.{u4} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4)))))) (DistribMulAction.toDistribSMul.{u3, u4} R S (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u4} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4))))) 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(Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) (CommSemiring.toSemiring.{u4} S _inst_4) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) _inst_7) R (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B 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_inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5))))) (SMulZeroClass.toSMul.{u3, u4} R S (AddMonoid.toZero.{u4} S (AddCommMonoid.toAddMonoid.{u4} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4)))))) (DistribSMul.toSMulZeroClass.{u3, u4} R S (AddMonoid.toAddZeroClass.{u4} S (AddCommMonoid.toAddMonoid.{u4} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4)))))) (DistribMulAction.toDistribSMul.{u3, u4} R S (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u4} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4))))) (Module.toDistribMulAction.{u3, u4} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4)))) (Algebra.toModule.{u3, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u4, u3, u2, u4} (AlgHom.{u3, u2, u4} R A S _inst_1 _inst_2 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_5 _inst_7) R A S (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u4} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4))))) (Module.toDistribMulAction.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5)) (Module.toDistribMulAction.{u3, u4} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4)))) (Algebra.toModule.{u3, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_7)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u4, u3, u2, u4} (AlgHom.{u3, u2, u4} R A S _inst_1 _inst_2 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_5 _inst_7) R A S (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4))) (Module.toDistribMulAction.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5)) (Module.toDistribMulAction.{u3, u4} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4)))) (Algebra.toModule.{u3, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_7)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u2, u4, max u2 u4} R A S _inst_1 _inst_2 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_5 _inst_7 (AlgHom.{u3, u2, u4} R A S _inst_1 _inst_2 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_5 _inst_7) (AlgHom.algHomClass.{u3, u2, u4} R A S _inst_1 _inst_2 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_5 _inst_7))))) f a)
+ forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} {S : Type.{u4}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Semiring.{u1} B] [_inst_4 : CommSemiring.{u4} S] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_2] [_inst_6 : Algebra.{u3, u1} R B _inst_1 _inst_3] [_inst_7 : Algebra.{u3, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_4)] (f : AlgHom.{u3, u2, u4} R A S _inst_1 _inst_2 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_5 _inst_7) (g : AlgHom.{u3, u1, u4} R B S _inst_1 _inst_3 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_6 _inst_7) (a : A), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) => S) (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (AlgHom.{u3, u2, max u1 u2} R A (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) _inst_1 _inst_2 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) _inst_5 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6)) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) a) (SMulHomClass.toFunLike.{max u2 u1, u3, u2, max u2 u1} (AlgHom.{u3, u2, max u1 u2} R A (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) _inst_1 _inst_2 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) _inst_5 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6)) R A (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (SMulZeroClass.toSMul.{u3, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u3, u2} R A (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5))))) (SMulZeroClass.toSMul.{u3, max u2 u1} R (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (AddMonoid.toZero.{max u2 u1} (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (AddCommMonoid.toAddMonoid.{max u2 u1} (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (Semiring.toNonAssocSemiring.{max u2 u1} (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6)))))) (DistribSMul.toSMulZeroClass.{u3, max u2 u1} R (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (AddMonoid.toAddZeroClass.{max u2 u1} (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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_inst_5 B _inst_3 _inst_6)))))) (SMulZeroClass.toSMul.{u3, u4} R S (AddMonoid.toZero.{u4} S (AddCommMonoid.toAddMonoid.{u4} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4)))))) (DistribSMul.toSMulZeroClass.{u3, u4} R S (AddMonoid.toAddZeroClass.{u4} S (AddCommMonoid.toAddMonoid.{u4} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4)))))) (DistribMulAction.toDistribSMul.{u3, u4} R S (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u4} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4))))) 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(Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) (CommSemiring.toSemiring.{u4} S _inst_4) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) _inst_7) R (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B 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(Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) _inst_5 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6)) (AlgHom.algHomClass.{u3, u2, max u2 u1} R A (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) _inst_1 _inst_2 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) _inst_5 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6)))))) (Algebra.TensorProduct.includeLeft.{u3, u2, u1} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) a)) (FunLike.coe.{max (succ u2) (succ u4), succ u2, succ u4} 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_inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5))))) (SMulZeroClass.toSMul.{u3, u4} R S (AddMonoid.toZero.{u4} S (AddCommMonoid.toAddMonoid.{u4} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4)))))) (DistribSMul.toSMulZeroClass.{u3, u4} R S (AddMonoid.toAddZeroClass.{u4} S (AddCommMonoid.toAddMonoid.{u4} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4)))))) (DistribMulAction.toDistribSMul.{u3, u4} R S (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u4} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4))))) (Module.toDistribMulAction.{u3, u4} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4)))) (Algebra.toModule.{u3, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u4, u3, u2, u4} (AlgHom.{u3, u2, u4} R A S _inst_1 _inst_2 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_5 _inst_7) R A S (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u4} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4))))) (Module.toDistribMulAction.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5)) (Module.toDistribMulAction.{u3, u4} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4)))) (Algebra.toModule.{u3, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_7)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u4, u3, u2, u4} (AlgHom.{u3, u2, u4} R A S _inst_1 _inst_2 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_5 _inst_7) R A S (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4))) (Module.toDistribMulAction.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5)) (Module.toDistribMulAction.{u3, u4} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4)))) (Algebra.toModule.{u3, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_7)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u2, u4, max u2 u4} R A S _inst_1 _inst_2 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_5 _inst_7 (AlgHom.{u3, u2, u4} R A S _inst_1 _inst_2 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_5 _inst_7) (AlgHom.algHomClass.{u3, u2, u4} R A S _inst_1 _inst_2 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_5 _inst_7))))) f a)
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.product_map_left_apply Algebra.TensorProduct.productMap_left_applyₓ'. -/
theorem productMap_left_apply (a : A) : productMap f g ((includeLeft : A →ₐ[R] A ⊗ B) a) = f a := by
simp
@@ -1391,7 +1391,7 @@ theorem productMap_left : (productMap f g).comp includeLeft = f :=
lean 3 declaration is
forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} {S : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Semiring.{u3} B] [_inst_4 : CommSemiring.{u4} S] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_6 : Algebra.{u1, u3} R B _inst_1 _inst_3] [_inst_7 : Algebra.{u1, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_4)] (f : AlgHom.{u1, u2, u4} R A S _inst_1 _inst_2 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_5 _inst_7) (g : AlgHom.{u1, u3, u4} R B S _inst_1 _inst_3 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_6 _inst_7) (b : B), Eq.{succ u4} S (coeFn.{max (succ (max u2 u3)) (succ u4), max (succ (max u2 u3)) (succ u4)} (AlgHom.{u1, max u2 u3, u4} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_3 _inst_6)) S _inst_1 (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u3} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) (CommSemiring.toSemiring.{u4} S _inst_4) (Algebra.TensorProduct.TensorProduct.algebra.{u1, u2, u3} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) _inst_7) (fun (_x : AlgHom.{u1, max u2 u3, u4} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_3 _inst_6)) S _inst_1 (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u3} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) (CommSemiring.toSemiring.{u4} S _inst_4) (Algebra.TensorProduct.TensorProduct.algebra.{u1, u2, u3} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) _inst_7) => (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_3 _inst_6)) -> S) ([anonymous].{u1, max u2 u3, u4} R (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_3 _inst_6)) S _inst_1 (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u3} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) (CommSemiring.toSemiring.{u4} S _inst_4) (Algebra.TensorProduct.TensorProduct.algebra.{u1, u2, u3} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) _inst_7) (Algebra.TensorProduct.productMap.{u1, u2, u3, u4} R A B S _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f g) (coeFn.{max (succ u3) (succ (max u2 u3)), max (succ u3) (succ (max u2 u3))} (AlgHom.{u1, u3, max u2 u3} R B (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_3 _inst_6)) _inst_1 _inst_3 (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u3} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) _inst_6 (Algebra.TensorProduct.TensorProduct.algebra.{u1, u2, u3} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6)) (fun (_x : AlgHom.{u1, u3, max u2 u3} R B (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_3 _inst_6)) _inst_1 _inst_3 (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u3} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) _inst_6 (Algebra.TensorProduct.TensorProduct.algebra.{u1, u2, u3} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6)) => B -> (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_3 _inst_6))) ([anonymous].{u1, u3, max u2 u3} R B (TensorProduct.{u1, u2, u3} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_3 _inst_6)) _inst_1 _inst_3 (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u3} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) _inst_6 (Algebra.TensorProduct.TensorProduct.algebra.{u1, u2, u3} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6)) (Algebra.TensorProduct.includeRight.{u1, u2, u3} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) b)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (AlgHom.{u1, u3, u4} R B S _inst_1 _inst_3 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_6 _inst_7) (fun (_x : AlgHom.{u1, u3, u4} R B S _inst_1 _inst_3 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_6 _inst_7) => B -> S) ([anonymous].{u1, u3, u4} R B S _inst_1 _inst_3 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_6 _inst_7) g b)
but is expected to have type
- forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} {S : Type.{u4}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Semiring.{u1} B] [_inst_4 : CommSemiring.{u4} S] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_2] [_inst_6 : Algebra.{u3, u1} R B _inst_1 _inst_3] [_inst_7 : Algebra.{u3, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_4)] (f : AlgHom.{u3, u2, u4} R A S _inst_1 _inst_2 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_5 _inst_7) (g : AlgHom.{u3, u1, u4} R B S _inst_1 _inst_3 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_6 _inst_7) (b : B), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) => S) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (AlgHom.{u3, u1, max u1 u2} R B (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) _inst_1 _inst_3 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) _inst_6 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6)) B (fun (a : B) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : B) => TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) a) (SMulHomClass.toFunLike.{max u1 u2, u3, u1, max u1 u2} (AlgHom.{u3, u1, max u1 u2} R B (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) _inst_1 _inst_3 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) _inst_6 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6)) R B (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (SMulZeroClass.toSMul.{u3, u1} R B (AddMonoid.toZero.{u1} B (AddCommMonoid.toAddMonoid.{u1} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))))) (DistribSMul.toSMulZeroClass.{u3, u1} R B (AddMonoid.toAddZeroClass.{u1} B (AddCommMonoid.toAddMonoid.{u1} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))))) (DistribMulAction.toDistribSMul.{u3, u1} R B (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3)))) (Module.toDistribMulAction.{u3, u1} R B (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6))))) (SMulZeroClass.toSMul.{u3, max u1 u2} R (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (AddMonoid.toZero.{max u1 u2} (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (AddCommMonoid.toAddMonoid.{max u1 u2} (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (Semiring.toNonAssocSemiring.{max u1 u2} (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6)))))) (DistribSMul.toSMulZeroClass.{u3, max u1 u2} R (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (AddMonoid.toAddZeroClass.{max u1 u2} (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (Semiring.toNonAssocSemiring.{max u1 u2} (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6)))))) (DistribMulAction.toDistribSMul.{u3, max u1 u2} R (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (Semiring.toNonAssocSemiring.{max u1 u2} (TensorProduct.{u3, u2, u1} R _inst_1 A B 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+ forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} {S : Type.{u4}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Semiring.{u1} B] [_inst_4 : CommSemiring.{u4} S] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_2] [_inst_6 : Algebra.{u3, u1} R B _inst_1 _inst_3] [_inst_7 : Algebra.{u3, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_4)] (f : AlgHom.{u3, u2, u4} R A S _inst_1 _inst_2 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_5 _inst_7) (g : AlgHom.{u3, u1, u4} R B S _inst_1 _inst_3 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_6 _inst_7) (b : B), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) => S) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (AlgHom.{u3, u1, max u1 u2} R B (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) _inst_1 _inst_3 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) _inst_6 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6)) B (fun (a : B) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : B) => TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) a) (SMulHomClass.toFunLike.{max u1 u2, u3, u1, max u1 u2} (AlgHom.{u3, u1, max u1 u2} R B (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) _inst_1 _inst_3 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6) _inst_6 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6)) R B (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (SMulZeroClass.toSMul.{u3, u1} R B (AddMonoid.toZero.{u1} B (AddCommMonoid.toAddMonoid.{u1} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))))) (DistribSMul.toSMulZeroClass.{u3, u1} R B (AddMonoid.toAddZeroClass.{u1} B (AddCommMonoid.toAddMonoid.{u1} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))))) (DistribMulAction.toDistribSMul.{u3, u1} R B (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3)))) (Module.toDistribMulAction.{u3, u1} R B (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6))))) (SMulZeroClass.toSMul.{u3, max u1 u2} R (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (AddMonoid.toZero.{max u1 u2} (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (AddCommMonoid.toAddMonoid.{max u1 u2} (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (Semiring.toNonAssocSemiring.{max u1 u2} (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6)))))) (DistribSMul.toSMulZeroClass.{u3, max u1 u2} R (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (AddMonoid.toAddZeroClass.{max u1 u2} (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (AddCommMonoid.toAddMonoid.{max u1 u2} (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (Semiring.toNonAssocSemiring.{max u1 u2} (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u3, u2, u1} R _inst_1 A _inst_2 _inst_5 B _inst_3 _inst_6)))))) (DistribMulAction.toDistribSMul.{u3, max u1 u2} R (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (TensorProduct.{u3, u2, u1} R _inst_1 A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_5) (Algebra.toModule.{u3, u1} R B _inst_1 _inst_3 _inst_6)) (Semiring.toNonAssocSemiring.{max u1 u2} (TensorProduct.{u3, u2, u1} R _inst_1 A B 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_inst_5 B _inst_3 _inst_6)))))) (SMulZeroClass.toSMul.{u3, u4} R S (AddMonoid.toZero.{u4} S (AddCommMonoid.toAddMonoid.{u4} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4)))))) (DistribSMul.toSMulZeroClass.{u3, u4} R S (AddMonoid.toAddZeroClass.{u4} S (AddCommMonoid.toAddMonoid.{u4} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4)))))) (DistribMulAction.toDistribSMul.{u3, u4} R S (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u4} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4))))) 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(Module.toDistribMulAction.{u3, u4} R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_4)))) (Algebra.toModule.{u3, u4} R S _inst_1 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_7)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u1, u4, max u1 u4} R B S _inst_1 _inst_3 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_6 _inst_7 (AlgHom.{u3, u1, u4} R B S _inst_1 _inst_3 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_6 _inst_7) (AlgHom.algHomClass.{u3, u1, u4} R B S _inst_1 _inst_3 (CommSemiring.toSemiring.{u4} S _inst_4) _inst_6 _inst_7))))) g b)
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.product_map_right_apply Algebra.TensorProduct.productMap_right_applyₓ'. -/
theorem productMap_right_apply (b : B) : productMap f g (includeRight b) = g b := by simp
#align algebra.tensor_product.product_map_right_apply Algebra.TensorProduct.productMap_right_apply
@@ -1474,7 +1474,7 @@ variable {R}
lean 3 declaration is
forall {k : Type.{u_1}} [_inst_1 : CommRing.{u_1} k] {R : Type.{u_2}} [_inst_2 : Ring.{u_2} R] [_inst_3 : Algebra.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2)] {M : Type.{u_3}} [_inst_4 : AddCommMonoid.{u_3} M] [_inst_5 : Module.{u_1, u_3} k M (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) _inst_4] {ι : Type.{u_4}} (b : Basis.{u_4, u_1, u_3} ι k M (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) _inst_4 _inst_5) (r : R) (m : M), Eq.{max (succ u_4) (succ u_2)} (Finsupp.{u_4, u_2} ι R (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))))) (coeFn.{max (succ (max u_2 u_3)) (succ (max u_4 u_2)), max (succ (max u_2 u_3)) (succ (max u_4 u_2))} (LinearEquiv.{u_1, u_1, max u_2 u_3, max u_4 u_2} k k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (Algebra.TensorProduct.basisAux._proof_1.{u_1} k _inst_1) (Algebra.TensorProduct.basisAux._proof_2.{u_1} k _inst_1) (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))))) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.module.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3))) (fun (_x : LinearEquiv.{u_1, u_1, max u_2 u_3, max u_4 u_2} k k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (Algebra.TensorProduct.basisAux._proof_1.{u_1} k _inst_1) (Algebra.TensorProduct.basisAux._proof_2.{u_1} k _inst_1) (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))))) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.module.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3))) => (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) -> (Finsupp.{u_4, u_2} ι R (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))))) (LinearEquiv.hasCoeToFun.{u_1, u_1, max u_2 u_3, max u_4 u_2} k k (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))))) (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.module.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3)) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (Algebra.TensorProduct.basisAux._proof_1.{u_1} k _inst_1) (Algebra.TensorProduct.basisAux._proof_2.{u_1} k _inst_1)) (Algebra.TensorProduct.basisAux.{u_1, u_2, u_3, u_4, u_5, u_6} k _inst_1 R _inst_2 _inst_3 M _inst_4 _inst_5 ι b) (TensorProduct.tmul.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5 r m)) (SMul.smul.{u_2, max u_4 u_2} R (Finsupp.{u_4, u_2} ι R (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} 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(CommRing.toRing.{u_1} k _inst_1)))))) (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (coeFn.{max (succ u_1) (succ u_2), max (succ u_1) (succ u_2)} (RingHom.{u_1, u_2} k R (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R _inst_2))) (fun (_x : RingHom.{u_1, u_2} k R (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R _inst_2))) => k -> R) (RingHom.hasCoeToFun.{u_1, u_2} k R (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R _inst_2))) 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k _inst_1))) (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R _inst_2))))) (algebraMap.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3)) (coeFn.{max (succ u_3) (succ (max u_4 u_1)), max (succ u_3) (succ (max u_4 u_1))} (LinearEquiv.{u_1, u_1, u_3, max u_4 u_1} k k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (RingHomInvPair.ids.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1))) (RingHomInvPair.ids.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1))) M (Finsupp.{u_4, u_1} ι k (MulZeroClass.toHasZero.{u_1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u_1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1))))))) _inst_4 (Finsupp.addCommMonoid.{u_4, u_1} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))))) _inst_5 (Finsupp.module.{u_4, u_1, u_1} ι k k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1))))) (Semiring.toModule.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1))))) (fun (_x : LinearEquiv.{u_1, u_1, u_3, max u_4 u_1} k k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (RingHomInvPair.ids.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1))) (RingHomInvPair.ids.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1))) M (Finsupp.{u_4, u_1} ι k (MulZeroClass.toHasZero.{u_1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u_1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1))))))) _inst_4 (Finsupp.addCommMonoid.{u_4, u_1} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))))) _inst_5 (Finsupp.module.{u_4, u_1, u_1} ι k k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1))))) (Semiring.toModule.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1))))) => M -> (Finsupp.{u_4, u_1} ι k (MulZeroClass.toHasZero.{u_1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u_1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))))))) (LinearEquiv.hasCoeToFun.{u_1, u_1, u_3, max u_4 u_1} k k M (Finsupp.{u_4, u_1} ι k (MulZeroClass.toHasZero.{u_1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u_1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1))))))) (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) _inst_4 (Finsupp.addCommMonoid.{u_4, u_1} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))))) _inst_5 (Finsupp.module.{u_4, u_1, u_1} ι k k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1))))) (Semiring.toModule.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (RingHomInvPair.ids.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1))) (RingHomInvPair.ids.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (Basis.repr.{u_4, u_1, u_3} ι k M (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) _inst_4 _inst_5 b) m)))
but is expected to have type
- forall {k : Type.{u_3}} [_inst_1 : CommRing.{u_3} k] {R : Type.{u_1}} [_inst_2 : Ring.{u_1} R] [_inst_3 : Algebra.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2)] {M : Type.{u_4}} [_inst_4 : AddCommMonoid.{u_4} M] [_inst_5 : Module.{u_3, u_4} k M (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) _inst_4] {ι : Type.{u_2}} (b : Basis.{u_2, u_3, u_4} ι k M (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) _inst_4 _inst_5) (r : R) (m : M), Eq.{max (succ u_1) (succ u_2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) => Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (TensorProduct.tmul.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5 r m)) (FunLike.coe.{max (max (succ u_1) (succ u_4)) (succ u_2), max (succ u_1) (succ u_4), max (succ u_1) (succ u_2)} (LinearEquiv.{u_3, u_3, max u_4 u_1, max u_1 u_2} k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_2, u_1, u_3} ι R k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3))) (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (fun (_x : TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) => Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) _x) (SMulHomClass.toFunLike.{max (max u_1 u_4) u_2, u_3, max u_1 u_4, max u_1 u_2} (LinearEquiv.{u_3, u_3, max u_4 u_1, max u_1 u_2} k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_2, u_1, u_3} ι R k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3))) k (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (SMulZeroClass.toSMul.{u_3, max u_1 u_4} k (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (AddMonoid.toZero.{max u_1 u_4} (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (AddCommMonoid.toAddMonoid.{max u_1 u_4} (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5))) (DistribSMul.toSMulZeroClass.{u_3, max u_1 u_4} k (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (AddMonoid.toAddZeroClass.{max u_1 u_4} (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (AddCommMonoid.toAddMonoid.{max u_1 u_4} (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5))) (DistribMulAction.toDistribSMul.{u_3, max u_1 u_4} k (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (MonoidWithZero.toMonoid.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (AddCommMonoid.toAddMonoid.{max u_1 u_4} (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5)) (Module.toDistribMulAction.{u_3, max u_1 u_4} k (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5))))) (SMulZeroClass.toSMul.{u_3, max u_1 u_2} k (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (AddMonoid.toZero.{max u_1 u_2} (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2))))))) (DistribSMul.toSMulZeroClass.{u_3, max u_1 u_2} k (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (AddMonoid.toAddZeroClass.{max u_1 u_2} (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2))))))) (DistribMulAction.toDistribSMul.{u_3, max u_1 u_2} k (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (MonoidWithZero.toMonoid.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))))) (Module.toDistribMulAction.{u_3, max u_1 u_2} k (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2))))) (Finsupp.module.{u_2, u_1, u_3} ι R k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u_1 u_4) u_2, u_3, max u_1 u_4, max u_1 u_2} (LinearEquiv.{u_3, u_3, max u_4 u_1, max u_1 u_2} k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_2, u_1, u_3} ι R k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3))) k (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (MonoidWithZero.toMonoid.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (AddCommMonoid.toAddMonoid.{max u_1 u_4} (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5)) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))))) (Module.toDistribMulAction.{u_3, max u_1 u_4} k (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5)) (Module.toDistribMulAction.{u_3, max u_1 u_2} k (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2))))) (Finsupp.module.{u_2, u_1, u_3} ι R k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3))) (SemilinearMapClass.distribMulActionHomClass.{u_3, max u_1 u_4, max u_1 u_2, max (max u_1 u_4) u_2} k (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (LinearEquiv.{u_3, u_3, max u_4 u_1, max u_1 u_2} k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_2, u_1, u_3} ι R k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3))) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_2, u_1, u_3} ι R k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3)) (SemilinearEquivClass.instSemilinearMapClass.{u_3, u_3, max u_1 u_4, max u_1 u_2, max (max u_1 u_4) u_2} k k (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (LinearEquiv.{u_3, u_3, max u_4 u_1, max u_1 u_2} k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_2, u_1, u_3} ι R k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3))) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_2, u_1, u_3} ι R k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3)) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u_3, u_3, max u_1 u_4, max u_1 u_2} k k (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) 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(Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_2, u_1, u_3} ι R k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3)) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))))) (Algebra.TensorProduct.basisAux.{u_6, u_3, u_1, u_4, u_2} k _inst_1 R _inst_2 _inst_3 M _inst_4 _inst_5 ι b) (TensorProduct.tmul.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5 r m)) (HSMul.hSMul.{u_1, max u_1 u_2, max u_1 u_2} R (Finsupp.{u_2, u_1} ι R (MulZeroOneClass.toZero.{u_1} R (NonAssocSemiring.toMulZeroOneClass.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))))) (Finsupp.{u_2, u_1} ι R (MulZeroOneClass.toZero.{u_1} R (NonAssocSemiring.toMulZeroOneClass.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))))) (instHSMul.{u_1, max u_1 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(Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (MulZeroClass.toSMulWithZero.{u_1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2))))))))) r (Finsupp.mapRange.{u_2, u_3, u_1} ι k R (MulZeroOneClass.toZero.{u_3} k (NonAssocSemiring.toMulZeroOneClass.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (MulZeroOneClass.toZero.{u_1} R (NonAssocSemiring.toMulZeroOneClass.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (FunLike.coe.{max (succ u_3) (succ u_1), succ u_3, succ u_1} (RingHom.{u_3, u_1} k R (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) k (fun (_x : k) => (fun 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u_3 u_1, u_3, u_1} (RingHom.{u_3, u_1} k R (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) k R (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (RingHom.instRingHomClassRingHom.{u_3, u_1} k R (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))))) 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))) _inst_5 (Finsupp.module.{u_2, u_3, u_3} ι k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Semiring.toModule.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) k M (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (SMulZeroClass.toSMul.{u_3, u_4} k M (AddMonoid.toZero.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M _inst_4)) (DistribSMul.toSMulZeroClass.{u_3, u_4} k M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M _inst_4)) (DistribMulAction.toDistribSMul.{u_3, u_4} k M (MonoidWithZero.toMonoid.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (AddCommMonoid.toAddMonoid.{u_4} M _inst_4) (Module.toDistribMulAction.{u_3, u_4} k M (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) _inst_4 _inst_5)))) (SMulZeroClass.toSMul.{u_3, max u_3 u_2} k (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (AddMonoid.toZero.{max u_3 u_2} (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (AddCommMonoid.toAddMonoid.{max u_3 u_2} (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u_3, max u_3 u_2} k (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (AddMonoid.toAddZeroClass.{max u_3 u_2} (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (AddCommMonoid.toAddMonoid.{max u_3 u_2} (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))))) (DistribMulAction.toDistribSMul.{u_3, max u_3 u_2} k (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (MonoidWithZero.toMonoid.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (AddCommMonoid.toAddMonoid.{max u_3 u_2} (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))))) (Module.toDistribMulAction.{u_3, max u_3 u_2} k (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))) (Finsupp.module.{u_2, u_3, u_3} ι k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Semiring.toModule.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u_3 u_4) u_2, u_3, u_4, max u_3 u_2} (LinearEquiv.{u_3, u_3, u_4, max u_3 u_2} k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) M (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) _inst_4 (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))) _inst_5 (Finsupp.module.{u_2, u_3, u_3} ι k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Semiring.toModule.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) k M (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (MonoidWithZero.toMonoid.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (AddCommMonoid.toAddMonoid.{u_4} M _inst_4) (AddCommMonoid.toAddMonoid.{max u_3 u_2} (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))))) (Module.toDistribMulAction.{u_3, u_4} k M (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) _inst_4 _inst_5) (Module.toDistribMulAction.{u_3, max u_3 u_2} k (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))) (Finsupp.module.{u_2, u_3, u_3} ι k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Semiring.toModule.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u_3, u_4, max u_3 u_2, max (max u_3 u_4) u_2} k M (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (LinearEquiv.{u_3, u_3, u_4, max u_3 u_2} k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) M (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) _inst_4 (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))) _inst_5 (Finsupp.module.{u_2, u_3, u_3} ι k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Semiring.toModule.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) _inst_4 (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))) _inst_5 (Finsupp.module.{u_2, u_3, u_3} ι k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Semiring.toModule.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (SemilinearEquivClass.instSemilinearMapClass.{u_3, u_3, u_4, max u_3 u_2, max (max u_3 u_4) u_2} k k M (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (LinearEquiv.{u_3, u_3, u_4, max u_3 u_2} k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) M (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) _inst_4 (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))) _inst_5 (Finsupp.module.{u_2, u_3, u_3} ι k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Semiring.toModule.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) _inst_4 (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))) _inst_5 (Finsupp.module.{u_2, u_3, u_3} ι k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Semiring.toModule.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u_3, u_3, u_4, max u_3 u_2} k k M (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) _inst_4 (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))) _inst_5 (Finsupp.module.{u_2, u_3, u_3} ι k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Semiring.toModule.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))))) (Basis.repr.{u_2, u_3, u_4} ι k M (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) _inst_4 _inst_5 b) m)))
+ forall {k : Type.{u_3}} [_inst_1 : CommRing.{u_3} k] {R : Type.{u_1}} [_inst_2 : Ring.{u_1} R] [_inst_3 : Algebra.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2)] {M : Type.{u_4}} [_inst_4 : AddCommMonoid.{u_4} M] [_inst_5 : Module.{u_3, u_4} k M (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) _inst_4] {ι : Type.{u_2}} (b : Basis.{u_2, u_3, u_4} ι k M (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) _inst_4 _inst_5) (r : R) (m : M), Eq.{max (succ u_1) (succ u_2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) => Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (TensorProduct.tmul.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5 r m)) (FunLike.coe.{max (max (succ u_1) (succ u_4)) (succ u_2), max (succ u_1) (succ u_4), max (succ u_1) (succ u_2)} (LinearEquiv.{u_3, u_3, max u_4 u_1, max u_1 u_2} k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_2, u_1, u_3} ι R k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3))) (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (fun (_x : TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) => Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) _x) (SMulHomClass.toFunLike.{max (max u_1 u_4) u_2, u_3, max u_1 u_4, max u_1 u_2} (LinearEquiv.{u_3, u_3, max u_4 u_1, max u_1 u_2} k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_2, u_1, u_3} ι R k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3))) k (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (SMulZeroClass.toSMul.{u_3, max u_1 u_4} k (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (AddMonoid.toZero.{max u_1 u_4} (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (AddCommMonoid.toAddMonoid.{max u_1 u_4} (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5))) (DistribSMul.toSMulZeroClass.{u_3, max u_1 u_4} k (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (AddMonoid.toAddZeroClass.{max u_1 u_4} (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (AddCommMonoid.toAddMonoid.{max u_1 u_4} (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5))) (DistribMulAction.toDistribSMul.{u_3, max u_1 u_4} k (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (MonoidWithZero.toMonoid.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (AddCommMonoid.toAddMonoid.{max u_1 u_4} (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5)) (Module.toDistribMulAction.{u_3, max u_1 u_4} k (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5))))) (SMulZeroClass.toSMul.{u_3, max u_1 u_2} k (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (AddMonoid.toZero.{max u_1 u_2} (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2))))))) (DistribSMul.toSMulZeroClass.{u_3, max u_1 u_2} k (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (AddMonoid.toAddZeroClass.{max u_1 u_2} (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2))))))) (DistribMulAction.toDistribSMul.{u_3, max u_1 u_2} k (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (MonoidWithZero.toMonoid.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))))) (Module.toDistribMulAction.{u_3, max u_1 u_2} k (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2))))) (Finsupp.module.{u_2, u_1, u_3} ι R k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u_1 u_4) u_2, u_3, max u_1 u_4, max u_1 u_2} (LinearEquiv.{u_3, u_3, max u_4 u_1, max u_1 u_2} k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_2, u_1, u_3} ι R k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3))) k (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (MonoidWithZero.toMonoid.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (AddCommMonoid.toAddMonoid.{max u_1 u_4} (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5)) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))))) (Module.toDistribMulAction.{u_3, max u_1 u_4} k (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5)) (Module.toDistribMulAction.{u_3, max u_1 u_2} k (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2))))) (Finsupp.module.{u_2, u_1, u_3} ι R k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3))) (SemilinearMapClass.distribMulActionHomClass.{u_3, max u_1 u_4, max u_1 u_2, max (max u_1 u_4) u_2} k (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (LinearEquiv.{u_3, u_3, max u_4 u_1, max u_1 u_2} k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_2, u_1, u_3} ι R k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3))) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_2, u_1, u_3} ι R k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3)) (SemilinearEquivClass.instSemilinearMapClass.{u_3, u_3, max u_1 u_4, max u_1 u_2, max (max u_1 u_4) u_2} k k (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (LinearEquiv.{u_3, u_3, max u_4 u_1, max u_1 u_2} k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_2, u_1, u_3} ι R k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3))) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_2, u_1, u_3} ι R k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3)) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u_3, u_3, max u_1 u_4, max u_1 u_2} k k (TensorProduct.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_2, u_1} ι R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (TensorProduct.addCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_2, u_1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_2, u_1, u_3} ι R k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3)) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))))) (Algebra.TensorProduct.basisAux.{u_6, u_3, u_1, u_4, u_2} k _inst_1 R _inst_2 _inst_3 M _inst_4 _inst_5 ι b) (TensorProduct.tmul.{u_3, u_1, u_4} k (CommRing.toCommSemiring.{u_3} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2)))) _inst_4 (Algebra.toModule.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3) _inst_5 r m)) (HSMul.hSMul.{u_1, max u_1 u_2, max u_1 u_2} R (Finsupp.{u_2, u_1} ι R (MulZeroOneClass.toZero.{u_1} R (NonAssocSemiring.toMulZeroOneClass.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))))) (Finsupp.{u_2, u_1} ι R (MulZeroOneClass.toZero.{u_1} R (NonAssocSemiring.toMulZeroOneClass.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))))) (instHSMul.{u_1, max u_1 u_2} R (Finsupp.{u_2, u_1} ι R (MulZeroOneClass.toZero.{u_1} R (NonAssocSemiring.toMulZeroOneClass.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))))) (SMulZeroClass.toSMul.{u_1, max u_1 u_2} R (Finsupp.{u_2, u_1} ι R (MulZeroOneClass.toZero.{u_1} R (NonAssocSemiring.toMulZeroOneClass.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))))) (Finsupp.zero.{u_2, u_1} ι R (MulZeroOneClass.toZero.{u_1} R (NonAssocSemiring.toMulZeroOneClass.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))))) (Finsupp.smulZeroClass.{u_2, u_1, u_1} ι R R (MulZeroOneClass.toZero.{u_1} R (NonAssocSemiring.toMulZeroOneClass.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (SMulWithZero.toSMulZeroClass.{u_1, u_1} R R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (MulZeroOneClass.toZero.{u_1} R (NonAssocSemiring.toMulZeroOneClass.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (MulZeroClass.toSMulWithZero.{u_1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R _inst_2))))))))) r (Finsupp.mapRange.{u_2, u_3, u_1} ι k R (MulZeroOneClass.toZero.{u_3} k (NonAssocSemiring.toMulZeroOneClass.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (MulZeroOneClass.toZero.{u_1} R (NonAssocSemiring.toMulZeroOneClass.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (FunLike.coe.{max (succ u_3) (succ u_1), succ u_3, succ u_1} (RingHom.{u_3, u_1} k R (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) k (fun (_x : k) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : k) => R) _x) (MulHomClass.toFunLike.{max u_3 u_1, u_3, u_1} (RingHom.{u_3, u_1} k R (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) k R (NonUnitalNonAssocSemiring.toMul.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u_3 u_1, u_3, u_1} (RingHom.{u_3, u_1} k R (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) k R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u_3 u_1, u_3, u_1} (RingHom.{u_3, u_1} k R (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) k R (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (RingHom.instRingHomClassRingHom.{u_3, u_1} k R (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))))) (algebraMap.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3)) (map_zero.{u_1, u_3, max u_3 u_1} k R (RingHom.{u_3, u_1} k R (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (MulZeroOneClass.toZero.{u_3} k (NonAssocSemiring.toMulZeroOneClass.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (MulZeroOneClass.toZero.{u_1} R (NonAssocSemiring.toMulZeroOneClass.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)))) (MonoidWithZeroHomClass.toZeroHomClass.{max u_3 u_1, u_3, u_1} (RingHom.{u_3, u_1} k R (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) k R (NonAssocSemiring.toMulZeroOneClass.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (NonAssocSemiring.toMulZeroOneClass.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) (RingHomClass.toMonoidWithZeroHomClass.{max u_3 u_1, u_3, u_1} (RingHom.{u_3, u_1} k R (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))) k R (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2)) (RingHom.instRingHomClassRingHom.{u_3, u_1} k R (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R _inst_2))))) (algebraMap.{u_3, u_1} k R (CommRing.toCommSemiring.{u_3} k _inst_1) (Ring.toSemiring.{u_1} R _inst_2) _inst_3)) (FunLike.coe.{max (max (succ u_3) (succ u_4)) (succ u_2), succ u_4, max (succ u_3) (succ u_2)} (LinearEquiv.{u_3, u_3, u_4, max u_3 u_2} k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) M (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) _inst_4 (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))) _inst_5 (Finsupp.module.{u_2, u_3, u_3} ι k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Semiring.toModule.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : M) => Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) _x) (SMulHomClass.toFunLike.{max (max u_3 u_4) u_2, u_3, u_4, max u_3 u_2} (LinearEquiv.{u_3, u_3, u_4, max u_3 u_2} k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) M (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) _inst_4 (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))) _inst_5 (Finsupp.module.{u_2, u_3, u_3} ι k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Semiring.toModule.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) k M (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (SMulZeroClass.toSMul.{u_3, u_4} k M (AddMonoid.toZero.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M _inst_4)) (DistribSMul.toSMulZeroClass.{u_3, u_4} k M (AddMonoid.toAddZeroClass.{u_4} M (AddCommMonoid.toAddMonoid.{u_4} M _inst_4)) (DistribMulAction.toDistribSMul.{u_3, u_4} k M (MonoidWithZero.toMonoid.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (AddCommMonoid.toAddMonoid.{u_4} M _inst_4) (Module.toDistribMulAction.{u_3, u_4} k M (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) _inst_4 _inst_5)))) (SMulZeroClass.toSMul.{u_3, max u_3 u_2} k (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (AddMonoid.toZero.{max u_3 u_2} (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (AddCommMonoid.toAddMonoid.{max u_3 u_2} (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u_3, max u_3 u_2} k (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (AddMonoid.toAddZeroClass.{max u_3 u_2} (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (AddCommMonoid.toAddMonoid.{max u_3 u_2} (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))))) (DistribMulAction.toDistribSMul.{u_3, max u_3 u_2} k (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (MonoidWithZero.toMonoid.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (AddCommMonoid.toAddMonoid.{max u_3 u_2} (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))))) (Module.toDistribMulAction.{u_3, max u_3 u_2} k (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))) (Finsupp.module.{u_2, u_3, u_3} ι k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Semiring.toModule.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u_3 u_4) u_2, u_3, u_4, max u_3 u_2} (LinearEquiv.{u_3, u_3, u_4, max u_3 u_2} k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) M (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) _inst_4 (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))) _inst_5 (Finsupp.module.{u_2, u_3, u_3} ι k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Semiring.toModule.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) k M (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (MonoidWithZero.toMonoid.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (AddCommMonoid.toAddMonoid.{u_4} M _inst_4) (AddCommMonoid.toAddMonoid.{max u_3 u_2} (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))))) (Module.toDistribMulAction.{u_3, u_4} k M (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) _inst_4 _inst_5) (Module.toDistribMulAction.{u_3, max u_3 u_2} k (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))) (Finsupp.module.{u_2, u_3, u_3} ι k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Semiring.toModule.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u_3, u_4, max u_3 u_2, max (max u_3 u_4) u_2} k M (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (LinearEquiv.{u_3, u_3, u_4, max u_3 u_2} k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) M (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) _inst_4 (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))) _inst_5 (Finsupp.module.{u_2, u_3, u_3} ι k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Semiring.toModule.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) _inst_4 (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))) _inst_5 (Finsupp.module.{u_2, u_3, u_3} ι k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Semiring.toModule.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (SemilinearEquivClass.instSemilinearMapClass.{u_3, u_3, u_4, max u_3 u_2, max (max u_3 u_4) u_2} k k M (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (LinearEquiv.{u_3, u_3, u_4, max u_3 u_2} k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) M (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) _inst_4 (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))) _inst_5 (Finsupp.module.{u_2, u_3, u_3} ι k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Semiring.toModule.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) _inst_4 (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))) _inst_5 (Finsupp.module.{u_2, u_3, u_3} ι k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Semiring.toModule.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u_3, u_3, u_4, max u_3 u_2} k k M (Finsupp.{u_2, u_3} ι k (MonoidWithZero.toZero.{u_3} k (Semiring.toMonoidWithZero.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) _inst_4 (Finsupp.addCommMonoid.{u_2, u_3} ι k (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))) _inst_5 (Finsupp.module.{u_2, u_3, u_3} ι k k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_3} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))))) (Semiring.toModule.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHom.id.{u_3} k (Semiring.toNonAssocSemiring.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1))) (RingHomInvPair.ids.{u_3} k (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)))))))) (Basis.repr.{u_2, u_3, u_4} ι k M (CommSemiring.toSemiring.{u_3} k (CommRing.toCommSemiring.{u_3} k _inst_1)) _inst_4 _inst_5 b) m)))
Case conversion may be inaccurate. Consider using '#align algebra.tensor_product.basis_aux_tmul Algebra.TensorProduct.basisAux_tmulₓ'. -/
theorem basisAux_tmul (r : R) (m : M) :
basisAux R b (r ⊗ₜ m) = r • Finsupp.mapRange (algebraMap k R) (map_zero _) (b.repr m) :=
@@ -1487,7 +1487,7 @@ theorem basisAux_tmul (r : R) (m : M) :
lean 3 declaration is
forall {k : Type.{u_1}} [_inst_1 : CommRing.{u_1} k] {R : Type.{u_2}} [_inst_2 : Ring.{u_2} R] [_inst_3 : Algebra.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2)] {M : Type.{u_3}} [_inst_4 : AddCommMonoid.{u_3} M] [_inst_5 : Module.{u_1, u_3} k M (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) _inst_4] {ι : Type.{u_4}} (b : Basis.{u_4, u_1, u_3} ι k M (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) _inst_4 _inst_5) (r : R) (x : TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5), Eq.{max (succ u_4) (succ u_2)} (Finsupp.{u_4, u_2} ι R (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))))) (coeFn.{max (succ (max u_2 u_3)) (succ (max u_4 u_2)), max (succ (max u_2 u_3)) (succ (max u_4 u_2))} (LinearEquiv.{u_1, u_1, max u_2 u_3, max u_4 u_2} k k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (Algebra.TensorProduct.basisAux._proof_1.{u_1} k _inst_1) (Algebra.TensorProduct.basisAux._proof_2.{u_1} k _inst_1) (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))))) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.module.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3))) (fun (_x : LinearEquiv.{u_1, u_1, max u_2 u_3, max u_4 u_2} k k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (Algebra.TensorProduct.basisAux._proof_1.{u_1} k _inst_1) (Algebra.TensorProduct.basisAux._proof_2.{u_1} k _inst_1) (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))))) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.module.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3))) => (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) -> (Finsupp.{u_4, u_2} ι R (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))))) (LinearEquiv.hasCoeToFun.{u_1, u_1, max u_2 u_3, max u_4 u_2} k k (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))))) (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.module.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3)) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (Algebra.TensorProduct.basisAux._proof_1.{u_1} k _inst_1) (Algebra.TensorProduct.basisAux._proof_2.{u_1} k _inst_1)) (Algebra.TensorProduct.basisAux.{u_1, u_2, u_3, u_4, u_5, u_6} k _inst_1 R _inst_2 _inst_3 M _inst_4 _inst_5 ι b) (SMul.smul.{u_2, max u_2 u_3} R (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (TensorProduct.leftHasSMul.{u_1, u_2, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R (Ring.toMonoid.{u_2} R _inst_2) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5 (Module.toDistribMulAction.{u_2, u_2} R R (Ring.toSemiring.{u_2} R _inst_2) (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Semiring.toModule.{u_2} R (Ring.toSemiring.{u_2} R _inst_2))) (Algebra.to_smulCommClass.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3)) r x)) (SMul.smul.{u_2, max u_4 u_2} R (Finsupp.{u_4, u_2} ι R (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))))) (SMulZeroClass.toHasSmul.{u_2, max u_4 u_2} R (Finsupp.{u_4, u_2} ι R (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))))) (Finsupp.zero.{u_4, u_2} ι R (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))))) (Finsupp.smulZeroClass.{u_4, u_2, u_2} ι R R (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (SMulWithZero.toSmulZeroClass.{u_2, u_2} R R (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (MulZeroClass.toSMulWithZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))))))) r (coeFn.{max (succ (max u_2 u_3)) (succ (max u_4 u_2)), max (succ (max u_2 u_3)) (succ (max u_4 u_2))} (LinearEquiv.{u_1, u_1, max u_2 u_3, max u_4 u_2} k k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (Algebra.TensorProduct.basisAux._proof_1.{u_1} k _inst_1) (Algebra.TensorProduct.basisAux._proof_2.{u_1} k _inst_1) (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))))) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.module.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3))) (fun (_x : LinearEquiv.{u_1, u_1, max u_2 u_3, max u_4 u_2} k k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (Algebra.TensorProduct.basisAux._proof_1.{u_1} k _inst_1) (Algebra.TensorProduct.basisAux._proof_2.{u_1} k _inst_1) (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))))) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.module.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3))) => (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) -> (Finsupp.{u_4, u_2} ι R (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))))) (LinearEquiv.hasCoeToFun.{u_1, u_1, max u_2 u_3, max u_4 u_2} k k (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MulZeroClass.toHasZero.{u_2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))))) (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.module.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toAddCommGroup.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3)) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (Ring.toSemiring.{u_1} k (CommRing.toRing.{u_1} k _inst_1)))) (Algebra.TensorProduct.basisAux._proof_1.{u_1} k _inst_1) (Algebra.TensorProduct.basisAux._proof_2.{u_1} k _inst_1)) (Algebra.TensorProduct.basisAux.{u_1, u_2, u_3, u_4, u_7, u_8} k _inst_1 R _inst_2 _inst_3 M _inst_4 _inst_5 ι b) x))
but is expected to have type
- forall {k : Type.{u_1}} [_inst_1 : CommRing.{u_1} k] {R : Type.{u_2}} [_inst_2 : Ring.{u_2} R] [_inst_3 : Algebra.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2)] {M : Type.{u_3}} [_inst_4 : AddCommMonoid.{u_3} M] [_inst_5 : Module.{u_1, u_3} k M (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) _inst_4] {ι : Type.{u_4}} (b : Basis.{u_4, u_1, u_3} ι k M (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) _inst_4 _inst_5) (r : R) (x : TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5), Eq.{max (succ u_2) (succ u_4)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) => Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (HSMul.hSMul.{u_2, max u_2 u_3, max u_2 u_3} R (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (instHSMul.{u_2, max u_2 u_3} R (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (TensorProduct.leftHasSMul.{u_1, u_2, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R (MonoidWithZero.toMonoid.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2))) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5 (Module.toDistribMulAction.{u_2, u_2} R R (Ring.toSemiring.{u_2} R _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Semiring.toModule.{u_2} R (Ring.toSemiring.{u_2} R _inst_2))) (Algebra.to_smulCommClass.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3))) r x)) (FunLike.coe.{max (max (succ u_2) (succ u_3)) (succ u_4), max (succ u_2) (succ u_3), max 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(Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3))) (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R 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(Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) => Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) _x) (SMulHomClass.toFunLike.{max (max u_2 u_3) u_4, u_1, max u_2 u_3, max u_2 u_4} (LinearEquiv.{u_1, u_1, max u_3 u_2, max u_2 u_4} k k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3))) k (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (SMulZeroClass.toSMul.{u_1, max u_2 u_3} k (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 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(CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5))) (DistribMulAction.toDistribSMul.{u_1, max u_2 u_3} k (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (MonoidWithZero.toMonoid.{u_1} k (Semiring.toMonoidWithZero.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5)) (Module.toDistribMulAction.{u_1, max u_2 u_3} k (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5))))) (SMulZeroClass.toSMul.{u_1, max u_2 u_4} k (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (AddMonoid.toZero.{max u_2 u_4} (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (AddCommMonoid.toAddMonoid.{max u_2 u_4} (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))))) (DistribSMul.toSMulZeroClass.{u_1, max u_2 u_4} k (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (AddMonoid.toAddZeroClass.{max u_2 u_4} (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (AddCommMonoid.toAddMonoid.{max u_2 u_4} (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))))) (DistribMulAction.toDistribSMul.{u_1, max u_2 u_4} k (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (MonoidWithZero.toMonoid.{u_1} k (Semiring.toMonoidWithZero.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (AddCommMonoid.toAddMonoid.{max u_2 u_4} (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))))) (Module.toDistribMulAction.{u_1, max u_2 u_4} k (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (Finsupp.module.{u_4, u_2, u_1} ι R k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u_2 u_3) u_4, u_1, max u_2 u_3, max u_2 u_4} (LinearEquiv.{u_1, u_1, max u_3 u_2, max u_2 u_4} k k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3))) k (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (MonoidWithZero.toMonoid.{u_1} k (Semiring.toMonoidWithZero.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5)) (AddCommMonoid.toAddMonoid.{max u_2 u_4} (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))))) (Module.toDistribMulAction.{u_1, max u_2 u_3} k (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5)) (Module.toDistribMulAction.{u_1, max u_2 u_4} k (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (Finsupp.module.{u_4, u_2, u_1} ι R k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3))) (SemilinearMapClass.distribMulActionHomClass.{u_1, max u_2 u_3, max u_2 u_4, max (max u_2 u_3) u_4} k (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (LinearEquiv.{u_1, u_1, max u_3 u_2, max u_2 u_4} k k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3))) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3)) (SemilinearEquivClass.instSemilinearMapClass.{u_1, u_1, max u_2 u_3, max u_2 u_4, max (max u_2 u_3) u_4} k k (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (LinearEquiv.{u_1, u_1, max u_3 u_2, max u_2 u_4} k k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3))) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3)) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u_1, u_1, max u_2 u_3, max u_2 u_4} k k (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3)) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))))))) (Algebra.TensorProduct.basisAux.{u_6, u_1, u_2, u_3, u_4} k _inst_1 R _inst_2 _inst_3 M _inst_4 _inst_5 ι b) (HSMul.hSMul.{u_2, max u_2 u_3, max u_2 u_3} R (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (instHSMul.{u_2, max u_2 u_3} R (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (TensorProduct.leftHasSMul.{u_1, u_2, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R (MonoidWithZero.toMonoid.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2))) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5 (Module.toDistribMulAction.{u_2, u_2} R R (Ring.toSemiring.{u_2} R _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Semiring.toModule.{u_2} R (Ring.toSemiring.{u_2} R _inst_2))) (Algebra.to_smulCommClass.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3))) r x)) (HSMul.hSMul.{u_2, max u_2 u_4, max u_2 u_4} R ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) => Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) x) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) => Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) x) (instHSMul.{u_2, max u_2 u_4} R ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) => Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) x) (SMulZeroClass.toSMul.{u_2, max u_2 u_4} R ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R 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(MonoidWithZero.toMonoid.{u_1} k (Semiring.toMonoidWithZero.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5)) (Module.toDistribMulAction.{u_1, max u_2 u_3} k (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5))))) (SMulZeroClass.toSMul.{u_1, max u_2 u_4} k (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (AddMonoid.toZero.{max u_2 u_4} (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (AddCommMonoid.toAddMonoid.{max u_2 u_4} (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))))) (DistribSMul.toSMulZeroClass.{u_1, max u_2 u_4} k (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (AddMonoid.toAddZeroClass.{max u_2 u_4} (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (AddCommMonoid.toAddMonoid.{max u_2 u_4} (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))))) (DistribMulAction.toDistribSMul.{u_1, max u_2 u_4} k (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (MonoidWithZero.toMonoid.{u_1} k (Semiring.toMonoidWithZero.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (AddCommMonoid.toAddMonoid.{max u_2 u_4} (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))))) (Module.toDistribMulAction.{u_1, max u_2 u_4} k (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (Finsupp.module.{u_4, u_2, u_1} ι R k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u_2 u_3) u_4, u_1, max u_2 u_3, max u_2 u_4} (LinearEquiv.{u_1, u_1, max u_3 u_2, max u_2 u_4} k k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3))) k (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (MonoidWithZero.toMonoid.{u_1} k (Semiring.toMonoidWithZero.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5)) (AddCommMonoid.toAddMonoid.{max u_2 u_4} (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))))) (Module.toDistribMulAction.{u_1, max u_2 u_3} k (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5)) (Module.toDistribMulAction.{u_1, max u_2 u_4} k (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (Finsupp.module.{u_4, u_2, u_1} ι R k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3))) (SemilinearMapClass.distribMulActionHomClass.{u_1, max u_2 u_3, max u_2 u_4, max (max u_2 u_3) u_4} k (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (LinearEquiv.{u_1, u_1, max u_3 u_2, max u_2 u_4} k k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3))) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3)) (SemilinearEquivClass.instSemilinearMapClass.{u_1, u_1, max u_2 u_3, max u_2 u_4, max (max u_2 u_3) u_4} k k (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (LinearEquiv.{u_1, u_1, max u_3 u_2, max u_2 u_4} k k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3))) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3)) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u_1, u_1, max u_2 u_3, max u_2 u_4} k k (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3)) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))))))) (Algebra.TensorProduct.basisAux.{u_7, u_1, u_2, u_3, u_4} k _inst_1 R _inst_2 _inst_3 M _inst_4 _inst_5 ι b) x))
+ forall {k : Type.{u_1}} [_inst_1 : CommRing.{u_1} k] {R : Type.{u_2}} [_inst_2 : Ring.{u_2} R] [_inst_3 : Algebra.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2)] {M : Type.{u_3}} [_inst_4 : AddCommMonoid.{u_3} M] [_inst_5 : Module.{u_1, u_3} k M (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) _inst_4] {ι : Type.{u_4}} (b : Basis.{u_4, u_1, u_3} ι k M (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) _inst_4 _inst_5) (r : R) (x : TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5), Eq.{max (succ u_2) (succ u_4)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) => Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (HSMul.hSMul.{u_2, max u_2 u_3, max u_2 u_3} R (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (instHSMul.{u_2, max u_2 u_3} R (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (TensorProduct.leftHasSMul.{u_1, u_2, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R 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(NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5))) (DistribMulAction.toDistribSMul.{u_1, max u_2 u_3} k (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (MonoidWithZero.toMonoid.{u_1} k (Semiring.toMonoidWithZero.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k 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(NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5))))) (SMulZeroClass.toSMul.{u_1, max u_2 u_4} k (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (AddMonoid.toZero.{max u_2 u_4} (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (AddCommMonoid.toAddMonoid.{max u_2 u_4} (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))))) (DistribSMul.toSMulZeroClass.{u_1, max u_2 u_4} k (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (AddMonoid.toAddZeroClass.{max u_2 u_4} (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (AddCommMonoid.toAddMonoid.{max u_2 u_4} (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))))) (DistribMulAction.toDistribSMul.{u_1, max u_2 u_4} k (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (MonoidWithZero.toMonoid.{u_1} k (Semiring.toMonoidWithZero.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (AddCommMonoid.toAddMonoid.{max u_2 u_4} (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))))) (Module.toDistribMulAction.{u_1, max u_2 u_4} k (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (Finsupp.module.{u_4, u_2, u_1} ι R k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u_2 u_3) u_4, u_1, max u_2 u_3, max u_2 u_4} (LinearEquiv.{u_1, u_1, max u_3 u_2, max u_2 u_4} k k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHom.id.{u_1} k (Semiring.toNonAssocSemiring.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (RingHomInvPair.ids.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1))) (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.module.{u_4, u_2, u_1} ι R k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3))) k (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (MonoidWithZero.toMonoid.{u_1} k (Semiring.toMonoidWithZero.{u_1} k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)))) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5)) (AddCommMonoid.toAddMonoid.{max u_2 u_4} (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))))) (Module.toDistribMulAction.{u_1, max u_2 u_3} k (TensorProduct.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (TensorProduct.addCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u_1, u_2, u_3} k (CommRing.toCommSemiring.{u_1} k _inst_1) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2)))) _inst_4 (Algebra.toModule.{u_1, u_2} k R (CommRing.toCommSemiring.{u_1} k _inst_1) (Ring.toSemiring.{u_2} R _inst_2) _inst_3) _inst_5)) (Module.toDistribMulAction.{u_1, max u_2 u_4} k (Finsupp.{u_4, u_2} ι R (MonoidWithZero.toZero.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R _inst_2)))) (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSemiring.{u_1} k _inst_1)) (Finsupp.addCommMonoid.{u_4, u_2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R _inst_2))))) (Finsupp.module.{u_4, u_2, u_1} ι R k (CommSemiring.toSemiring.{u_1} k (CommRing.toCommSe